Sample records for nonlinear structural response

  1. Structural optimization for nonlinear dynamic response. (United States)

    Dou, Suguang; Strachan, B Scott; Shaw, Steven W; Jensen, Jakob S


    Much is known about the nonlinear resonant response of mechanical systems, but methods for the systematic design of structures that optimize aspects of these responses have received little attention. Progress in this area is particularly important in the area of micro-systems, where nonlinear resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance condition, thereby providing a means for tailoring its nonlinear response. The method is applied to the fundamental nonlinear resonance of a clamped-clamped beam and to the coupled mode response of a frame structure, and the results show that one can modify essential normal form coefficients by an order of magnitude by relatively simple changes in the shape of these elements. We expect the proposed approach, and its extensions, to be useful for the design of systems used for fundamental studies of nonlinear behaviour as well as for the development of commercial devices that exploit nonlinear behaviour.

  2. Structural optimization for nonlinear dynamic response

    DEFF Research Database (Denmark)

    Dou, Suguang; Strachan, B. Scott; Shaw, Steven W.


    condition, thereby providing a means for tailoring its nonlinear response. The method is applied to the fundamental nonlinear resonance of a clamped–clamped beam and to the coupled mode response of a frame structure, and the results show that one can modify essential normal form coefficients by an order...... resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described...... by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance...

  3. Nonlinear frequency response analysis of structural vibrations (United States)

    Weeger, Oliver; Wever, Utz; Simeon, Bernd


    In this paper we present a method for nonlinear frequency response analysis of mechanical vibrations of 3-dimensional solid structures. For computing nonlinear frequency response to periodic excitations, we employ the well-established harmonic balance method. A fundamental aspect for allowing a large-scale application of the method is model order reduction of the discretized equation of motion. Therefore we propose the utilization of a modal projection method enhanced with modal derivatives, providing second-order information. For an efficient spatial discretization of continuum mechanics nonlinear partial differential equations, including large deformations and hyperelastic material laws, we employ the concept of isogeometric analysis. Isogeometric finite element methods have already been shown to possess advantages over classical finite element discretizations in terms of higher accuracy of numerical approximations in the fields of linear vibration and static large deformation analysis. With several computational examples, we demonstrate the applicability and accuracy of the modal derivative reduction method for nonlinear static computations and vibration analysis. Thus, the presented method opens a promising perspective on application of nonlinear frequency analysis to large-scale industrial problems.

  4. Optical nonlinear response of a single nonlinear dielectric layer sandwiched between two linear dielectric structures

    Energy Technology Data Exchange (ETDEWEB)

    Lidorikis, E. [Ames Laboratory--USDOE and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011 (United States); Busch, K. [Ames Laboratory--USDOE and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011 (United States)]|[Instituet fuer Theorie der Kondensierten Materie, Universitaet Karlsruhe, D-76128, Karlsruhe (Germany); Li, Q. [Ames Laboratory--USDOE and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011 (United States); Chan, C.T. [Ames Laboratory--USDOE and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011 (United States)]|[Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong (China); Soukoulis, C.M. [Ames Laboratory--USDOE and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011 (United States)


    We consider the general problem of electromagnetic wave propagation through a one-dimensional system consisting of a nonlinear medium sandwiched between two linear structures. Special emphasis is given to systems where the latter comprise Bragg reflectors. We obtain an exact expression for the nonlinear response of such dielectric superlattices when the nonlinear impurity is very thin, or in the {delta}-function limit. We find that both the switching-up and switching-down intensities of the bistable response can be made very low, when the frequency of the incident wave matches that of the impurity mode of the structure. Numerical results for a nonlinear layer of finite width display qualitatively similar behavior, thus confirming the usefulness of the simpler {delta}-function model. In addition, an analytical solution for the resonance states of an infinitely extended finite-width superlattice with a finite-width nonlinear impurity is presented. {copyright} {ital 1997} {ital The American Physical Society}

  5. On the dimension of complex responses in nonlinear structural vibrations (United States)

    Wiebe, R.; Spottswood, S. M.


    The ability to accurately model engineering systems under extreme dynamic loads would prove a major breakthrough in many aspects of aerospace, mechanical, and civil engineering. Extreme loads frequently induce both nonlinearities and coupling which increase the complexity of the response and the computational cost of finite element models. Dimension reduction has recently gained traction and promises the ability to distill dynamic responses down to a minimal dimension without sacrificing accuracy. In this context, the dimensionality of a response is related to the number of modes needed in a reduced order model to accurately simulate the response. Thus, an important step is characterizing the dimensionality of complex nonlinear responses of structures. In this work, the dimensionality of the nonlinear response of a post-buckled beam is investigated. Significant detail is dedicated to carefully introducing the experiment, the verification of a finite element model, and the dimensionality estimation algorithm as it is hoped that this system may help serve as a benchmark test case. It is shown that with minor modifications, the method of false nearest neighbors can quantitatively distinguish between the response dimension of various snap-through, non-snap-through, random, and deterministic loads. The state-space dimension of the nonlinear system in question increased from 2-to-10 as the system response moved from simple, low-level harmonic to chaotic snap-through. Beyond the problem studied herein, the techniques developed will serve as a prescriptive guide in developing fast and accurate dimensionally reduced models of nonlinear systems, and eventually as a tool for adaptive dimension-reduction in numerical modeling. The results are especially relevant in the aerospace industry for the design of thin structures such as beams, panels, and shells, which are all capable of spatio-temporally complex dynamic responses that are difficult and computationally expensive to

  6. Nonlinear analysis of the forced response of structural elements (United States)

    Nayfeh, A. H.; Mook, D. T.; Sridhar, S.


    A general procedure is presented for the nonlinear analysis of the forced response of structural elements to harmonic excitations. Internal resonances (i.e., modal interactions) are taken into account. All excitations are considered, with special consideration given to resonant excitations. The general procedure is applied to clamped-hinged beams. The results reveal that exciting a higher mode may lead to a larger response in a lower interacting mode, contrary to the results of linear analyses.

  7. Structure property relationships for the nonlinear optical response of fullerenes (United States)

    Rustagi, Kailash C.; Ramaniah, Lavanya M.; Nair, Selvakumar V.


    We present a phenomenological theory of nonlinear optical response of fullerenes. An empirical tight-binding model is used in conjunction with a classical electromagnetic picture for the screening. Since in bulk media such a picture of screening corresponds to the self- consistent field approach, the only additional approximation involved in our approach is the neglect of nonlocality. We obtain reliable estimates for the linear and nonlinear susceptibilities of C60, C70, C76 and other pure carbon fullerenes and also substituted fullerenes. The relatively large values of (beta) that we obtain for C76 and substituted fullerenes appear promising for the development of fullerene-based nonlinear optical materials. Our phenomenological picture of screening provides a good understanding of the linear absorption spectra of higher fullerenes and predicts that a comparison of the one-photon and multi-photon spectra will provide an insight into screening effects in these systems.

  8. Seismic response analysis of a nuclear reactor structure considering nonlinear soil-structure interaction

    Energy Technology Data Exchange (ETDEWEB)

    Bhaumik, Lopamudra, E-mail: [University of Illinois at Urbana-Champaign (United States); Raychowdhury, Prishati, E-mail: [Indian Institute of Technology Kanpur (India)


    Highlights: • Seismic response analysis of an internal shearwall of a reactor is done. • Incremental dynamic analysis is performed with 30 recorded ground motions. • Equivalent viscous damping increases up to twice when nonlinear SSI is considered. • Roof drift demand increases up to 25% upon consideration of foundation nonlinearity. • Base shear, base moment and ductility reduce up to 62%, 40%, and 35%, respectively. - Abstract: This study focuses on the seismic response analysis of an internal shearwall of a typical Indian reactor resting on a medium dense sandy silty soil, incorporating the nonlinear behavior of the soil-foundation interface. The modeling is done in an open-source finite element framework, OpenSees, where the soil-structure interaction (SSI) is modeled using a Beam-on-Nonlinear-Winkler-Foundation (BNWF) approach. Static pushover analysis and cyclic analysis are performed followed by an incremental dynamic analysis (IDA) with 30 recorded ground motions. For performing IDA, the spectral acceleration of each motion corresponding to the fundamental period, S{sub a}(T{sub 1})is incremented from 0.1 g to 1.0 g with an increment step of 0.1 g. It is observed from the cyclic analysis that the equivalent viscous damping of the system increases upto twice upon incorporation of inelastic SSI. The IDA results demonstrate that the average peak base shear, base moment and displacement ductility demand reduces as much as 62%, 40%, and 35%, respectively, whereas the roof drift demand increases up to 25% upon consideration of foundation nonlinearity for the highest intensity motion. These observations indicate the need of critical consideration of nonlinear soil-structure interaction as any deficient modeling of the same may lead to an inaccurate estimation of the seismic demands of the structure.

  9. Nonlinear structural joint model updating based on instantaneous characteristics of dynamic responses (United States)

    Wang, Zuo-Cai; Xin, Yu; Ren, Wei-Xin


    This paper proposes a new nonlinear joint model updating method for shear type structures based on the instantaneous characteristics of the decomposed structural dynamic responses. To obtain an accurate representation of a nonlinear system's dynamics, the nonlinear joint model is described as the nonlinear spring element with bilinear stiffness. The instantaneous frequencies and amplitudes of the decomposed mono-component are first extracted by the analytical mode decomposition (AMD) method. Then, an objective function based on the residuals of the instantaneous frequencies and amplitudes between the experimental structure and the nonlinear model is created for the nonlinear joint model updating. The optimal values of the nonlinear joint model parameters are obtained by minimizing the objective function using the simulated annealing global optimization method. To validate the effectiveness of the proposed method, a single-story shear type structure subjected to earthquake and harmonic excitations is simulated as a numerical example. Then, a beam structure with multiple local nonlinear elements subjected to earthquake excitation is also simulated. The nonlinear beam structure is updated based on the global and local model using the proposed method. The results show that the proposed local nonlinear model updating method is more effective for structures with multiple local nonlinear elements. Finally, the proposed method is verified by the shake table test of a real high voltage switch structure. The accuracy of the proposed method is quantified both in numerical and experimental applications using the defined error indices. Both the numerical and experimental results have shown that the proposed method can effectively update the nonlinear joint model.

  10. Equivalent Dynamic Stiffness Mapping technique for identifying nonlinear structural elements from frequency response functions (United States)

    Wang, X.; Zheng, G. T.


    A simple and general Equivalent Dynamic Stiffness Mapping technique is proposed for identifying the parameters or the mathematical model of a nonlinear structural element with steady-state primary harmonic frequency response functions (FRFs). The Equivalent Dynamic Stiffness is defined as the complex ratio between the internal force and the displacement response of unknown element. Obtained with the test data of responses' frequencies and amplitudes, the real and imaginary part of Equivalent Dynamic Stiffness are plotted as discrete points in a three dimensional space over the displacement amplitude and the frequency, which are called the real and the imaginary Equivalent Dynamic Stiffness map, respectively. These points will form a repeatable surface as the Equivalent Dynamic stiffness is only a function of the corresponding data as derived in the paper. The mathematical model of the unknown element can then be obtained by surface-fitting these points with special functions selected by priori knowledge of the nonlinear type or with ordinary polynomials if the type of nonlinearity is not pre-known. An important merit of this technique is its capability of dealing with strong nonlinearities owning complicated frequency response behaviors such as jumps and breaks in resonance curves. In addition, this technique could also greatly simplify the test procedure. Besides there is no need to pre-identify the underlying linear parameters, the method uses the measured data of excitation forces and responses without requiring a strict control of the excitation force during the test. The proposed technique is demonstrated and validated with four classical single-degree-of-freedom (SDOF) numerical examples and one experimental example. An application of this technique for identification of nonlinearity from multiple-degree-of-freedom (MDOF) systems is also illustrated.

  11. Inverse solution technique of steady-state responses for local nonlinear structures (United States)

    Wang, Xing; Guan, Xin; Zheng, Gangtie


    An inverse solution technique with the ability of obtaining complete steady-state primary harmonic responses of local nonlinear structures in the frequency domain is proposed in the present paper. In this method, the nonlinear dynamic equations of motion is first condensed from many to only one algebraic amplitude-frequency equation of relative motion. Then this equation is transformed into a polynomial form, and with its frequency as the unknown variable, the polynomial equation is solved by tracing all the solutions of frequency with the increase of amplitude. With this solution technique, some complicated dynamic behaviors such as sharp tuning, anomalous jumps, breaks in responses and detached resonance curves could be obtained. The proposed method is demonstrated and validated through a finite element beam under force excitations and a lumped parameter model with a local nonlinear element under base excitations. The phenomenon of detached resonance curves in the frequency response and its coupling effects with multiple linear modes in the latter example are observed.

  12. Permanence of Periodic Predator-Prey System with General Nonlinear Functional Response and Stage Structure for Both Predator and Prey

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    Xuming Huang


    Full Text Available We study the permanence of periodic predator-prey system with general nonlinear functional responses and stage structure for both predator and prey and obtain that the predator and the prey species are permanent.

  13. Time-domain analysis of nonlinear motion responses and structural loads on ships and offshore structures: development of WISH programs

    Directory of Open Access Journals (Sweden)

    Yonghwan Kim


    Full Text Available The present paper introduced a computer program, called WISH, which is based on a time-domain Rankine panel method. The WISH has been developed for practical use to predict the linear and nonlinear ship motion and structural loads in waves. The WISH adopts three different levels of seakeeping analysis: linear, weakly-nonlinear and weak-scatterer approaches. Later, WISH-FLEX has been developed to consider hydroelasticity effects on hull-girder structure. This program can solve the springing and whipping problems by coupling between the hydrodynamic and structural problems. More recently this development has been continued to more diverse problems, including the motion responses of multiple adjacent bodies, the effects of seakeeping in ship maneuvering, and the floating-body motion in finite-depth domain with varying bathymetry. This paper introduces a brief theoretical and numerical background of the WISH package, and some validation results. Also several applications to real ships and offshore structures are shown.

  14. Orthogonal expansion of ground motion and PDEM-based seismic response analysis of nonlinear structures

    Institute of Scientific and Technical Information of China (English)

    Li Jie; Liu Zhangjun; Chen Jianbing


    This paper introduces an orthogonal expansion method for general stochastic processes. In the method, a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochastic process and then a correlated matrix decomposition technique, which transforms a correlated random vector into a vector of standard uncorrelated random variables, is used to complete a double orthogonal decomposition of the stochastic processes. Considering the relationship between the Hartley transform and Fourier transform of a real-valued function, it is suggested that the first orthogonal expansion in the above process is carried out using the Hartley basis function instead of the trigonometric basis function in practical applications. The seismic ground motion is investigated using the above method. In order to capture the main probabilistic characteristics of the seismic ground motion, it is proposed to directly carry out the orthogonal expansion of the seismic displacements. The case study shows that the proposed method is feasible to represent the seismic ground motion with only a few random variables. In the second part of the paper, the probability density evolution method (PDEM) is employed to study the stochastic response of nonlinear structures subjected to earthquake excitations. In the PDEM, a completely uncoupled one-dimensional partial differential equation, the generalized density evolution equation, plays a central role in governing the stochastic seismic responses of the nonlinear structure. The solution to this equation will yield the instantaneous probability density function of the responses. Computational algorithms to solve the probability density evolution equation are described, An example, which deals with a nonlinear frame structure subjected to stochastic ground motions, is illustrated to validate the above approach.

  15. Fluid-structure interaction for nonlinear response of shells conveying pulsatile flow (United States)

    Tubaldi, Eleonora; Amabili, Marco; Païdoussis, Michael P.


    Circular cylindrical shells with flexible boundary conditions conveying pulsatile flow and subjected to pulsatile pressure are investigated. The equations of motion are obtained based on the nonlinear Novozhilov shell theory via Lagrangian approach. The flow is set in motion by a pulsatile pressure gradient. The fluid is modeled as a Newtonian pulsatile flow and it is formulated using a hybrid model that contains the unsteady effects obtained from the linear potential flow theory and the pulsatile viscous effects obtained from the unsteady time-averaged Navier-Stokes equations. A numerical bifurcation analysis employs a refined reduced order model to investigate the dynamic behavior. The case of shells containing quiescent fluid subjected to the action of a pulsatile transmural pressure is also addressed. Geometrically nonlinear vibration response to pulsatile flow and transmural pressure are here presented via frequency-response curves and time histories. The vibrations involving both a driven mode and a companion mode, which appear due to the axial symmetry, are also investigated. This theoretical framework represents a pioneering study that could be of great interest for biomedical applications. In particular, in the future, a more refined model of the one here presented will possibly be applied to reproduce the dynamic behavior of vascular prostheses used for repairing and replacing damaged and diseased thoracic aorta in cases of aneurysm, dissection or coarctation. For this purpose, a pulsatile time-dependent blood flow model is here considered by applying physiological waveforms of velocity and pressure during the heart beating period. This study provides, for the first time in literature, a fully coupled fluid-structure interaction model with deep insights in the nonlinear vibrations of circular cylindrical shells subjected to pulsatile pressure and pulsatile flow.

  16. Seismic response of structures: from non-stationary to non-linear effects (United States)

    Carlo Ponzo, Felice; Ditommaso, Rocco; Mucciarelli, Marco; Smith, Tobias


    The need for an effective seismic protection of buildings, and all the problems related to their management and maintenance over time, have led to a growing interest associated to develop of new integrated techniques for structural health monitoring and for damage detection and location during both ambient vibration and seismic events. It is well known that the occurrence of damage on any kind of structure is able to modify its dynamic characteristics. Indeed, the main parameters affected by the changes in stiffness characteristics are: periods of vibration, mode shapes and all the related equivalent viscous damping factors. With the aim to evaluate structural dynamic characteristics, their variation over time and after earthquakes, several Non Destructive Evaluation (NDE) methods have been proposed in the last years. Most of these are based on simplified relationship that provide the maximum inter-story drift evaluated combining structural variations in terms of: peak ground acceleration and/or structural eigenfrequencies and/or equivalent viscous damping factors related the main modes of the monitored structure. The NDE methods can be classified into four different levels. The progress of the level increases the quality and the number of the information. The most popular are certainly Level I methods being simple in implementation and economic in management. These kinds of methods are mainly based on the fast variation (less than 1 minute) of the structural fundamental frequency and the related variation of the equivalent viscous damping factor. Generally, it is possible to distinguish two types of variations: the long term variations, which may also be linked to external factors (temperature change, water content in the foundation soils, etc.) and short period variations (for example, due to seismic events), where apparent frequencies variations could occurred due to non-stationary phenomena (particular combination of input and structural response). In these

  17. Response and reliability analysis of nonlinear uncertain dynamical structures by the probability density evolution method

    DEFF Research Database (Denmark)

    Nielsen, Søren R. K.; Peng, Yongbo; Sichani, Mahdi Teimouri


    The paper deals with the response and reliability analysis of hysteretic or geometric nonlinear uncertain dynamical systems of arbitrary dimensionality driven by stochastic processes. The approach is based on the probability density evolution method proposed by Li and Chen (Stochastic dynamics...... of structures, 1st edn. Wiley, London, 2009; Probab Eng Mech 20(1):33–44, 2005), which circumvents the dimensional curse of traditional methods for the determination of non-stationary probability densities based on Markov process assumptions and the numerical solution of the related Fokker–Planck and Kolmogorov......–Feller equations. The main obstacle of the method is that a multi-dimensional convolution integral needs to be carried out over the sample space of a set of basic random variables, for which reason the number of these need to be relatively low. In order to handle this problem an approach is suggested, which...

  18. Response attenuation in a large-scale structure subjected to blast excitation utilizing a system of essentially nonlinear vibration absorbers (United States)

    Wierschem, Nicholas E.; Hubbard, Sean A.; Luo, Jie; Fahnestock, Larry A.; Spencer, Billie F.; McFarland, D. Michael; Quinn, D. Dane; Vakakis, Alexander F.; Bergman, Lawrence A.


    Limiting peak stresses and strains in a structure subjected to high-energy, short-duration transient loadings, such as blasts, is a challenging problem, largely due to the well-known insensitivity of the first few cycles of the structural response to damping. Linear isolation, while a potential solution, requires a very low fundamental natural frequency to be effective, resulting in large nearly-rigid body displacement of the structure, while linear vibration absorbers have little or no effect on the early-time response where relative motions, and thus stresses and strains, are at their highest levels. The problem has become increasingly important in recent years with the expectation of blast-resistance as a design requirement in new construction. In this paper, the problem is examined experimentally and computationally in the context of offset-blast loading applied to a custom-built nine story steel frame structure. A fully-passive response mitigation system consisting of six lightweight, essentially nonlinear vibration absorbers (termed nonlinear energy sinks - NESs) is optimized and deployed on the upper two floors of this structure. Two NESs have vibro-impact nonlinearities and the other four possess smooth but essentially nonlinear stiffnesses. Results of the computational and experimental study demonstrate the efficacy of the proposed passive nonlinear mitigation system to rapidly and efficiently attenuate the global structural response, even at early time (i.e., starting at the first response cycle), thus minimizing the peak demand on the structure. This is achieved by nonlinear redistribution of the blast energy within the modal space through low-to-high energy scattering due to the action of the NESs. The experimental results validate the theoretical predictions.

  19. Nonlinear seismic response analysis of reinforced concrete tube in tube structure

    Institute of Scientific and Technical Information of China (English)

    WANG Hai-bo; SHEN Pu-sheng


    Super-highly reinforced concrete tube in tube structure is a developing structure system of high-rise building. The more reasonable derivation process of the multi-vertical-line-element model stiffness matrix is given.On the premise of pointing out the problems of present multi-spring element model, combined with present multivertical-line-element model for analyzing on shear wall, the model is expanded to spatial one, and the stiffness matrix of which is derived. Combined with hysteretic axial model and hysteretic shear model, it is suitable for columns,wall limbs and beams with all kinds of section form. Some examples are calculated and compared with test results,which shows that the models have relatively good accuracy. On the base of the experimental phenomenon and failure mechanism for tube in tube structure specimen, nonlinear seismic responses analysis program on the basis of the advantaged element model for tube in tube structure is developed. Calculation results are in good agreement with those of the pseudo-dynamic tests and the failure mechanism can be well reflected.

  20. Evaluation of nonlinear structural dynamic responses using a fast-running spring-mass formulation

    Energy Technology Data Exchange (ETDEWEB)

    Benjamin, A.S.; Altman, B.S.; Gruda, J.D.


    In today`s world, accurate finite-element simulations of large nonlinear systems may require meshes composed of hundreds of thousands of degrees of freedom. Even with today`s fast computers and the promise of ever-faster ones in the future, central processing unit (CPU) expenditures for such problems could be measured in days. Many contemporary engineering problems, such as those found in risk assessment, probabilistic structural analysis, and structural design optimization, cannot tolerate the cost or turnaround time for such CPU-intensive analyses, because these applications require a large number of cases to be run with different inputs. For many risk assessment applications, analysts would prefer running times to be measurable in minutes. There is therefore a need for approximation methods which can solve such problems far more efficiently than the very detailed methods and yet maintain an acceptable degree of accuracy. For this purpose, we have been working on two methods of approximation: neural networks and spring-mass models. This paper presents our work and results to date for spring-mass modeling and analysis, since we are further along in this area than in the neural network formulation. It describes the physical and numerical models contained in a code we developed called STRESS, which stands for ``Spring-mass Transient Response Evaluation for structural Systems``. The paper also presents results for a demonstration problem, and compares these with results obtained for the same problem using PRONTO3D, a state-of-the-art finite element code which was also developed at Sandia.

  1. Nonlinear dynamics of structures

    CERN Document Server

    Oller, Sergio


    This book lays the foundation of knowledge that will allow a better understanding of nonlinear phenomena that occur in structural dynamics.   This work is intended for graduate engineering students who want to expand their knowledge on the dynamic behavior of structures, specifically in the nonlinear field, by presenting the basis of dynamic balance in non‐linear behavior structures due to the material and kinematics mechanical effects.   Particularly, this publication shows the solution of the equation of dynamic equilibrium for structure with nonlinear time‐independent materials (plasticity, damage and frequencies evolution), as well as those time dependent non‐linear behavior materials (viscoelasticity and viscoplasticity). The convergence conditions for the non‐linear dynamic structure solution  are studied, and the theoretical concepts and its programming algorithms are presented.  

  2. Nonlinear Dynamic Response of Concrete Structure with Soil-Structure Interaction


    Talberg, Marte Sørbrøden


    A common assumption for a structure that is subjected to an earthquake is that the structure is considered fixed at the base. In this thesis, analyses where the soil is deformed and the foundation may be moved and rotate have been done, and it has been investigated if this can reduce forces or displacements in the structure. This have been done through the use of soil-structure interaction (SSI). In this thesis well known beam-column element formulations will be presented, and the benefi...

  3. Equivalent linear and nonlinear site response analysis for design and risk assessment of safety-related nuclear structures

    Energy Technology Data Exchange (ETDEWEB)

    Bolisetti, Chandrakanth, E-mail: [University at Buffalo, The State University of New York, North Campus, 212 Ketter Hall, Amherst, NY 14260 (United States); Whittaker, Andrew S., E-mail: [University at Buffalo, The State University of New York, North Campus, 212 Ketter Hall, Amherst, NY 14260 (United States); Mason, H. Benjamin, E-mail: [Oregon State University, 101 Kearney Hall, Corvallis, OR 97331 (United States); Almufti, Ibrahim, E-mail: [Advanced Technology + Research, ARUP, 560 Mission Street, Suite 700, San Francisco, CA (United States); Willford, Michael, E-mail: [Advanced Technology + Research, ARUP, 560 Mission Street, Suite 700, San Francisco, CA (United States)


    Highlights: • Performed equivalent linear and nonlinear site response analyses using industry-standard numerical programs. • Considered a wide range of sites and input ground motions. • Noted the practical issues encountered while using these programs. • Examined differences between the responses calculated from different programs. • Results of biaxial and uniaxial analyses are compared. - Abstract: Site response analysis is a precursor to soil-structure interaction analysis, which is an essential component in the seismic analysis of safety-related nuclear structures. Output from site response analysis provides input to soil-structure interaction analysis. Current practice in calculating site response for safety-related nuclear applications mainly involves the equivalent linear method in the frequency-domain. Nonlinear time-domain methods are used by some for the assessment of buildings, bridges and petrochemical facilities. Several commercial programs have been developed for site response analysis but none of them have been formally validated for large strains and high frequencies, which are crucial for the performance assessment of safety-related nuclear structures. This study sheds light on the applicability of some industry-standard equivalent linear (SHAKE) and nonlinear (DEEPSOIL and LS-DYNA) programs across a broad range of frequencies, earthquake shaking intensities, and sites ranging from stiff sand to hard rock, all with a focus on application to safety-related nuclear structures. Results show that the equivalent linear method is unable to reproduce the high frequency acceleration response, resulting in almost constant spectral accelerations in the short period range. Analysis using LS-DYNA occasionally results in some unrealistic high frequency acceleration ‘noise’, which can be removed by smoothing the piece-wise linear backbone curve. Analysis using DEEPSOIL results in abrupt variations in the peak strains of consecutive soil layers

  4. Finite Element Modeling and Analysis of Nonlinear Impact and Frictional Motion Responses Including Fluid—Structure Coupling Effects

    Directory of Open Access Journals (Sweden)

    Yong Zhao


    Full Text Available A nonlinear three dimensional (3D single rack model and a nonlinear 3D whole pool multi-rack model are developed for the spent fuel storage racks of a nuclear power plant (NPP to determine impacts and frictional motion responses when subjected to 3D excitations from the supporting building floor. The submerged free standing rack system and surrounding water are coupled due to hydrodynamic fluid-structure interaction (FSI using potential theory. The models developed have features that allow consideration of geometric and material nonlinearities including (1 the impacts of fuel assemblies to rack cells, a rack to adjacent racks or pool walls, and rack support legs to the pool floor; (2 the hydrodynamic coupling of fuel assemblies with their storing racks, and of a rack with adjacent racks, pool walls, and the pool floor; and (3 the dynamic motion behavior of rocking, twisting, and frictional sliding of rack modules. Using these models 3D nonlinear time history dynamic analyses are performed per the U.S. Nuclear Regulatory Commission (USNRC criteria. Since few such modeling, analyses, and results using both the 3D single and whole pool multiple rack models are available in the literature, this paper emphasizes description of modeling and analysis techniques using the SOLVIA general purpose nonlinear finite element code. Typical response results with different Coulomb friction coefficients are presented and discussed.

  5. Mathematical model of the primary CD8 T cell immune response: stability analysis of a nonlinear age-structured system. (United States)

    Terry, Emmanuelle; Marvel, Jacqueline; Arpin, Christophe; Gandrillon, Olivier; Crauste, Fabien


    The primary CD8 T cell immune response, due to a first encounter with a pathogen, happens in two phases: an expansion phase, with a fast increase of T cell count, followed by a contraction phase. This contraction phase is followed by the generation of memory cells. These latter are specific of the antigen and will allow a faster and stronger response when encountering the antigen for the second time. We propose a nonlinear mathematical model describing the T CD8 immune response to a primary infection, based on three nonlinear ordinary differential equations and one nonlinear age-structured partial differential equation, describing the evolution of CD8 T cell count and pathogen amount. We discuss in particular the roles and relevance of feedback controls that regulate the response. First we reduce our system to a system with a nonlinear differential equation with a distributed delay. We study the existence of two steady states, and we analyze the asymptotic stability of these steady states. Second we study the system with a discrete delay, and analyze global asymptotic stability of steady states. Finally, we show some simulations that we can obtain from the model and confront them to experimental data.

  6. Nonlinear dynamic response analysis of localized damaged laminated composite structures in the context of component mode synthesis (United States)

    Mahmoudi, S.; Trivaudey, F.; Bouhaddi, N.


    The aim of this study is the prediction of the dynamic response of damaged laminated composite structures in the context of component mode synthesis. Hence, a method of damage localization of complex structures is proposed. The dynamic behavior of transversely isotropic layers is expressed through elasticity coupled with damage based on an existing macro model for cracked structures. The damage is located only in some regions of the whole structure, which is decomposed on substructures. The incremental linear dynamic governing equations are obtained by using the classical linear Kirchhoff-Love theory of plates. Then, considering the damage-induced nonlinearity, the obtained nonlinear dynamic equations are solved in time domain. However, a detailed finite element modelling of such structure on the scale of localized damage would generate very high computational costs. To reduce this cost, Component Mode Synthesis method (CMS) is used for modelling a nonlinear fine-scale substructure damaged, connected to linear dynamic models of the remaining substructures, which can be condensed and not updated at each iteration. Numerical results show that the mechanical properties of the structure highly change when damage is taken into account. Under an impact load, damage increases and reaches its highest value with the maximum of the applied load and then remains unchanged. Besides, the eigenfrequencies of the damaged structure decrease comparing with those of an undamaged one. This methodology can be used for monitoring strategies and lifetime estimations of hybrid complex structures due to the damage state is known in space and time.

  7. Identification of the Response of a Controlled Building Structure Subjected to Seismic Load by Using Nonlinear System Models

    Directory of Open Access Journals (Sweden)

    Mosbeh R. Kaloop


    Full Text Available The present study investigates the prediction efficiency of nonlinear system-identification models, in assessing the behavior of a coupled structure-passive vibration controller. Two system-identification models, including Nonlinear AutoRegresive with eXogenous inputs (NARX and adaptive neuro-fuzzy inference system (ANFIS, are used to model the behavior of an experimentally scaled three-story building incorporated with a tuned mass damper (TMD subjected to seismic loads. The experimental study is performed to generate the input and output data sets for training and testing the designed models. The parameters of root-mean-squared error, mean absolute error and determination coefficient statistics are used to compare the performance of the aforementioned models. A TMD controller system works efficiently to mitigate the structural vibration. The results revealed that the NARX and ANFIS models could be used to identify the response of a controlled structure. The parameters of both two time-delays of the structure response and the seismic load were proven to be effective tools in identifying the performance of the models. A comparison based on the parametric evaluation of the two methods showed that the NARX model outperforms the ANFIS model in identifying structures response.

  8. Distributed nonlinear optical response

    DEFF Research Database (Denmark)

    Nikolov, Nikola Ivanov


    The purpose of the research presented here is to investigate basic physical properties in nonlinear optical materials with delayed or nonlocal nonlinearity. Soliton propagation, spectral broadening and the influence of the nonlocality or delay of the nonlinearity are the main focusses in the work...

  9. Fast response of the optical nonlinearity in a GaAs/AlGaAs asymmetric triple quantum well structure

    CERN Document Server

    Ahn, S H; Sawaki, N


    The time response of the optical nonlinear behavior in a GaAs/AlGaAs asymmetric triple quantum well structure is estimated by using a picosecond pump-probe method at 77 K. From the results of the transmission of the probe pulse as a function of the delay time at the excitation wavelengths, a rise time of 5 approx 10 ps and a fall time of 8 approx 16 ps are obtained. The nonlinear behavior is attributed to the triple resonance of the electronic states due to the build-up of the internal field induced by the separation of photo-excited electrons and holes. It is found that the rise time is determined by the tunneling transfer time of the electrons in the narrowest well to an adjacent well separated by a thin potential barrier.

  10. Classical density-functional theory of inhomogeneous water including explicit molecular structure and nonlinear dielectric response. (United States)

    Lischner, Johannes; Arias, T A


    We present an accurate free-energy functional for liquid water written in terms of a set of effective potential fields in which fictitious noninteracting water molecules move. The functional contains an exact expression of the entropy of noninteracting molecules and thus provides an ideal starting point for the inclusion of complex intermolecular interactions which depend on the orientation of the interacting molecules. We show how an excess free-energy functional can be constructed to reproduce the following properties of water: the dielectric response; the experimental site-site correlation functions; the surface tension; the bulk modulus of the liquid and the variation of this modulus with pressure; the density of the liquid and the vapor phase; and liquid-vapor coexistence. As a demonstration, we present results for the application of this theory to the behavior of liquid water in a parallel plate capacitor. In particular, we make predictions for the dielectric response of water in the nonlinear regime, finding excellent agreement with known data.

  11. An experimental and numerical study on nonlinear impact responses of steel-plated structures in an Arctic environment


    Kim, K. J.; Lee, J. H.; Park, D. K.; Jung, B. G.; Han, X.(Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany); Paik, J. K.


    Ships and offshore platforms that operate in Arctic regions at low temperatures are likely subjected to impact loads that arise from collisions with icebergs. The aim of this paper was to examine the nonlinear impact response of steel-plated structures in an Arctic environment. In addition to material tensile tests for characterisation of the mechanical properties of polar-class high-tensile steel of grade DH36, an experimental study was undertaken in a dropped-object test facility on steel-p...

  12. The impact of nonlinear functional responses on the long-term evolution of food web structure. (United States)

    Drossel, Barbara; McKane, Alan J; Quince, Christopher


    We investigate the long-term web structure emerging in evolutionary food web models when different types of functional responses are used. We find that large and complex webs with several trophic layers arise only if the population dynamics is such that it allows predators to focus on their best prey species. This can be achieved using modified Lotka-Volterra or Holling/Beddington functional responses with effective couplings that depend on the predator's efficiency at exploiting the prey, or a ratio-dependent functional response with adaptive foraging. In contrast, if standard Lotka-Volterra or Holling/Beddington functional responses are used, long-term evolution generates webs with almost all species being basal, and with additionally many links between these species. Interestingly, in all cases studied, a large proportion of weak links result naturally from the evolution of the food webs.

  13. Nonlinear Magnetoelectric Response of Planar Ferromagnetic-Piezoelectric Structures to Sub-Millisecond Magnetic Pulses

    Directory of Open Access Journals (Sweden)

    Mikhail Shamonin


    Full Text Available The magnetoelectric response of bi- and symmetric trilayer composite structures to pulsed magnetic fields is experimentally investigated in detail. The structures comprise layers of commercially available piezoelectric (lead zirconate titanate and magnetostrictive (permendur or nickel materials. The magnetic-field pulses have the form of a half-wave sine function with duration of 450 µs and amplitudes ranging from 500 Oe to 38 kOe. The time dependence of the resulting voltage is presented and explained by theoretical estimations. Appearance of voltage oscillations with frequencies much larger than the reciprocal pulse length is observed for sufficiently large amplitudes (~1–10 kOe of the magnetic-field pulse. The origin of these oscillations is the excitation of bending and planar acoustic oscillations in the structures. Dependencies of the magnetoelectric voltage coefficient on the excitation frequency and the applied magnetic field are calculated by digital signal processing and compared with those obtained by the method of harmonic field modulation. The results are of interest for developing magnetoelectric sensors of pulsed magnetic fields as well as for rapid characterization of magnetoelectric composite structures.

  14. RETRACTED: The Nonlinear Compressive Response and Deformation of an Auxetic Cellular Structure under In-Plane Loading

    Directory of Open Access Journals (Sweden)

    Wei Zhang


    Full Text Available At the request of the Author, the following article Zhang, W, Hou, W, Hu, Ping and Ma, Z (2014 The Nonlinear Compressive Response and Deformation of an Auxetic Cellular Structure under In-Plane Loading Advances in Mechanical Engineering published 17 November 2014. doi: 10.1155/2014/214681has been retracted due to errors discovered by the authors. On Page 3, the definition of component force in Equation 4 is incorrect. (2 On Page 4, the definition of component force in Equation 11 is incorrect. Moreover this equation should not have parameterM(length of cell wall, because a mistake was made in the process of calculation. Because of the above reasons, the conclusion obtained from the mechanical model is incorrect and should instead state that the Elastic Buckling and Plastic Collapse are both yield modes of this structure (3 On Page 5, the FEA model used in this article is not appropriate, because the deformation of single cell is not homogeneous, which means that the geometrical non-linear effect on single cell model is greater. So in the actual whole structure we may not obtain the results that were described in Page 6 Paragraph 2. (4 The data in figures 8 (page 6 and 9 (page 7 is incorrect and the values of effective Young’s modulus and plateau stress are much larger than reasonable values. The definition of effective stress is wrong in the FEA model, which means the effective stress should be calculated by the total width of cell instead of length of horizontal cell wall. For example, in Figure 8, the plateau stress can reach 140Mpa, this is not reasonable because there are many holes in this cellular structure, and its mechanical properties should be much lower than material properties of cell wall. The reasonable plateau stress should be around 2Mpa. The authors takes responsibility for these errors and regret the publication of invalid results. The nonlinear compressive response and deformation of an auxetic cellular structure that has

  15. Non-linear finite element analysis for prediction of seismic response of buildings considering soil-structure interaction

    Directory of Open Access Journals (Sweden)

    E. Çelebi


    Full Text Available The objective of this paper focuses primarily on the numerical approach based on two-dimensional (2-D finite element method for analysis of the seismic response of infinite soil-structure interaction (SSI system. This study is performed by a series of different scenarios that involved comprehensive parametric analyses including the effects of realistic material properties of the underlying soil on the structural response quantities. Viscous artificial boundaries, simulating the process of wave transmission along the truncated interface of the semi-infinite space, are adopted in the non-linear finite element formulation in the time domain along with Newmark's integration. The slenderness ratio of the superstructure and the local soil conditions as well as the characteristics of input excitations are important parameters for the numerical simulation in this research. The mechanical behavior of the underlying soil medium considered in this prediction model is simulated by an undrained elasto-plastic Mohr-Coulomb model under plane-strain conditions. To emphasize the important findings of this type of problems to civil engineers, systematic calculations with different controlling parameters are accomplished to evaluate directly the structural response of the vibrating soil-structure system. When the underlying soil becomes stiffer, the frequency content of the seismic motion has a major role in altering the seismic response. The sudden increase of the dynamic response is more pronounced for resonance case, when the frequency content of the seismic ground motion is close to that of the SSI system. The SSI effects under different seismic inputs are different for all considered soil conditions and structural types.

  16. Analysis of Nonlinear Soil-Structure Interaction Effects on the response of Three-Dimensional Frame Structures using a One-Direction Three-ComponentWave Propagation Model

    CERN Document Server

    d'Avila, Maria Paola Santisi


    In this paper, a model of one-directional propagation of three-component seismic waves in a nonlinear multilayered soil profile is coupled with a multi-story multi-span frame model to consider, in a simple way, the soil-structure interaction modelled in a finite element scheme. Modeling the three-component wave propagation enables the effects of a soil multiaxial stress state to be taken into account. These reduce soil strength and increase nonlinear effects, compared with the axial stress state. The simultaneous propagation of three components allows the prediction of the incident direction of seismic loading at the ground surface and the analysis of the behavior of a frame structure shaken by a three-component earthquake. A parametric study is carried out to characterize the changes in the ground motion due to dynamic features of the structure, for different incident wavefield properties and soil nonlinear effects. A seismic response depending on parameters such as the frequency content of soil and structur...

  17. Nonlinear Dynamics of Structures with Material Degradation (United States)

    Soltani, P.; Wagg, D. J.; Pinna, C.; Whear, R.; Briody, C.


    Structures usually experience deterioration during their working life. Oxidation, corrosion, UV exposure, and thermo-mechanical fatigue are some of the most well-known mechanisms that cause degradation. The phenomenon gradually changes structural properties and dynamic behaviour over their lifetime, and can be more problematic and challenging in the presence of nonlinearity. In this paper, we study how the dynamic behaviour of a nonlinear system changes as the thermal environment causes certain parameters to vary. To this end, a nonlinear lumped mass modal model is considered and defined under harmonic external force. Temperature dependent material functions, formulated from empirical test data, are added into the model. Using these functions, bifurcation parameters are defined and the corresponding nonlinear responses are observed by numerical continuation. A comparison between the results gives a preliminary insight into how temperature induced properties affects the dynamic response and highlights changes in stability conditions of the structure.

  18. Acoustic-gravity nonlinear structures

    Directory of Open Access Journals (Sweden)

    D. Jovanović


    Full Text Available A catalogue of nonlinear vortex structures associated with acoustic-gravity perturbations in the Earth's atmosphere is presented. Besides the previously known Kelvin-Stewart cat's eyes, dipolar and tripolar structures, new solutions having the form of a row of counter-rotating vortices, and several weakly two-dimensional vortex chains are given. The existence conditions for these nonlinear structures are discussed with respect to the presence of inhomogeneities of the shear flows. The mode-coupling mechanism for the nonlinear generation of shear flows in the presence of linearly unstable acoustic-gravity waves, possibly also leading to intermittency and chaos, is presented.

  19. Influence of the aircraft crash induced local nonlinearities on the overall dynamic response of a RC structure through a parametric study

    Energy Technology Data Exchange (ETDEWEB)

    Rouzaud, C., E-mail: [LMT (ENS Cachan, CNRS, Université Paris Saclay) 61 avenue du Président Wilson, 94235 Cachan (France); Université Paris-Est, Institut de Recherche en Constructibilité, ESTP 28 avenue du Président Wilson, 94230 Cachan (France); AREVA, 10 rue Juliette Récamier, 69006 Lyon (France); Gatuingt, F. [LMT (ENS Cachan, CNRS, Université Paris Saclay) 61 avenue du Président Wilson, 94235 Cachan (France); Hervé, G. [Université Paris-Est, Institut de Recherche en Constructibilité, ESTP 28 avenue du Président Wilson, 94230 Cachan (France); Moussallam, N. [AREVA, 10 rue Juliette Récamier, 69006 Lyon (France); Dorival, O. [Icam, Site de Toulouse, 75 avenue de Grande-Bretagne, 31076 Toulouse Cedex 3 (France); Université de Toulouse, Institut Clément Ader (ICA), INSA, UPS, Mines Albi, ISAE 135 avenue de Rangueil, 31077 Toulouse Cedex (France)


    Highlights: • Structures could resist to the induced accelerations which they might undergo. • The characterization of non-linearities in the signal of an aircraft impact. • The non linear impact area are studied through a sensitivity analysis. • This analysis should allow to achieve a link between aircraft impact parameters. - Abstract: In the process of nuclear power plant design, the safety of structures is an important aspect. Civil engineering structures have to resist the accelerations induced by, for example, seismic loads or shaking loads resulting from the aircraft impact. This is even more important for the in-structures equipments that have also to be qualified against the vibrations generated by this kind of hazards. In the case of aircraft crash, as a large variety of scenarios has to be envisaged, it is necessary to use methods that are less CPU-time consuming and that consider appropriately the nonlinearities. The analysis presented in this paper deals with the problem of the characterization of nonlinearities (damaged area, transmitted force) in the response of a structure subjected to an aircraft impact. The purpose of our study is part of the development of a new decoupled nonlinear and elastic way for calculating the shaking of structures following an aircraft impact which could be very numerically costly if studied with classical finite element methods. The aim is to identify which parameters control the dimensions of the nonlinear zone and so will have a direct impact on the induced vibrations. In a design context, several load cases (and simulations) are analyzed in order to consider a wide range of impact (different loading surfaces, momentum) and data sets of the target (thickness, reinforcements). In this work, the nonlinear area generated by the impact is localized and studied through a parametric analysis associated with a sensitivity analysis to identify the boundaries between the elastic domain and this nonlinear area.

  20. Intrinsic nonlinear response of surface plasmon polaritons

    CERN Document Server

    Im, Song-Jin; Kim, Gum-Hyok


    We offer a model to describe the intrinsic nonlinear response of surface plasmon polaritons (SPPs). Relation of the complex nonlinear coefficient of SPPs to the third-order nonlinear susceptibility of the metal is provided. As reported in a recent study, gold is highly lossy and simultaneously highly nonlinear due to interband absorption and interband thermo-modulation at a wavelength shorter than 700 nm. The effect of the high loss of the metal on the SPP nonlinear propagation is taken into account in our model. With the model we show difference in sign of real and imaginary parts between the nonlinear propagation coefficient and the nonlinear susceptibility of component material for the first time to our knowledge. Our model could have practical importance in studying plasmonic devices utilizing the nonlinear phase modulation and the nonlinear absorption of SPPs. For example, it allows one to extract the complex nonlinear susceptibility of gold through a measurement of SPP nonlinear propagation at the visib...

  1. Nonlinear and Variable Structure Excitation Controller for Power System Stability

    Institute of Scientific and Technical Information of China (English)

    Wang Ben; Ronnie Belmans


    A new nonlinear variable structure excitation controller is proposed. Its design combines the differential geometry theory and the variable structure controlling theory. The mathematical model in the form of "an affine nonlinear system" is set up for the control of a large-scale power system. The static and dynamic performances of the nonlinear variable structure controller are simulated. The response of system with the controller proposed is compared to that of the nonlinear optimal controller when the system is subjected to a variety of disturbances. Simulation results show that the nonlinear variable structure excitation controller gives more satisfactorily static and dynamic performance and better robustness.

  2. Model updating of nonlinear structures from measured FRFs (United States)

    Canbaloğlu, Güvenç; Özgüven, H. Nevzat


    There are always certain discrepancies between modal and response data of a structure obtained from its mathematical model and experimentally measured ones. Therefore it is a general practice to update the theoretical model by using experimental measurements in order to have a more accurate model. Most of the model updating methods used in structural dynamics are for linear systems. However, in real life applications most of the structures have nonlinearities, which restrict us applying model updating techniques available for linear structures, unless they work in linear range. Well-established frequency response function (FRF) based model updating methods would easily be extended to a nonlinear system if the FRFs of the underlying linear system (linear FRFs) could be experimentally measured. When frictional type of nonlinearity co-exists with other types of nonlinearities, it is not possible to obtain linear FRFs experimentally by using low level forcing. In this study a method (named as Pseudo Receptance Difference (PRD) method) is presented to obtain linear FRFs of a nonlinear structure having multiple nonlinearities including friction type of nonlinearity. PRD method, calculates linear FRFs of a nonlinear structure by using FRFs measured at various forcing levels, and simultaneously identifies all nonlinearities in the system. Then, any model updating method can be used to update the linear part of the mathematical model. In this present work, PRD method is used to predict the linear FRFs from measured nonlinear FRFs, and the inverse eigensensitivity method is employed to update the linear finite element (FE) model of the nonlinear structure. The proposed method is validated with different case studies using nonlinear lumped single-degree of freedom system, as well as a continuous system. Finally, a real nonlinear T-beam test structure is used to show the application and the accuracy of the proposed method. The accuracy of the updated nonlinear model of the

  3. Elasto-capillary collapse of floating structures - Non-linear response of elastic structures under capillary forces

    CERN Document Server

    Adami, N; Roman, B; Bico, J; Caps, H


    Flexible rings and rectangle structures floating at the surface of water are prone to deflect under the action of surface pressure induced by the addition of surfactant molecules on the bath. While the frames of rectangles bend inward or outward for any surface pressure difference, circles are only deformed by compression beyond a critical buckling load. However, compressed frames also undergo a secondary buckling instability leading to a rhoboidal shape. Following the pioneering works of \\cite{Hu} and \\cite{Zell}, we describe both experimentally and theoretically the different elasto-capillary deflection and buckling modes as a function of the material parameters. In particular we show how this original fluid structure interaction may be used to probe the adsorption of surfactant molecules at liquid interfaces.

  4. Nonlinear optics of complex plasmonic structures: linear and third-order optical response of orthogonally coupled metallic nanoantennas (United States)

    Metzger, Bernd; Hentschel, Mario; Nesterov, Maxim; Schumacher, Thorsten; Lippitz, Markus; Giessen, Harald


    We investigate the polarization-resolved linear and third-order optical response of plasmonic nanostructure arrays that consist of orthogonally coupled gold nanoantennas. By rotating the incident light polarization direction, either one of the two eigenmodes of the coupled system or a superposition of the eigenmodes can be excited. We find that when an eigenmode is driven by the external light field, the generated third-harmonic signals exhibit the same polarization direction as the fundamental field. In contrast, when a superposition of the two eigenmodes is excited, third-harmonic can efficiently be radiated at the perpendicular polarization direction. Furthermore, the interference of the coherent third-harmonic signals radiated from both nanorods proves that the phase between the two plasmonic oscillators changes in the third-harmonic signal over 3π when the laser is spectrally tuned over the resonance, rather than over π as in the case of the fundamental field. Finally, almost all details of the linear and the nonlinear spectra can be described by an anharmonic coupled oscillator model, which we discuss in detail and which provides deep insight into the linear and the nonlinear optical response of coupled plasmonic nanoantennas.

  5. Metamaterials with tailored nonlinear optical response. (United States)

    Husu, Hannu; Siikanen, Roope; Mäkitalo, Jouni; Lehtolahti, Joonas; Laukkanen, Janne; Kuittinen, Markku; Kauranen, Martti


    We demonstrate that the second-order nonlinear optical response of noncentrosymmetric metal nanoparticles (metamolecules) can be efficiently controlled by their mutual ordering in an array. Two samples with minor change in ordering have nonlinear responses differing by a factor of up to 50. The results arise from polarization-dependent plasmonic resonances modified by long-range coupling associated with metamolecular ordering. The approach opens new ways for tailoring the nonlinear responses of metamaterials and their tensorial properties.

  6. The Effective AC Response of Nonlinear Composites

    Institute of Scientific and Technical Information of China (English)

    WEI En-Bo; GU Guo-Qing


    A perturbative approach is used to study the AC response of nonlinear composite media, which obey a current-field relation of the form J = σ E + χ|E|2 E with components having nonlinear response at finite frequencies. For a sinusoidal applied field, we extend the local potential in terms of sinusoidal components at fundamental frequency and high-order harmonic frequencies to treat the nonlinear composites. For nonlinear composite media vith a low concentrations of spherical inclusions, we give the formulae of the nonlinear effective AC susceptibility χ*3ω at the third harmonic frequency.

  7. A Modal Model to Simulate Typical Structural Dynamic Nonlinearity

    Energy Technology Data Exchange (ETDEWEB)

    Pacini, Benjamin Robert [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Mayes, Randall L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Roettgen, Daniel R [Univ. of Wisconsin, Madison, WI (United States)


    Some initial investigations have been published which simulate nonlinear response with almost traditional modal models: instead of connecting the modal mass to ground through the traditional spring and damper, a nonlinear Iwan element was added. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. This work expands on these previous studies. An impact experiment is performed on a structure which exhibits typical structural dynamic nonlinear response, i.e. weak frequency dependence and strong damping dependence on the amplitude of vibration. Use of low level modal test results in combination with high level impacts are processed using various combinations of modal filtering, the Hilbert Transform and band-pass filtering to develop response data that are then fit with various nonlinear elements to create a nonlinear pseudo-modal model. Simulations of forced response are compared with high level experimental data for various nonlinear element assumptions.

  8. A nonlinear variable structure stabilizer for power system stability

    Energy Technology Data Exchange (ETDEWEB)

    Cao, Y.; Jiang, L.; Cheng, S.; Chen, D. (Huazhong Univ. of Science and Technology, Wuhan (China). Dept. of Electrical Power Engineering); Malik, O.P.; Hope, G.S. (Univ. of Calgary, Alberta (Canada). Dept. of Electrical and Computer Engineering)


    A nonlinear variable structure stabilizer is proposed in this paper. Design of this stabilizer involves the nonlinear transformation technique, the variable structure control technique and the linear system theory. Performance of the proposed nonlinear variable structure controller in a single machine connected to an infinite bus power and a multi-machine system with multi-mode oscillations is simulated. The responses of the system with the proposed stabilizer are compared with those obtained with some other kinds of stabilizers when the system is subjected to a variety of disturbances. Simulation results show that the nonlinear variable structure stabilizer gives satisfactory dynamic performance and good robustness.

  9. Ultrafast Structure Switching through Nonlinear Phononics (United States)

    Juraschek, D. M.; Fechner, M.; Spaldin, N. A.


    We describe a mechanism by which nonlinear phononics allows ultrafast coherent and directional control of transient structural distortions. With ErFeO3 as a model system, we use density functional theory to calculate the structural properties as input into an anharmonic phonon model that describes the response of the system to a pulsed optical excitation. We find that the trilinear coupling of two orthogonal infrared-active phonons to a Raman-active phonon causes a transient distortion of the lattice. In contrast to the quadratic-linear coupling that has been previously explored, the direction of the distortion is determined by the polarization of the exciting light, introducing a novel mechanism for nonlinear phononic switching. Since the occurrence of the coupling is determined by the symmetry of the system we propose that it is a universal feature of orthorhombic and tetragonal perovskites.

  10. Highly nonlinear stress-relaxation response of articular cartilage in indentation: Importance of collagen nonlinearity. (United States)

    Mäkelä, J T A; Korhonen, R K


    Modern fibril-reinforced computational models of articular cartilage can include inhomogeneous tissue composition and structure, and nonlinear mechanical behavior of collagen, proteoglycans and fluid. These models can capture well experimental single step creep and stress-relaxation tests or measurements under small strains in unconfined and confined compression. Yet, it is known that in indentation, especially at high strain velocities, cartilage can express highly nonlinear response. Different fibril reinforced poroelastic and poroviscoelastic models were used to assess measured highly nonlinear stress-relaxation response of rabbit articular cartilage in indentation. Experimentally measured depth-dependent volume fractions of different tissue constituents and their mechanical nonlinearities were taken into account in the models. In particular, the collagen fibril network was modeled using eight separate models that implemented five different constitutive equations to describe the nonlinearity. These consisted of linear elastic, nonlinear viscoelastic and multiple nonlinear elastic representations. The model incorporating the most nonlinearly increasing Young׳s modulus of collagen fibrils as a function of strain captured best the experimental data. Relative difference between the model and experiment was ~3%. Surprisingly, the difference in the peak forces between the experiment and the model with viscoelastic collagen fibrils was almost 20%. Implementation of the measured volume fractions did not improve the ability of the model to capture the measured mechanical data. These results suggest that a highly nonlinear formulation for collagen fibrils is needed to replicate multi-step stress-relaxation response of rabbit articular cartilage in indentation with high strain rates.

  11. Earthquake analysis of structures using nonlinear models


    Cemalovic, Miran


    Throughout the governing design codes, several different methods are presented for the evaluation of seismic problems. This thesis assesses the non-linear static and dynamic procedures presented in EN 1998-1 through the structural response of a RC wall-frame building. The structure is designed in detail according to the guidelines for high ductility (DCH) in EN 1998-1. The applied procedures are meticulously evaluated and the requirements in EN 1998-1 are reviewed. In addition, the finite ele...

  12. Noise-enhanced nonlinear response and the role of modular structure for signal detection in neuronal networks. (United States)

    Lopes, M A; Lee, K-E; Goltsev, A V; Mendes, J F F


    We show that sensory noise can enhance the nonlinear response of neuronal networks, and when delivered together with a weak signal, it improves the signal detection by the network. We reveal this phenomenon in neuronal networks that are in a dynamical state preceding a saddle-node bifurcation corresponding to the appearance of sustained network oscillations. In this state, even a weak subthreshold pulse can evoke a large-amplitude oscillation of neuronal activity. The signal-to-noise ratio reaches a maximum at an optimum level of sensory noise, manifesting stochastic resonance (SR) at the population level. We demonstrate SR by use of simulations and numerical integration of rate equations in a cortical model. Using this model, we mimic the experiments of Gluckman et al. [Phys. Rev. Lett. 77, 4098 (1996)PRLTAO0031-900710.1103/PhysRevLett.77.4098] that have given evidence of SR in mammalian brain. We also study neuronal networks in which neurons are grouped in modules and every module works in the regime of SR. We find that even a few modules can strongly enhance the reliability of signal detection in comparison with the case when a modular organization is absent.

  13. Nonlinear structural analysis using integrated force method

    Indian Academy of Sciences (India)

    N R B Krishnam Raju; J Nagabhushanam


    Though the use of the integrated force method for linear investigations is well-recognised, no efforts were made to extend this method to nonlinear structural analysis. This paper presents the attempts to use this method for analysing nonlinear structures. General formulation of nonlinear structural analysis is given. Typically highly nonlinear bench-mark problems are considered. The characteristic matrices of the elements used in these problems are developed and later these structures are analysed. The results of the analysis are compared with the results of the displacement method. It has been demonstrated that the integrated force method is equally viable and efficient as compared to the displacement method.

  14. An update on modeling dose-response relationships: Accounting for correlated data structure and heterogeneous error variance in linear and nonlinear mixed models. (United States)

    Gonçalves, M A D; Bello, N M; Dritz, S S; Tokach, M D; DeRouchey, J M; Woodworth, J C; Goodband, R D


    Advanced methods for dose-response assessments are used to estimate the minimum concentrations of a nutrient that maximizes a given outcome of interest, thereby determining nutritional requirements for optimal performance. Contrary to standard modeling assumptions, experimental data often present a design structure that includes correlations between observations (i.e., blocking, nesting, etc.) as well as heterogeneity of error variances; either can mislead inference if disregarded. Our objective is to demonstrate practical implementation of linear and nonlinear mixed models for dose-response relationships accounting for correlated data structure and heterogeneous error variances. To illustrate, we modeled data from a randomized complete block design study to evaluate the standardized ileal digestible (SID) Trp:Lys ratio dose-response on G:F of nursery pigs. A base linear mixed model was fitted to explore the functional form of G:F relative to Trp:Lys ratios and assess model assumptions. Next, we fitted 3 competing dose-response mixed models to G:F, namely a quadratic polynomial (QP) model, a broken-line linear (BLL) ascending model, and a broken-line quadratic (BLQ) ascending model, all of which included heteroskedastic specifications, as dictated by the base model. The GLIMMIX procedure of SAS (version 9.4) was used to fit the base and QP models and the NLMIXED procedure was used to fit the BLL and BLQ models. We further illustrated the use of a grid search of initial parameter values to facilitate convergence and parameter estimation in nonlinear mixed models. Fit between competing dose-response models was compared using a maximum likelihood-based Bayesian information criterion (BIC). The QP, BLL, and BLQ models fitted on G:F of nursery pigs yielded BIC values of 353.7, 343.4, and 345.2, respectively, thus indicating a better fit of the BLL model. The BLL breakpoint estimate of the SID Trp:Lys ratio was 16.5% (95% confidence interval [16.1, 17.0]). Problems with

  15. Nonlinear damage detection in composite structures using bispectral analysis (United States)

    Ciampa, Francesco; Pickering, Simon; Scarselli, Gennaro; Meo, Michele


    Literature offers a quantitative number of diagnostic methods that can continuously provide detailed information of the material defects and damages in aerospace and civil engineering applications. Indeed, low velocity impact damages can considerably degrade the integrity of structural components and, if not detected, they can result in catastrophic failure conditions. This paper presents a nonlinear Structural Health Monitoring (SHM) method, based on ultrasonic guided waves (GW), for the detection of the nonlinear signature in a damaged composite structure. The proposed technique, based on a bispectral analysis of ultrasonic input waveforms, allows for the evaluation of the nonlinear response due to the presence of cracks and delaminations. Indeed, such a methodology was used to characterize the nonlinear behaviour of the structure, by exploiting the frequency mixing of the original waveform acquired from a sparse array of sensors. The robustness of bispectral analysis was experimentally demonstrated on a damaged carbon fibre reinforce plastic (CFRP) composite panel, and the nonlinear source was retrieved with a high level of accuracy. Unlike other linear and nonlinear ultrasonic methods for damage detection, this methodology does not require any baseline with the undamaged structure for the evaluation of the nonlinear source, nor a priori knowledge of the mechanical properties of the specimen. Moreover, bispectral analysis can be considered as a nonlinear elastic wave spectroscopy (NEWS) technique for materials showing either classical or non-classical nonlinear behaviour.

  16. Structural characterization, spectroscopic signatures, nonlinear optical response, and antioxidant property of 4-benzyloxybenzaldehyde and its binding activity with microtubule-associated tau protein (United States)

    Anbu, V.; Vijayalakshmi, K. A.; Karthick, T.; Tandon, Poonam; Narayana, B.


    In the proposed work, the non-linear optical response, spectroscopic signature and binding activity of 4-Benzyloxybenzaldehyde (4BB) has been investigated. In order to find the vibrational contribution of functional groups in mixed or coupled modes in the experimental FT-IR and FT-Raman spectra, the potential energy distribution (PED) based on the internal coordinates have been computed. Since the molecule exists in the form of dimer in solid state, the electronic structure of dimer has been proposed in order to explain the intermolecular hydrogen bonding interactions via aldehyde group. The experimental and simulated powder X-ray diffraction data was compared and the miller indices which define the crystallographic planes in the crystal lattices were identified. Optical transmittance and absorbance measurement were taken at ambient temperature in order to investigate the transparency and optical band gap. For screening the material for nonlinear applications, theoretical second order hyperpolarizability studies were performed and compared with the standard reference urea. To validate the theoretical results, powder second harmonic generation (SHG) studies were carried out using Kurtz and Perry technique. The results show that the molecule studied in this work exhibit considerable non-linear optical (NLO) response. In addition to the characterization and NLO studies, we also claimed based on the experimental and theoretical data that the molecule shows antioxidant property and inhibition capability. Since the title molecule shows significant binding with Tau protein that helps to stabilize microtubules in the nervous system, the molecular docking investigation was performed to find the inhibition constant, binding affinity and active binding residues.

  17. Relationships between nonlinear normal modes and response to random inputs (United States)

    Schoneman, Joseph D.; Allen, Matthew S.; Kuether, Robert J.


    The ability to model nonlinear structures subject to random excitation is of key importance in designing hypersonic aircraft and other advanced aerospace vehicles. When a structure is linear, superposition can be used to construct its response to a known spectrum in terms of its linear modes. Superposition does not hold for a nonlinear system, but several works have shown that a system's dynamics can still be understood qualitatively in terms of its nonlinear normal modes (NNMs). This work investigates the connection between a structure's undamped nonlinear normal modes and the spectrum of its response to high amplitude random forcing. Two examples are investigated: a spring-mass system and a clamped-clamped beam modeled within a geometrically nonlinear finite element package. In both cases, an intimate connection is observed between the smeared peaks in the response spectrum and the frequency-energy dependence of the nonlinear normal modes. In order to understand the role of coupling between the underlying linear modes, reduced order models with and without modal coupling terms are used to separate the effect of each NNM's backbone from the nonlinear couplings that give rise to internal resonances. In the cases shown here, uncoupled, single-degree-of-freedom nonlinear models are found to predict major features in the response with reasonable accuracy; a highly inexpensive approximation such as this could be useful in design and optimization studies. More importantly, the results show that a reduced order model can be expected to give accurate results only if it is also capable of accurately predicting the frequency-energy dependence of the nonlinear modes that are excited.


    Research on nonlinear problems structural dynamics is briefly summarized. Panel flutter was investigated to make a critical comparison between theory...panel flutter in aerospace vehicles, plausible simplifying assumptions are examined in the light of experimental results. Structural dynamics research

  19. Effective ac response in weakly nonlinear composites

    Energy Technology Data Exchange (ETDEWEB)

    Wei Enbo [Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071 (China); Yang Zidong [College of Power Engineering, University of Shanghai Science and Technology, Shanghai 200093 (China); Gu Guoqing [Information College of Science and Technology, East China Normal University, Shanghai 200062 (China)


    The perturbation method is developed to deal with the problem of determining the effective nonlinear conductivity of Kerr-like nonlinear media under an external ac electric field. As an example, we have considered the cylindrical inclusion embedded in a host under the sinusoidal external field E{sub 1} sin (<{omega}t) + E{sub 3} sin (3<{omega}t) with frequencies{omega} and 3{omega}. The potentials of composites at higher harmonics are derived in both local inclusion particle and host regions. The effective responses of bulk nonlinear composites at basic frequency and harmonics are given for cylindrical composites in the dilute limit. Moreover, the relationships between the nonlinear effective responses at the basic frequency and the third harmonics are derived.

  20. Optimal design for nonlinear response models

    CERN Document Server

    Fedorov, Valerii V


    Optimal Design for Nonlinear Response Models discusses the theory and applications of model-based experimental design with a strong emphasis on biopharmaceutical studies. The book draws on the authors' many years of experience in academia and the pharmaceutical industry. While the focus is on nonlinear models, the book begins with an explanation of the key ideas, using linear models as examples. Applying the linearization in the parameter space, it then covers nonlinear models and locally optimal designs as well as minimax, optimal on average, and Bayesian designs. The authors also discuss ada

  1. Computation of the effective nonlinear mechanical response of lattice materials considering geometrical nonlinearities (United States)

    ElNady, Khaled; Goda, Ibrahim; Ganghoffer, Jean-François


    The asymptotic homogenization technique is presently developed in the framework of geometrical nonlinearities to derive the large strains effective elastic response of network materials viewed as repetitive beam networks. This works extends the small strains homogenization method developed with special emphasis on textile structures in Goda et al. (J Mech Phys Solids 61(12):2537-2565, 2013). A systematic methodology is established, allowing the prediction of the overall mechanical properties of these structures in the nonlinear regime, reflecting the influence of the geometrical and mechanical micro-parameters of the network structure on the overall response of the chosen equivalent continuum. Internal scale effects of the initially discrete structure are captured by the consideration of a micropolar effective continuum model. Applications to the large strain response of 3D hexagonal lattices and dry textiles exemplify the powerfulness of the proposed method. The effective mechanical responses obtained for different loadings are validated by FE simulations performed over a representative unit cell.

  2. BRST structure of non-linear superalgebras

    CERN Document Server

    Asorey, M; Radchenko, O V; Sugamoto, A


    In this paper we analyse the structure of the BRST structure of nonlinear superalgebras. We consider quadratic non-linear superalgebras where a commutator (in terms of (super) Poisson brackets) of the generators is a quadratic polynomial of the generators. We find the explicit form of the BRST charge up to cubic order in Faddeev-Popov ghost fields for arbitrary quadratic nonlinear superalgebras. We point out the existence of constraints on structure constants of the superalgebra when the nilpotent BRST charge is quadratic in Faddeev-Popov ghost fields. The general results are illustrated by simple examples of superalgebras.

  3. Bacteriorhodopsin: Tunable Optical Nonlinear Magnetic Response

    CERN Document Server

    Bovino, F A; Sibilia, C; Giardina, M; Váró, G; Gergely, C


    We report on a strong and tunable magnetic optical nonlinear response of Bacteriorhodopsin (BR) under "off resonance" femtosecond (fs) pulse excitation, by detecting the polarization map of the noncollinear second harmonic signal of an oriented BR film, as a function of the input beam power. BR is a light-driven proton pump with a unique photochemistry initiated by the all trans retinal chromophore embedded in the protein. An elegant application of this photonic molecular machine has been recently found in the new area of optogenetics, where genetic expression of BR in brain cells conferred a light responsivity to the cells enabling thus specific stimulation of neurons. The observed strong tunable magnetic nonlinear response of BR might trigger promising applications in the emerging area of pairing optogenetics and functional magnetic resonance imaging susceptible to provide an unprecedented complete functional mapping of neural circuits.

  4. Optimization of nonlinear structural resonance using the incremental harmonic balance method

    DEFF Research Database (Denmark)

    Dou, Suguang; Jensen, Jakob Søndergaard


    We present an optimization procedure for tailoring the nonlinear structural resonant response with time-harmonic loads. A nonlinear finite element method is used for modeling beam structures with a geometric nonlinearity and the incremental harmonic balance method is applied for accurate nonlinea...

  5. Supratransmission in a disordered nonlinear periodic structure (United States)

    Yousefzadeh, B.; Phani, A. Srikantha


    We study the interaction among dispersion, nonlinearity, and disorder effects in the context of wave transmission through a discrete periodic structure, subjected to continuous harmonic excitation in its stop band. We consider a damped nonlinear periodic structure of finite length with disorder. Disorder is introduced throughout the structure by small changes in the stiffness parameters drawn from a uniform statistical distribution. Dispersion effects forbid wave transmission within the stop band of the linear periodic structure. However, nonlinearity leads to supratransmission phenomenon, by which enhanced wave transmission occurs within the stop band of the periodic structure when forced at an amplitude exceeding a certain threshold. The frequency components of the transmitted waves lie within the pass band of the linear structure, where disorder is known to cause Anderson localization. There is therefore a competition between dispersion, nonlinearity, and disorder in the context of supratransmission. We show that supratransmission persists in the presence of disorder. The influence of disorder decreases in general as the forcing frequency moves away from the pass band edge, reminiscent of dispersion effects subsuming disorder effects in linear periodic structures. We compute the dependence of the supratransmission force threshold on nonlinearity and strength of coupling between units. We observe that nonlinear forces are confined to the driven unit for weakly coupled systems. This observation, together with the truncation of higher-order nonlinear terms, permits us to develop closed-form expressions for the supratransmission force threshold. In sum, in the frequency range studied here, disorder does not influence the supratransmission force threshold in the ensemble-average sense, but it does reduce the average transmitted wave energy.

  6. Nonlinear Dynamics and Control of Flexible Structures (United States)


    Freedom," Ph.D. Thesis, Department of Theoretical and Applied Mechanics, Cornell University, in preparation. 5I I URI Reorts Islam , Saiful and Mircea...Theoretical and Applied Mechanics I S. Islam Civil and Environmental Engineering I 2! I 3 URI Accomplishments 3 -Nonlinear Dynamics and Chaos in Flexible...Structures with Symmetry," 31 (1991) 265-285. Islam , S. and M. Grigoriu, "Nonlinear Random Vibration of Pin-Jointed Trusses with Imperfections," in

  7. Geometric and material nonlinear analysis of tensegrity structures

    Institute of Scientific and Technical Information of China (English)

    Hoang Chi Tran; Jaehong Lee


    A numerical method is presented for the large deflection in elastic analysis of tensegrity structures including both geometric and material nonlinearities.The geometric nonlinearity is considered based on both total Lagrangian and updated Lagrangian formulations,while the material nonlinearity is treated through elastoplastic stressstrain relationship.The nonlinear equilibrium equations are solved using an incremental-iterative scheme in conjunction with the modified Newton-Raphson method.A computer program is developed to predict the mechanical responses of tensegrity systems under tensile,compressive and flexural loadings.Numerical results obtained are compared with those reported in the literature to demonstrate the accuracy and efficiency of the proposed program.The flexural behavior of the double layer quadruplex tensegrity grid is sufficiently good for lightweight large-span structural applications.On the other hand,its bending strength capacity is not sensitive to the self-stress level.

  8. Optomechanical response of a nonlinear mechanical resonator (United States)

    Shevchuk, Olga; Singh, Vibhor; Steele, Gary A.; Blanter, Ya. M.


    We investigate theoretically in detail the nonlinear effects in the response of an optical/microwave cavity coupled to a Duffing mechanical resonator. The cavity is driven by a laser at a red or blue mechanical subband, and a probe laser measures the reflection close to the cavity resonance. Under these conditions, we find that the cavity exhibits optomechanically induced reflection (OMIR) or absorption (OMIA) and investigate the optomechanical response in the limit of nonlinear driving of the mechanics. Similar to linear mechanical drive, in an overcoupled cavity the red sideband drive may lead to both OMIA and OMIR depending on the strength of the drive, whereas the blue sideband drive only leads to OMIR. The dynamics of the phase of the mechanical resonator leads to the difference between the shapes of the response of the cavity and the amplitude response of the driven Duffing oscillator, for example, at weak red sideband drive the OMIA dip has no inflection point. We also verify that mechanical nonlinearities beyond Duffing model have little effect on the size of the OMIA dip though they affect the width of the dip.

  9. Computation simulation of the nonlinear response of suspension bridges

    Energy Technology Data Exchange (ETDEWEB)

    McCallen, D.B.; Astaneh-Asl, A.


    Accurate computational simulation of the dynamic response of long- span bridges presents one of the greatest challenges facing the earthquake engineering community The size of these structures, in terms of physical dimensions and number of main load bearing members, makes computational simulation of transient response an arduous task. Discretization of a large bridge with general purpose finite element software often results in a computational model of such size that excessive computational effort is required for three dimensional nonlinear analyses. The aim of the current study was the development of efficient, computationally based methodologies for the nonlinear analysis of cable supported bridge systems which would allow accurate characterization of a bridge with a relatively small number of degrees of freedom. This work has lead to the development of a special purpose software program for the nonlinear analysis of cable supported bridges and the methodologies and software are described and illustrated in this paper.

  10. Soil-structure interaction including nonlinear soil


    Gicev, Vlado


    There are two types of models of soil-structure system depending upon the rigidity of foundation: models with rigid and models with flexible foundation. Main features of the soil-structure interaction phenomenon: -wave scattering, -radiation damping, -reduction of the system frequencies. In this presentation, the influence of interaction on the development of nonlinear zones in the soil is studied.

  11. Nonlinear dynamic analysis of quasi-symmetric anisotropic structures (United States)

    Noor, Ahmed K.; Peters, Jeanne M.


    An efficient computational method for the nonlinear dynamic analysis of quasi-symmetric anisotropic structures is proposed. The application of mixed models simplifies the analytical development and improves the accuracy of the response predictions, and operator splitting allows the reduction of the analysis model of the quasi-symmetric structure to that of the corresponding symmetric structure. The preconditoned conjugate gradient provides a stable and effective technique for generating the unsymmetric response of the structure as the sum of a symmetrized response plus correction modes. The effectiveness of the strategy is demonstrated with the example of a laminated anisotropic shallow shell of quadrilateral planform subjected to uniform normal loading.

  12. Nonlinear system identification in offshore structural reliability

    Energy Technology Data Exchange (ETDEWEB)

    Spanos, P.D. [Rice Univ., Houston, TX (United States); Lu, R. [Hudson Engineering Corporation, Houston, TX (United States)


    Nonlinear forces acting on offshore structures are examined from a system identification perspective. The nonlinearities are induced by ocean waves and may become significant in many situations. They are not necessarily in the form of Morison`s equation. Various wave force models are examined. The force function is either decomposed into a set of base functions or it is expanded in terms of the wave and structural kinematics. The resulting nonlinear system is decomposed into a number of parallel no-memory nonlinear systems, each followed by a finite-memory linear system. A conditioning procedure is applied to decouple these linear sub-systems; a frequency domain technique involving autospectra and cross-spectra is employed to identify the linear transfer functions. The structural properties and those force transfer parameters are determine with the aid of the coherence functions. The method is verified using simulated data. It provides a versatile and noniterative approach for dealing with nonlinear interaction problems encountered in offshore structural analysis and design.

  13. Nonlinearities in Periodic Structures and Metamaterials

    CERN Document Server

    Denz, Cornelia; Kivshar, Yuri S


    Optical information processing of the future is associated with a new generation of compact nanoscale optical devices operating entirely with light. Moreover, adaptive features such as self-guiding, reconfiguration and switching become more and more important. Nonlinear devices offer an enormous potential for these applications. Consequently, innovative concepts for all-optical communication and information technologies based on nonlinear effects in photonic-crystal physics and nanoscale devices as metamaterials are of high interest. This book focuses on nonlinear optical phenomena in periodic media, such as photonic crystals, optically-induced, adaptive lattices, atomic lattices or metamaterials. The main purpose is to describe and overview new physical phenomena that result from the interplay between nonlinearities and structural periodicities and is a guide to actual and future developments for the expert reader in optical information processing, as well as in the physics of cold atoms in optical lattices.

  14. Simulating structural response to water impact


    Campbell, James C; Vignjevic, Rade


    Structural response to water impact is important for several areas, including the aerospace and marine industries. Aircraft must be designed to cope with ditching and offshore structures are subject to extreme wave impact and green water loading. The goal is a reliable technique for predicting the structural response to extreme water loading. This is a complex problem involving the interaction of non-linear fluid behaviour (breaking waves, fluid impact) with non-linear structural behaviour (l...

  15. Nonlinear Response of Strong Nonlinear System Arisen in Polymer Cushion

    Directory of Open Access Journals (Sweden)

    Jun Wang


    Full Text Available A dynamic model is proposed for a polymer foam-based nonlinear cushioning system. An accurate analytical solution for the nonlinear free vibration of the system is derived by applying He's variational iteration method, and conditions for resonance are obtained, which should be avoided in the cushioning design.

  16. Nonlinear dynamics and control of SDI structural components. Final report, September 1987-February 1990

    Energy Technology Data Exchange (ETDEWEB)

    Nayfeh, A.H.; Burns, J.A.; Cliff, E.M.


    The report summarizes results of experimental and theoretical investigations into the nonlinear response and control of structural elements. Methods for the analysis and design of control procedures applicable to certain nonlinear distributed parameter systems were investigated. Analytical and computational techniques were developed for evaluating the nonlinear effects on control designs. Bench-type experiments were conducted for validating some of the theoretical results.

  17. Effective Dielectric Response of Nonlinear Composites of Coated Metal Inclusions

    Institute of Scientific and Technical Information of China (English)

    CHEN Guo-Qing; WU Ya-Min


    The effective dielectric response of the composites in which nondilute coated metal particles are randomly embedded in a linear host is investigated. Two types of coated particles are considered, one is that the core is nonlinear, the other is that the shell is nonlinear. We derive general expressions for the effective linear dielectric function and the effective third-order nonlinear susceptibility, and take one step forward to perform numerical calculations on the coated metal/dielectric composites. Numerical results show that the effective linear and nonlinear dielectric responses can be greatly enhanced near the surface plasmon resonant frequency. Moreover, the resonant peaks are found within a range from 0.46ωp to 0.57ωp for spherical particles and from 0.59ωp to 0.7ωp for cylindrical inclusions. In the frequency region, the resonant peak can achieve the maximum, according to an optimal structural parameter and volume fraction. The resonant frequency exhibits a redshift with the increasing structural parameter k or volume fraction f or dimensionality factor D.

  18. Control of nonlinear flexible space structures (United States)

    Shi, Jianjun

    With the advances made in computer technology and efficiency of numerical algorithms over last decade, the MPC strategies have become quite popular among control community. However, application of MPC or GPC to flexible space structure control has not been explored adequately in the literature. The work presented in this thesis primarily focuses on application of GPC to control of nonlinear flexible space structures. This thesis is particularly devoted to the development of various approximate dynamic models, design and assessment of candidate controllers, and extensive numerical simulations for a realistic multibody flexible spacecraft, namely, Jupiter Icy Moons Orbiter (JIMO)---a Prometheus class of spacecraft proposed by NASA for deep space exploratory missions. A stable GPC algorithm is developed for Multi-Input-Multi-Output (MIMO) systems. An end-point weighting (penalty) is used in the GPC cost function to guarantee the nominal stability of the closed-loop system. A method is given to compute the desired end-point state from the desired output trajectory. The methodologies based on Fake Algebraic Riccati Equation (FARE) and constrained nonlinear optimization, are developed for synthesis of state weighting matrix. This makes this formulation more practical. A stable reconfigurable GPC architecture is presented and its effectiveness is demonstrated on both aircraft as well as spacecraft model. A representative in-orbit maneuver is used for assessing the performance of various control strategies using various design models. Different approximate dynamic models used for analysis include linear single body flexible structure, nonlinear single body flexible structure, and nonlinear multibody flexible structure. The control laws evaluated include traditional GPC, feedback linearization-based GPC (FLGPC), reconfigurable GPC, and nonlinear dissipative control. These various control schemes are evaluated for robust stability and robust performance in the presence of

  19. Applications of nonlinear system identification to structural health monitoring.

    Energy Technology Data Exchange (ETDEWEB)

    Farrar, C. R. (Charles R.); Sohn, H. (Hoon); Robertson, A. N. (Amy N.)


    The process of implementing a damage detection strategy for aerospace, civil and mechanical engineering infrastructure is referred to as structural health monitoring (SHM). In many cases damage causes a structure that initially behaves in a predominantly linear manner to exhibit nonlinear response when subject to its operating environment. The formation of cracks that subsequently open and close under operating loads is an example of such damage. The damage detection process can be significantly enhanced if one takes advantage of these nonlinear effects when extracting damage-sensitive features from measured data. This paper will provide an overview of nonlinear system identification techniques that are used for the feature extraction process. Specifically, three general approaches that apply nonlinear system identification techniques to the damage detection process are discussed. The first two approaches attempt to quantify the deviation of the system from its initial linear characteristics that is a direct result of damage. The third approach is to extract features from the data that are directly related to the specific nonlinearity associated with the damaged condition. To conclude this discussion, a summary of outstanding issues associated with the application of nonlinear system identification techniques to the SHM problem is presented.

  20. CISM course on exploiting nonlinear behaviour in structural dynamics

    CERN Document Server

    Virgin, Lawrence; Exploiting Nonlinear Behavior in Structural Dynamics


    The articles in this volume give an overview and introduction to nonlinear phenomena in structural dynamics. Topics treated are approximate methods for analyzing nonlinear systems (where the level of nonlinearity is assumed to be relatively small), vibration isolation, the mitigation of undesirable torsional vibration in rotating systems utilizing specifically nonlinear features in the dynamics, the vibration of nonlinear structures in which the motion is sufficiently large amplitude and structural systems with control.

  1. Nonlinear transient analysis of joint dominated structures (United States)

    Chapman, J. M.; Shaw, F. H.; Russell, W. C.


    A residual force technique is presented that can perform the transient analyses of large, flexible, and joint dominated structures. The technique permits substantial size reduction in the number of degrees of freedom describing the nonlinear structural models and can account for such nonlinear joint phenomena as free-play and hysteresis. In general, joints can have arbitrary force-state map representations but these are used in the form of residual force maps. One essential feature of the technique is to replace the arbitrary force-state maps describing the nonlinear joints with residual force maps describing the truss links. The main advantage of this replacement is that the incrementally small relative displacements and velocities across a joint are not monitored directly thereby avoiding numerical difficulties. Instead, very small and 'soft' residual forces are defined giving a numerically attractive form for the equations of motion and thereby permitting numerically stable integration algorithms. The technique was successfully applied to the transient analyses of a large 58 bay, 60 meter truss having nonlinear joints. A method to perform link testing is also presented.

  2. Frequency Response and Gap Tuning for Nonlinear Electrical Oscillator Networks (United States)

    Bhat, Harish S.; Vaz, Garnet J.


    We study nonlinear electrical oscillator networks, the smallest example of which consists of a voltage-dependent capacitor, an inductor, and a resistor driven by a pure tone source. By allowing the network topology to be that of any connected graph, such circuits generalize spatially discrete nonlinear transmission lines/lattices that have proven useful in high-frequency analog devices. For such networks, we develop two algorithms to compute the steady-state response when a subset of nodes are driven at the same fixed frequency. The algorithms we devise are orders of magnitude more accurate and efficient than stepping towards the steady-state using a standard numerical integrator. We seek to enhance a given network's nonlinear behavior by altering the eigenvalues of the graph Laplacian, i.e., the resonances of the linearized system. We develop a Newton-type method that solves for the network inductances such that the graph Laplacian achieves a desired set of eigenvalues; this method enables one to move the eigenvalues while keeping the network topology fixed. Running numerical experiments using three different random graph models, we show that shrinking the gap between the graph Laplacian's first two eigenvalues dramatically improves a network's ability to (i) transfer energy to higher harmonics, and (ii) generate large-amplitude signals. Our results shed light on the relationship between a network's structure, encoded by the graph Laplacian, and its function, defined in this case by the presence of strongly nonlinear effects in the frequency response. PMID:24223751

  3. Nonlinear response from the perspective of energy landscapes and beyond (United States)

    Heuer, Andreas; Schroer, Carsten F. E.; Diddens, Diddo; Rehwald, Christian; Blank-Burian, Markus


    The paper discusses the nonlinear response of disordered systems. In particular we show how the nonlinear response can be interpreted in terms of properties of the potential energy landscape. It is shown why the use of relatively small systems is very helpful for this approach. For a standard model system we check which system sizes are particular suited. In case of the driving of a single particle via an external force the concept of an effective temperature helps to scale the force dependence for different temperature on a single master curve. In all cases the mobility increases with increasing external force. These results are compared with a stochastic process described by a 1d Langevin equation where a similar scaling is observed. Furthermore it is shown that for different classes of disordered systems the mobility can also decrease with increasing force. The results can be related to the properties of the chosen potential energy landscape. Finally, results for the crossover from the linear to the nonlinear conductivity of ionic liquids are presented, inspired by recent experimental results in the Roling group. Apart from a standard imidazolium-based ionic liquid we study a system which is characterized by a low conductivity as compared to other ionic liquids and very small nonlinear effects. We show via a real space structural analysis that for this system a particularly strong pair formation is observed and that the strength of the pair formation is insensitive to the application of strong electric fields. Consequences of this observation are discussed.

  4. Nonlinear dynamic response of stay cables under axial harmonic excitation

    Institute of Scientific and Technical Information of China (English)

    Xu XIE; He ZHAN; Zhi-cheng ZHANG


    This paper proposes a new numerical simulation method for analyzing the parametric vibration of stay cables based on the theory of nonlinear dynamic response of structures under the asynchronous support excitation.The effects of important parameters related to parametric vibration of cables,I.e., characteristics of structure,excitation frequency,excitation amplitude,damping effect of the air and the viscous damping coefficient of the cables,were investigated by using the proposed method for the cables with significant length difference as examples.The analysis results show that nonlinear finite element method is a powerful technique in analyzing the parametric vibration of cables,the behavior of parametric vibration of the two cables with different Irvine parameters has similar properties,the amplitudes of parametric vibration of cables are related to the frequency and amplitude of harmonic support excitations and the effect of distributed viscous damping on parametric vibration of the cables is very small.

  5. Identification of Nonlinearities in Joints of a Wing Structure


    Sani M.S.M.; Ouyang H


    Nonlinear structural identification is essential in engineering. As new materials are being used andstructures become slender and lighter, nonlinear behaviour of structures becomes more important. There have been many studies into the development and application of system identification methods for structural nonlinearity based on changes in natural frequencies, mode shapes and damping ratios. A great challenge is to identify nonlinearity in large structural systems. Much work has been undert...

  6. Mathematical models for suspension bridges nonlinear structural instability

    CERN Document Server

    Gazzola, Filippo


    This work provides a detailed and up-to-the-minute survey of the various stability problems that can affect suspension bridges. In order to deduce some experimental data and rules on the behavior of suspension bridges, a number of historical events are first described, in the course of which several questions concerning their stability naturally arise. The book then surveys conventional mathematical models for suspension bridges and suggests new nonlinear alternatives, which can potentially supply answers to some stability questions. New explanations are also provided, based on the nonlinear structural behavior of bridges. All the models and responses presented in the book employ the theory of differential equations and dynamical systems in the broader sense, demonstrating that methods from nonlinear analysis can allow us to determine the thresholds of instability.

  7. A Modal Model to Simulate Typical Structural Dynamic Nonlinearity [PowerPoint

    Energy Technology Data Exchange (ETDEWEB)

    Mayes, Randall L.; Pacini, Benjamin Robert; Roettgen, Dan


    Some initial investigations have been published which simulate nonlinear response with almost traditional modal models: instead of connecting the modal mass to ground through the traditional spring and damper, a nonlinear Iwan element was added. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. This work expands on these previous studies. An impact experiment is performed on a structure which exhibits typical structural dynamic nonlinear response, i.e. weak frequency dependence and strong damping dependence on the amplitude of vibration. Use of low level modal test results in combination with high level impacts are processed using various combinations of modal filtering, the Hilbert Transform and band-pass filtering to develop response data that are then fit with various nonlinear elements to create a nonlinear pseudo-modal model. Simulations of forced response are compared with high level experimental data for various nonlinear element assumptions.

  8. Waves and Structures in Nonlinear Nondispersive Media General Theory and Applications to Nonlinear Acoustics

    CERN Document Server

    Gurbatov, S N; Saichev, A I


    "Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics” is devoted completely to nonlinear structures. The general theory is given here in parallel with mathematical models. Many concrete examples illustrate the general analysis of Part I. Part II is devoted to applications to nonlinear acoustics, including specific nonlinear models and exact solutions, physical mechanisms of nonlinearity, sawtooth-shaped wave propagation, self-action phenomena, nonlinear resonances and engineering application (medicine, nondestructive testing, geophysics, etc.). This book is designed for graduate and postgraduate students studying the theory of nonlinear waves of various physical nature. It may also be useful as a handbook for engineers and researchers who encounter the necessity of taking nonlinear wave effects into account of their work. Dr. Gurbatov S.N. is the head of Department, and Vice Rector for Research of Nizhny Novgorod State University. Dr. Rudenko O.V. is...

  9. Nonlinear Propagation of Light in One Dimensional Periodic Structures


    Goodman, Roy H.; Weinstein, Michael I.; Philip J Holmes


    We consider the nonlinear propagation of light in an optical fiber waveguide as modeled by the anharmonic Maxwell-Lorentz equations (AMLE). The waveguide is assumed to have an index of refraction which varies periodically along its length. The wavelength of light is selected to be in resonance with the periodic structure (Bragg resonance). The AMLE system considered incorporates the effects non-instantaneous response of the medium to the electromagnetic field (chromatic or material dispersion...

  10. Nonlinear helicons bearing multi-scale structures (United States)

    Abdelhamid, Hamdi M.; Yoshida, Zensho


    The helicon waves exhibit varying characters depending on plasma parameters, geometry, and wave numbers. Here, we elucidate an intrinsic multi-scale property embodied by the combination of the dispersive effect and nonlinearity. The extended magnetohydrodynamics model (exMHD) is capable of describing a wide range of parameter space. By using the underlying Hamiltonian structure of exMHD, we construct an exact nonlinear solution, which turns out to be a combination of two distinct modes, the helicon and Trivelpiece-Gould (TG) waves. In the regime of relatively low frequency or high density, however, the combination is made of the TG mode and an ion cyclotron wave (slow wave). The energy partition between these modes is determined by the helicities carried by the wave fields.

  11. Conditions on Structural Controllability of Nonlinear Systems: Polynomial Method

    Directory of Open Access Journals (Sweden)

    Qiang Ma


    Full Text Available In this paper the structural controllability of a class of a nonlinear system is investigated. The transfer function (matrix of nonlinear systems is obtained by putting the nonlinear system model on non-commutative ring. Conditions of structural controllability of nonlinear systems are presented according to the criterion of linear systems structural controllability in frequency domain. An example is used to testify the presented conditions finally.

  12. A nonlinear cointegration approach with applications to structural health monitoring (United States)

    Shi, H.; Worden, K.; Cross, E. J.


    One major obstacle to the implementation of structural health monitoring (SHM) is the effect of operational and environmental variabilities, which may corrupt the signal of structural degradation. Recently, an approach inspired from the community of econometrics, called cointegration, has been employed to eliminate the adverse influence from operational and environmental changes and still maintain sensitivity to structural damage. However, the linear nature of cointegration may limit its application when confronting nonlinear relations between system responses. This paper proposes a nonlinear cointegration method based on Gaussian process regression (GPR); the method is constructed under the Engle-Granger framework, and tests for unit root processes are conducted both before and after the GPR is applied. The proposed approach is examined with real engineering data from the monitoring of the Z24 Bridge.

  13. Analysis of nonlinear transient responses of piezoelectric resonators. (United States)

    Hagiwara, Manabu; Takahashi, Seita; Hoshina, Takuya; Takeda, Hiroaki; Tsurumi, Takaaki


    The electric transient response method is an effective technique to evaluate material constants of piezoelectric ceramics under high-power driving. In this study, we tried to incorporate nonlinear piezoelectric behaviors in the analysis of transient responses. As a base for handling the nonlinear piezoelectric responses, we proposed an assumption that the electric displacement is proportional to the strain without phase lag, which could be described by a real and constant piezoelectric e-coefficient. Piezoelectric constitutive equations including nonlinear responses were proposed to calculate transient responses of a piezoelectric resonator. The envelopes and waveforms of current and vibration velocity in transient responses observed in some piezoelectric ceramics could be fitted with the calculation including nonlinear responses. The procedure for calculation of mechanical quality factor Q(m) for piezoelectric resonators with nonlinear behaviors was also proposed.

  14. Nonlinear response of the quantum Hall system to a strong electromagnetic radiation (United States)

    Avetissian, H. K.; Mkrtchian, G. F.


    We study nonlinear response of a quantum Hall system in semiconductor-hetero-structures via third harmonic generation process and nonlinear Faraday effect. We demonstrate that Faraday rotation angle and third harmonic radiation intensity have a characteristic Hall plateaus feature. These nonlinear effects remain robust against the significant broadening of Landau levels. We predict realization of an experiment through the observation of the third harmonic signal and Faraday rotation angle, which are within the experimental feasibility.

  15. Gradient-based optimization in nonlinear structural dynamics

    DEFF Research Database (Denmark)

    Dou, Suguang

    The intrinsic nonlinearity of mechanical structures can give rise to rich nonlinear dynamics. Recently, nonlinear dynamics of micro-mechanical structures have contributed to developing new Micro-Electro-Mechanical Systems (MEMS), for example, atomic force microscope, passive frequency divider, fr...

  16. Artificial Neural Networks for Nonlinear Dynamic Response Simulation in Mechanical Systems

    DEFF Research Database (Denmark)

    Christiansen, Niels Hørbye; Høgsberg, Jan Becker; Winther, Ole


    It is shown how artificial neural networks can be trained to predict dynamic response of a simple nonlinear structure. Data generated using a nonlinear finite element model of a simplified wind turbine is used to train a one layer artificial neural network. When trained properly the network is able...

  17. Nonlinear Dielectric Response of Water Treed XLPE Cable Insulation

    Energy Technology Data Exchange (ETDEWEB)

    Hvidsten, Sverre


    frequency domain dielectric response was larger, and found to be more nonlinear than values measured in time domain. This thesis describes a new mechanism for the nonlinear dielectric response. It is assumed that at low or no applied electric stress the water treed region is characterised by spherical micro voids filled with liquid water separated by channels of crazed insulation. The effect of increasing the test voltage is to cause Maxwell mechanical tensile stresses strong enough to open up the crazing zones and elongate the water droplets into the mechanically weak crazing zones. Finite Element Method (FEM) calculations show that the effect of the re-opening of crazing zones by an increased test voltage, strongly increases the dielectric loss of the water treed insulation. This is qualitatively in good agreement with the experimental results obtained on water treed insulation, where increasing the test voltage above a certain value caused the losses to increase. The typical frequency independent dielectric response of water treed insulation can, however, not be explained by this model. Numerical calculations of losses, indicated that the mechanism of voltage assisted ingress of water is more likely in treed regions with rather low contents of water. The micro-FTIR measurements of single vented water trees indicated that such regions were likely to be present 3-400 (my)m within the tree tip, and close to the insulation screen. The process of refilling water into water tree structures is likely to be associated with a hysteresis effect. When removing (or reducing) the electric field, mechanical relaxation causes the channel to collapse and to slowly recover its former structure. Dielectric response measurements showed that a hysteresis was typically present when the response was nonlinear.

  18. Second Order Nonlinear Hydroelastic Analyses of Floating Bodies - the Primary Consideration of Nonlinear Structure

    DEFF Research Database (Denmark)

    Chen, X.; Cui, W.; Jensen, Jørgen Juncher


    The theory and typical numerical results of a second order nonlinear hydroelastic analysis of floating bodies are presented in a series of papers in which only nonlinearity in fluids is considered. Under the assumption of linear fluid, the hydroelastic analysis methods of nonlinear structure are ...

  19. 沥青面层结构参数对倒装路面结构非线性响应分析%Analysis of Nonlinear Response of Asphalt Surface Structural Parameters on Inverted Pavement Structure

    Institute of Scientific and Technical Information of China (English)

    胡海学; 肖庆一; 王志辉; 侯子义


    级配碎石过渡层能有效防止或减少半刚性基层反射裂缝,改善沥青路面排水条件,但级配碎石模量低,具有非线性应力应变特性,将其作为过渡层置于沥青面层与半刚性基层之间,会改变原路面结构应力状况.通过使用非线性路面设计程序,从沥青面层厚度、模量两个路面结构参数分析路表弯沉值、面层及半刚性基层层底拉应力、土基顶面压应变等控制指标.归纳总结沥青面层厚度以及回弹模量变化对路面各个结构层的拉、压、剪切等力学响应规律,对倒装结构组合设计具有重要的参考价值.%The graded aggregate transition layer can effectively prevent or reduce reflective cracks in the semi-rigid base course and improve the drainage conditions of asphalt road surface, but, graded aggregate has a low modulus and a nonlinear stress-strain behavior. If such graded aggregate is used as a transition layer between the asphalt surface layer and the semi-rigid base, it may change the stress of original pavement structure. By using pavement design software based on the nonlinear theory, surface deflection, tensile stress in underside of surface layer and semi-rigid base course, compressive strain on top of subgrade and other control indicators are analyzed from two structural parameters of thickness and modulus of asphalt surface layer. The law of mechanical response of the variation of thickness and modulus of resilience of asphalt pavement on the tensile, compressive and shear stress in various structural layers of road pavement is analyzed and summarized, providing important reference for the combined design of inverted pavement structures.

  20. Experimental and theoretical studies of spectral alteration in ultrasonic waves resulting from nonlinear elastic response in rock

    Energy Technology Data Exchange (ETDEWEB)

    Johnson, P.A.; McCall, K.R.; Meegan, G.D. Jr.


    Experiments in rock show a large nonlinear elastic wave response, far greater than that of gases, liquids and most other solids. The large response is attributed to structural defects in rock including microcracks and grain boundaries. In the earth, a large nonlinear response may be responsible for significant spectral alteration at amplitudes and distances currently considered to be well within the linear elastic regime.

  1. Experimental and theoretical studies of spectral alteration in ultrasonic waves resulting from nonlinear elastic response in rock

    Energy Technology Data Exchange (ETDEWEB)

    Johnson, P.A.; McCall, K.R.; Meegan, G.D. Jr.


    Experiments in rock show a large nonlinear elastic wave response, far greater than that of gases, liquids and most other solids. The large response is attributed to structural defects in rock including microcracks and grain boundaries. In the earth, a large nonlinear response may be responsible for significant spectral alteration at amplitudes and distances currently considered to be well within the linear elastic regime.

  2. Experimental and theoretical studies of spectral alteration in ultrasonic waves resulting from nonlinear elastic response in rock

    Energy Technology Data Exchange (ETDEWEB)

    Johnson, P.A.; McCall, K.R.; Meegan, G.D. Jr. [Los Alamos National Lab., NM (United States)


    Experiments in rock show a large nonlinear elastic wave response, far greater than that of gases, liquids and most other solids. The large response is attributed to structural defects in rock including microcracks and grain boundaries. In the earth, a large nonlinear response may be responsible for significant spectral alteration at amplitudes and distances currently considered to be well within the linear elastic regime.

  3. A Multiscale, Nonlinear, Modeling Framework Enabling the Design and Analysis of Composite Materials and Structures (United States)

    Bednarcyk, Brett A.; Arnold, Steven M.


    A framework for the multiscale design and analysis of composite materials and structures is presented. The ImMAC software suite, developed at NASA Glenn Research Center, embeds efficient, nonlinear micromechanics capabilities within higher scale structural analysis methods such as finite element analysis. The result is an integrated, multiscale tool that relates global loading to the constituent scale, captures nonlinearities at this scale, and homogenizes local nonlinearities to predict their effects at the structural scale. Example applications of the multiscale framework are presented for the stochastic progressive failure of a SiC/Ti composite tensile specimen and the effects of microstructural variations on the nonlinear response of woven polymer matrix composites.

  4. A numerical-perturbation method for the nonlinear analysis of structural vibrations (United States)

    Nayfeh, A. H.; Mook, D. T.; Lobitz, D. W.


    A numerical-perturbation method is proposed for the determination of the nonlinear forced response of structural elements. Purely analytical techniques are capable of determining the response of structural elements having simple geometries and simple variations in thickness and properties, but they are not applicable to elements with complicated structure and boundaries. Numerical techniques are effective in determining the linear response of complicated structures, but they are not optimal for determining the nonlinear response of even simple elements when modal interactions take place due to the complicated nature of the response. Therefore, the optimum is a combined numerical and perturbation technique. The present technique is applied to beams with varying cross sections.

  5. Bayesian Methods for Nonlinear System Identification of Civil Structures

    Directory of Open Access Journals (Sweden)

    Conte Joel P.


    Full Text Available This paper presents a new framework for the identification of mechanics-based nonlinear finite element (FE models of civil structures using Bayesian methods. In this approach, recursive Bayesian estimation methods are utilized to update an advanced nonlinear FE model of the structure using the input-output dynamic data recorded during an earthquake event. Capable of capturing the complex damage mechanisms and failure modes of the structural system, the updated nonlinear FE model can be used to evaluate the state of health of the structure after a damage-inducing event. To update the unknown time-invariant parameters of the FE model, three alternative stochastic filtering methods are used: the extended Kalman filter (EKF, the unscented Kalman filter (UKF, and the iterated extended Kalman filter (IEKF. For those estimation methods that require the computation of structural FE response sensitivities with respect to the unknown modeling parameters (EKF and IEKF, the accurate and computationally efficient direct differentiation method (DDM is used. A three-dimensional five-story two-by-one bay reinforced concrete (RC frame is used to illustrate the performance of the framework and compare the performance of the different filters in terms of convergence, accuracy, and robustness. Excellent estimation results are obtained with the UKF, EKF, and IEKF. Because of the analytical linearization used in the EKF and IEKF, abrupt and large jumps in the estimates of the modeling parameters are observed when using these filters. The UKF slightly outperforms the EKF and IEKF.

  6. Non-linear stochastic response of a shallow cable

    DEFF Research Database (Denmark)

    Larsen, Jesper Winther; Nielsen, Søren R.K.


    The paper considers the stochastic response of geometrical non-linear shallow cables. Large rain-wind induced cable oscillations with non-linear interactions have been observed in many large cable stayed bridges during the last decades. The response of the cable is investigated for a reduced two-degrees-of-freedom...

  7. Simulations of coherent nonlinear optical response of molecular vibronic dimers

    CERN Document Server

    Perlík, Václav


    We have implemented vibronic dynamics for simulations of the third order coherent response of electronic dimers. In the present communication we provide the full and detailed description of the dynamical model, recently used for simulations of chlorophyll-carotenoid dyads, terylene dimers, or hypericin. We allow for explicit vibronic level structure, by including selected vibrational modes into a "system". Bath dynamics include the Landau-Teller vibrational relaxation, electronic dephasing, and nonlinear vibronic (to bath) coupling. Simulations combine effects of transport and dephasing between vibronic levels. Transport is described by master equation within secular approximation, phase is accumulated in cumulants and its calculation follows the transport pathways during waiting time period.

  8. Fluid transport due to nonlinear fluid-structure interaction

    Energy Technology Data Exchange (ETDEWEB)

    Soendergaard Jensen, J.


    This work considers nonlinear fluid-structure interaction for a vibrating pipe containing fluid. Transverse pipe vibrations will force the fluid to move relative to the pipe creating uni-directional fluid flow towards the pipe end. The fluid flow induced affects the damping and the stiffness of the pipe. The behavior of the system in response to lateral resonant base excitation is analyzed numerically mode of vibration seems to be most effective for high mean fluid speed, whereas higher modes of vibration can be used to transport fluid with the same fluid speed but with smaller magnitude of pipe vibrations. The effect of the nonlinear geometrical terms is analyzed and these terms are shown to affect the response for higher modes of vibration. Experimental investigations show good agreement with theoretical predictions. (au) 16 refs.

  9. Fluid transport due to nonlinear fluid-structure interaction

    DEFF Research Database (Denmark)

    Jensen, Jakob Søndergaard


    This work considers nonlinear fluid-structure interaction for a vibrating pipe containing fluid. Transverse pipe vibrations will force the fluid to move relative to the pipe creating unidirectional fluid flow towards the pipe end. The fluid flow induced affects the damping and the stiffness...... of the pipe. The behavior of the system in response to lateral resonant base excitation is analysed numerically and by the use of a perturbation method (multiple scales). Exciting the pipe in the fundamental mode of vibration seems to be most effective for transferring energy from the shaker to the fluid......, whereas higher modes of vibration can be used to transport fluid with pipe vibrations of smaller amplitude. The effect of the nonlinear geometrical terms is analysed and these terms are shown to affect the response for higher modes of vibration. Experimental investigations show good agreement...

  10. Nonlinear dynamic response of beam and its application in nanomechanical resonator

    Institute of Scientific and Technical Information of China (English)

    Yin Zhang; Yun Liu; Kevin D. Murphy


    Nonlinear dynamic response of nanomechanical resonator is of very important characteristics in its application.Two categories of the tension-dominant and curvaturedominant nonlinearities are analyzed.The dynamic nonlinearity of four beam structures of nanomechanical resonator is quantitatively studied via a dimensional analysis approach.The dimensional analysis shows that for the nanomechanical resonator of tension-dominant nonlinearity,its dynamic nonlinearity decreases monotonically with increasing axial loading and increases monotonically with the increasing aspect ratio of length to thickness; the dynamic nonlinearity can only result in the hardening effects.However,for the nanomechanical resonator of the curvature-dominant nonlinearity,its dynamic nonlinearity is only dependent on axial loading.Compared with the tension-dominant nonlinearity,the curvature-dominant nonlinearity increases monotonically with increasing axial loading; its dynamic nonlinearity can result in both hardening and softening effects.The analysis on the dynamic nonlinearity can be very helpful to the tuning application of the nanomechanical resonator.

  11. Nonlinear optical response in Kronig-Penney type graphene superlattice in terahertz regime (United States)

    Jiang, Lijuan; Yuan, Rui-Yang; Zhao, Xin; Lv, Jing; Yan, Hui


    The terahertz nonlinear optical response in Kronig-Penney (KP) type graphene superlattice is demonstrated. The single-, triple- and quintuple-frequencies of the fifth-order nonlinear responses are investigated for different frequencies and temperatures with the angle φ along the periodicity of the superlattice toward the external field tuning from 0 to π/2. The results show that the fifth-order nonlinear optical conductance of graphene superlattice is enhanced in the terahertz regime when φ = 0, i.e. an external field is applied along the periodicity of the superlattice. The fifth-order nonlinear optical conductances at φ = 0 for different frequencies and temperatures are calculated. The results show that the nonlinear optical conductance is enhanced in low frequency and low temperature. Our results suggest that KP type graphene superlattices are preferred structures for developing graphene-based nonlinear photonics and optoelectronics devices.

  12. Structurally-Tailorable, Nonlinear, Snap-Through Spring (United States)

    Starnes, James H., Jr.; Farley, Gary L.; Mantay, Wayne R.


    Abrupt change in load/deflection response controllable and predictable. Structurally-tailorable, nonlinear, snap-through spring (STNSTS) exhibits controllable and predictable abrupt change in load/deflection response and based upon known phenomenon of snap-through structural response. Composed of pin-connected two-bar linkage which depicts combined tension/compression springs. As load applied to STNSTS, stiffness is function of internal spring and bending stiffness of pin-connected bars. As load increases, bars deform laterally until they collapse and snap through. Has application in passively-tailored rotor-blade flap, pitch, and lag response, to improve aerodynamic performance and stability characteristics of rotors; in aerodynamically- and aeroelastically-tailored wing spars and ribs, to produce tailored deformation state for improved effectiveness in maneuvering, aerodynamic performance, and stability characteristics; and in energy absorbers for automobile bumpers and aircraft land

  13. Nonlinear Correlations of Protein Sequences and Symmetries of Their Structures

    Institute of Scientific and Technical Information of China (English)

    LI Ming-Feng; HUANG Yan-Zhao; XIAO Yi


    @@ We investigate the nonlinear correlations of protein sequences by using the nonlinear prediction method developed in nonlinear dynamical theory.It is found that a lot of protein sequences show strong nonlinear correlations and have deterministic structures.Further investigations show that the strong nonlinear correlations of these protein sequences are due to the symmetries of their tertiary structures.Furthermore, the correlation lengths of the sequences are related to the degrees of the symmetries.These results support the duplication mechanism of protein evolution and also reveal one aspect how amino acid sequences encode their spatial structures.

  14. Delocalization of nonlinear optical responses in plasmonic nanoantennas

    CERN Document Server

    Viarbitskaya, Sviatlana; Cluzel, Benoit; Francs, Gérard Colas des; Bouhelier, Alexandre


    Remote excitation and emission of two-photon luminescence and second-harmonic generation are observed in micrometer long gold rod optical antennas upon local illumination with a tightly focused near-infrared femtosecond laser beam. We show that the nonlinear radiations can be emitted from the entire antenna and the measured far-field angular patterns bear the information regarding the nature and origins of the respective nonlinear processes. We demonstrate that the nonlinear responses are transported by the propagating surface plasmon at excitation frequency, enabling thereby polariton-mediated tailoring and design of nonlinear responses.

  15. Identification of Non-Linear Structures using Recurrent Neural Networks

    DEFF Research Database (Denmark)

    Kirkegaard, Poul Henning; Nielsen, Søren R. K.; Hansen, H. I.


    Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure.......Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure....

  16. Identification of Non-Linear Structures using Recurrent Neural Networks

    DEFF Research Database (Denmark)

    Kirkegaard, Poul Henning; Nielsen, Søren R. K.; Hansen, H. I.

    Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure.......Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure....

  17. Identification of Non-Linear Structures using Recurrent Neural Networks

    DEFF Research Database (Denmark)

    Kirkegaard, Poul Henning; Nielsen, Søren R. K.; Hansen, H. I.


    Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure.......Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure....


    Institute of Scientific and Technical Information of China (English)

    Qin Qian; Lin Wang; Qiao Ni


    The nonlinear responses of planar motions of a fluid-conveying pipe embedded in nonlinear elastic foundations are investigated via the differential quadrature method diseretization (DQMD) of the governing partial differential equation. For the analytical model, the effect of the nonlinear elastic foundation is modeled by a nonlinear restraining force. By using an iterative algorithm, a set of ordinary differential dynamical equations derived from the equation of motion of the system are solved numerically and then the bifurcations are analyzed. The numerical results, in which the existence of chaos is demonstrated, are presented in the form of phase portraits of the oscillations. The intermittency transition to chaos has been found to arise.

  19. Towards a unifying theory for the first-, second-, and third-order molecular (non)linear optical response (United States)

    Pérez-Moreno, Javier; Clays, Koen; Kuzyk, Mark G.


    We present a procedure for the modeling of the dispersion of the nonlinear optical response of complex molecular structures that is based strictly on the results from experimental characterization. We show how under some general conditions, the use of the Thomas-Kuhn sum-rules leads to a successful modeling of the nonlinear response of complex molecular structures.

  20. Short pulse equations and localized structures in frequency band gaps of nonlinear metamaterials

    Energy Technology Data Exchange (ETDEWEB)

    Tsitsas, N.L. [School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Zografos, Athens 15773 (Greece); Horikis, T.P. [Department of Mathematics, University of Ioannina, Ioannina 45110 (Greece); Shen, Y.; Kevrekidis, P.G.; Whitaker, N. [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515 (United States); Frantzeskakis, D.J., E-mail: dfrantz@phys.uoa.g [Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 157 84 (Greece)


    We consider short pulse propagation in nonlinear metamaterials characterized by a weak Kerr-type nonlinearity in their dielectric response. Two short-pulse equations (SPEs) are derived for the high- and low-frequency 'band gaps' (where linear electromagnetic waves are evanescent) with linear effective permittivity epsilon<0 and permeability mu>0. The structure of the solutions of the SPEs is also briefly discussed, and connections with the soliton solutions of the nonlinear Schroedinger equation are made.

  1. Harmonic Phase Response of Nonlinear Radar Targets (United States)


    to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT...of an improvised explosive device (IED). Previous nonlinear radar systems detect targets via transmission of a single frequency ω, stepping...electronically nonlinear components, such as transistors, diodes , and semiconductors. While many circuit devices, such as amplifiers, mixers, and

  2. Nonlinear rheological models for structured interfaces

    NARCIS (Netherlands)

    Sagis, L.M.C.


    The GENERIC formalism is a formulation of nonequilibrium thermodynamics ideally suited to develop nonlinear constitutive equations for the stress–deformation behavior of complex interfaces. Here we develop a GENERIC model for multiphase systems with interfaces displaying nonlinear viscoelastic stres

  3. Nonlinear excitations in two-dimensional molecular structures with impurities

    DEFF Research Database (Denmark)

    Gaididei, Yuri Borisovich; Rasmussen, Kim; Christiansen, Peter Leth


    We study the nonlinear dynamics of electronic excitations interacting with acoustic phonons in two-dimensional molecular structures with impurities. We show that the problem is reduced to the nonlinear Schrodinger equation with a varying coefficient. The latter represents the influence of the imp......We study the nonlinear dynamics of electronic excitations interacting with acoustic phonons in two-dimensional molecular structures with impurities. We show that the problem is reduced to the nonlinear Schrodinger equation with a varying coefficient. The latter represents the influence...... excitations. Analytical results are in good agreement with numerical simulations of the nonlinear Schrodinger equation....

  4. Semiclassical mode-coupling factorizations of coherent nonlinear optical response

    NARCIS (Netherlands)

    Jansen, TL; Mukamel, S


    The identification of relevant collective coordinates is crucial for the interpretation of coherent nonlinear spectroscopies of complex molecules and liquids. Using an h expansion of Liouville space generating functions, we show how to factorize multitime nonlinear response functions into products o

  5. A Photonic Basis for Deriving Nonlinear Optical Response (United States)

    Andrews, David L.; Bradshaw, David S.


    Nonlinear optics is generally first presented as an extension of conventional optics. Typically the subject is introduced with reference to a classical oscillatory electric polarization, accommodating correction terms that become significant at high intensities. The material parameters that quantify the extent of the nonlinear response are cast as…

  6. The surface plasmon polariton dispersion relations in a nonlinear-metal-nonlinear dielectric structure of arbitrary nonlinearity

    Institute of Scientific and Technical Information of China (English)

    Liu Bing-Can; Yu Li; Lu Zhi-Xin


    The analytic surface plasmon polaritons (SPPs) dispersion relation is studied in a system consisting of a thin metallic film bounded by two sides media of nonlinear dielectric of arbitrary nonlinearity is studied by applying a generalised first integral approach. We consider both asymmetric and symmetric structures. Especially, in the symmetric system, two possible modes can exist: the odd mode and the even mode. The dispersion relations of the two modes are obtained. Due to the nonlinear dielectric, the magnitude of the electric field at the interface appears and alters the dispersion relations. The changes in SPPs dispersion relations depending on film thicknesses and nonlinearity are studied.

  7. Advanced Seismic Fragility Modeling using Nonlinear Soil-Structure Interaction Analysis

    Energy Technology Data Exchange (ETDEWEB)

    Bolisetti, Chandu [Idaho National Lab. (INL), Idaho Falls, ID (United States); Coleman, Justin [Idaho National Lab. (INL), Idaho Falls, ID (United States); Talaat, Mohamed [Simpson-Gupertz & Heger, Waltham, MA (United States); Hashimoto, Philip [Simpson-Gupertz & Heger, Waltham, MA (United States)


    The goal of this effort is to compare the seismic fragilities of a nuclear power plant system obtained by a traditional seismic probabilistic risk assessment (SPRA) and an advanced SPRA that utilizes Nonlinear Soil-Structure Interaction (NLSSI) analysis. Soil-structure interaction (SSI) response analysis for a traditional SPRA involves the linear analysis, which ignores geometric nonlinearities (i.e., soil and structure are glued together and the soil material undergoes tension when the structure uplifts). The NLSSI analysis will consider geometric nonlinearities.

  8. Identification of Nonlinearities in Joints of a Wing Structure

    Directory of Open Access Journals (Sweden)

    Sani M.S.M.


    Full Text Available Nonlinear structural identification is essential in engineering. As new materials are being used andstructures become slender and lighter, nonlinear behaviour of structures becomes more important. There have been many studies into the development and application of system identification methods for structural nonlinearity based on changes in natural frequencies, mode shapes and damping ratios. A great challenge is to identify nonlinearity in large structural systems. Much work has been undertaken in the development of nonlinear system identification methods (e.g. Hilbert Transform, NARMAX, and Proper Orthogonal Decomposition, however, it is arguable that most of these methods are cumbersome when applied to realistic large structures that contain mostly linear modes with some local nonlinearity (e.g. aircraft engine pylon attachment to a wing. In this paper, a multi-shaker force appropriation method is developed to determine the underlying linear and nonlinear structural properties through the use of the measurement and generation of restoring force surfaces. One undamped mode is excited in each multi-shaker test. Essentially, this technique is a derivative of the restoring surface method and involves a non-linear curve fitting performed in modal space. A reduced finite element model is established and its effectiveness in revealing the nonlinear characteristics of the system is discussed. The method is demonstrated through both numerical simulations and experiments on a simple jointed laboratory structure with seeded faults, which represents an engine pylon structure that consists of a rectangular wing with two stores suspended underneath.

  9. The influence of and the identification of nonlinearity in flexible structures (United States)

    Zavodney, Lawrence D.


    Several models were built at NASA Langley and used to demonstrate the following nonlinear behavior: internal resonance in a free response, principal parametric resonance and subcritical instability in a cantilever beam-lumped mass structure, combination resonance in a parametrically excited flexible beam, autoparametric interaction in a two-degree-of-freedom system, instability of the linear solution, saturation of the excited mode, subharmonic bifurcation, and chaotic responses. A video tape documenting these phenomena was made. An attempt to identify a simple structure consisting of two light-weight beams and two lumped masses using the Eigensystem Realization Algorithm showed the inherent difficulty of using a linear based theory to identify a particular nonlinearity. Preliminary results show the technique requires novel interpretation, and hence may not be useful for structural modes that are coupled by a guadratic nonlinearity. A literature survey was also completed on recent work in parametrically excited nonlinear system. In summary, nonlinear systems may possess unique behaviors that require nonlinear identification techniques based on an understanding of how nonlinearity affects the dynamic response of structures. In this was, the unique behaviors of nonlinear systems may be properly identified. Moreover, more accutate quantifiable estimates can be made once the qualitative model has been determined.

  10. Stochastic Nonlinear Response of Woven CMCs (United States)

    Kuang, C. Liu; Arnold, Steven M.


    It is well known that failure of a material is a locally driven event. In the case of ceramic matrix composites (CMCs), significant variations in the microstructure of the composite exist and their significance on both deformation and life response need to be assessed. Examples of these variations include changes in the fiber tow shape, tow shifting/nesting and voids within and between tows. In the present work, the influence of scale specific architectural features of woven ceramic composite are examined stochastically at both the macroscale (woven repeating unit cell (RUC)) and structural scale (idealized using multiple RUCs). The recently developed MultiScale Generalized Method of Cells methodology is used to determine the overall deformation response, proportional elastic limit (first matrix cracking), and failure under tensile loading conditions and associated probability distribution functions. Prior results showed that the most critical architectural parameter to account for is weave void shape and content with other parameters being less in severity. Current results show that statistically only the post-elastic limit region (secondary hardening modulus and ultimate tensile strength) is impacted by local uncertainties both at the macro and structural level.

  11. Robust stabilization of general nonlinear systems with structural uncertainty

    Institute of Scientific and Technical Information of China (English)


    This paper deals with the robust stabilization and passivity of general nonlinear systems with structural uncertainty. By using Lyapunov function, it verifies that under some conditions the robust passivity implies the zero-state detectability, Furthermore, it also implies the robust stabilization for such nonlinear systems. We then establish a stabilization method for the nonlinear systems with structural uncertainty. The smooth state feedback law can be constructed with the solution of an equation. Finally, it is worth noting that the main contribution of the paper establishes the relation between robust passivity and feedback stabilization for the general nonlinear systems with structural uncertainty. The simulation shows the effectiveness of the method.

  12. Nonlinear characterization of a bolted, industrial structure using a modal framework (United States)

    Roettgen, Daniel R.; Allen, Matthew S.


    This article presents measurements from a sub assembly of an off-the-shelf automotive exhaust system containing a bolted-flange connection and uses a recently proposed modal framework to develop a nonlinear dynamic model for the structure. The nonlinear identification and characterization methods used are reviewed to highlight the strengths of the current approach and the areas where further development is needed. This marks the first use of these new testing and nonlinear identification tools, and the associated modal framework, on production hardware with a realistic joint and realistic torque levels. To screen the measurements for nonlinearities, we make use of a time frequency analysis routine designed for transient responses called the zeroed early-time fast Fourier transform (ZEFFT). This tool typically reveals the small frequency shifts and distortions that tend to occur near each mode that is affected by the nonlinearity. The damping in this structure is found to be significantly nonlinear and a Hilbert transform is used to characterize the damping versus amplitude behavior. A model is presented that captures these effects for each mode individually (e.g. assuming negligible nonlinear coupling between modes), treating each mode as a single degree-of-freedom oscillator with a spring and viscous damping element in parallel with a four parameter Iwan model. The parameters of this model are identified for each of the structure's modes that exhibited nonlinearity and the resulting nonlinear model is shown to capture the stiffness and damping accurately over a large range of response amplitudes.

  13. Nonlinear structural damage detection using support vector machines (United States)

    Xiao, Li; Qu, Wenzhong


    An actual structure including connections and interfaces may exist nonlinear. Because of many complicated problems about nonlinear structural health monitoring (SHM), relatively little progress have been made in this aspect. Statistical pattern recognition techniques have been demonstrated to be competitive with other methods when applied to real engineering datasets. When a structure existing 'breathing' cracks that open and close under operational loading may cause a linear structural system to respond to its operational and environmental loads in a nonlinear manner nonlinear. In this paper, a vibration-based structural health monitoring when the structure exists cracks is investigated with autoregressive support vector machine (AR-SVM). Vibration experiments are carried out with a model frame. Time-series data in different cases such as: initial linear structure; linear structure with mass changed; nonlinear structure; nonlinear structure with mass changed are acquired.AR model of acceleration time-series is established, and different kernel function types and corresponding parameters are chosen and compared, which can more accurate, more effectively locate the damage. Different cases damaged states and different damage positions have been recognized successfully. AR-SVM method for the insufficient training samples is proved to be practical and efficient on structure nonlinear damage detection.

  14. Weakly nonlinear dispersion and stop-band effects for periodic structures

    DEFF Research Database (Denmark)

    Sorokin, Vladislav; Thomsen, Jon Juel

    Continua and structures composed of periodically repeated elements (cells) are used in many fields of science and technology. Examples of continua are composite materials, consisting of alternating volumes of substances with different properties, mechanical filters and wave guides. Examples of en...... suggested. The work is carried out with financial support from the Danish Council for Independent Research and COFUND: DFF – 1337-00026...... of these methods for studying nonlinear problems isimpossible or cumbersome, since Floquet theory is applicable only for linear systems. Thus the nonlinear effects for periodic structures are not yet fully uncovered, while at the same time applications may demand effects of nonlinearity on structural response...

  15. Effective nonlinear AC response to composite with spherical particles

    Institute of Scientific and Technical Information of China (English)

    Chen Xiao-Gang; Liang Fang-Chu; Wei En-Bo


    An effective nonlinear alternative-current (AC) response to granular nonlinear-composite with spherical inclusions embedded in a host medium under the action of an external AC field is investigated by using a perturbation approach.The local potentials of composite at higher harmonics are derived both in a region of local inclusion particles and in a local host region under the action of a sinusoidal field E1 sinωt + E3sin3ωt. An effective nonlinear-response to composite and the relationship between the effective nonlinear-responses at the fundamental frequency and the third harmonics are also studied for the spherical inclusions in a dilute limit.

  16. Nonlinear Viscoelastic Characterization of Structural Adhesives. (United States)


    neat resin properties 20. ABSTRACT (Cainlnuo OR revaWco aide II necessay amd identify br blck number) Measurements of the nonlinear viscoelastic...which is utilized. 17. Key Words and Document Analysis. l7a. Descriptors Adhesives, nonlinear viscoelasticity, FM-73 and FM-300 neat resin properties 17b

  17. Nonlinear structural finite element model updating and uncertainty quantification (United States)

    Ebrahimian, Hamed; Astroza, Rodrigo; Conte, Joel P.


    This paper presents a framework for nonlinear finite element (FE) model updating, in which state-of-the-art nonlinear structural FE modeling and analysis techniques are combined with the maximum likelihood estimation method (MLE) to estimate time-invariant parameters governing the nonlinear hysteretic material constitutive models used in the FE model of the structure. The estimation uncertainties are evaluated based on the Cramer-Rao lower bound (CRLB) theorem. A proof-of-concept example, consisting of a cantilever steel column representing a bridge pier, is provided to verify the proposed nonlinear FE model updating framework.

  18. Bayesian nonlinear structural FE model and seismic input identification for damage assessment of civil structures (United States)

    Astroza, Rodrigo; Ebrahimian, Hamed; Li, Yong; Conte, Joel P.


    A methodology is proposed to update mechanics-based nonlinear finite element (FE) models of civil structures subjected to unknown input excitation. The approach allows to jointly estimate unknown time-invariant model parameters of a nonlinear FE model of the structure and the unknown time histories of input excitations using spatially-sparse output response measurements recorded during an earthquake event. The unscented Kalman filter, which circumvents the computation of FE response sensitivities with respect to the unknown model parameters and unknown input excitations by using a deterministic sampling approach, is employed as the estimation tool. The use of measurement data obtained from arrays of heterogeneous sensors, including accelerometers, displacement sensors, and strain gauges is investigated. Based on the estimated FE model parameters and input excitations, the updated nonlinear FE model can be interrogated to detect, localize, classify, and assess damage in the structure. Numerically simulated response data of a three-dimensional 4-story 2-by-1 bay steel frame structure with six unknown model parameters subjected to unknown bi-directional horizontal seismic excitation, and a three-dimensional 5-story 2-by-1 bay reinforced concrete frame structure with nine unknown model parameters subjected to unknown bi-directional horizontal seismic excitation are used to illustrate and validate the proposed methodology. The results of the validation studies show the excellent performance and robustness of the proposed algorithm to jointly estimate unknown FE model parameters and unknown input excitations.

  19. Nonlinear structure formation in Nonlocal Gravity

    CERN Document Server

    Barreira, Alexandre; Hellwing, Wojciech A; Baugh, Carlton M; Pascoli, Silvia


    We study the nonlinear growth of structure in nonlocal gravity models with the aid of N-body simulation and the spherical collapse and halo models. We focus on a model in which the inverse-squared of the d'Alembertian operator acts on the Ricci scalar in the action. For fixed cosmological parameters, this model differs from $\\Lambda{\\rm CDM}$ by having a lower late-time expansion rate and an enhanced and time-dependent gravitational strength ($\\sim 6\\%$ larger today). Compared to $\\Lambda{\\rm CDM}$ today, in the nonlocal model, massive haloes are slightly more abundant (by $\\sim 10\\%$ at $M \\sim 10^{14} M_{\\odot}/h$) and concentrated ($\\approx 8\\%$ enhancement over a range of mass scales), but their linear bias remains almost unchanged. We find that the Sheth-Tormen formalism describes the mass function and halo bias very well, with little need for recalibration of free parameters. The fitting of the halo concentrations is however essential to ensure the good performance of the halo model on small scales. For...

  20. Analysis of Nonlinear Structural Dynamics and Resonance in Trees

    Directory of Open Access Journals (Sweden)

    H. Doumiri Ganji


    Full Text Available Wind and gravity both impact trees in storms, but wind loads greatly exceed gravity loads in most situations. Complex behavior of trees in windstorms is gradually turning into a controversial concern among ecological engineers. To better understand the effects of nonlinear behavior of trees, the dynamic forces on tree structures during periods of high winds have been examined as a mass-spring system. In fact, the simulated dynamic forces created by strong winds are studied in order to determine the responses of the trees to such dynamic loads. Many of such nonlinear differential equations are complicated to solve. Therefore, this paper focuses on an accurate and simple solution, Differential Transformation Method (DTM, to solve the derived equation. In this regard, the concept of differential transformation is briefly introduced. The approximate solution to this equation is calculated in the form of a series with easily computable terms. Then, the method has been employed to achieve an acceptable solution to the presented nonlinear differential equation. To verify the accuracy of the proposed method, the obtained results from DTM are compared with those from the numerical solution. The results reveal that this method gives successive approximations of high accuracy solution.

  1. Predictive Dynamic Stimulation of Structures with Non-Smooth Nonlinearities (United States)


    bang- bang, dead band, and Duffing type nonlinearity. Nonlinear damping has been considered in the form of Coulomb damping, velocity-squared damping...or 2,000 DOF reduced to 5 or 10 DOF) of simple oscillator systems capture the free oscillation decay and the steady state response to harmonic...smooth or non-smooth), the linear based reduced model tends to overestimate the change in oscillation frequency due to the nonlinearity. Specifically

  2. Effects on the Floor Response Spectra by the Nonlinear Behavior of a Seismic Base Isolation System

    Energy Technology Data Exchange (ETDEWEB)

    Park, Hyungkui; Kim, Jung Han; Choi, Inkil [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)


    An evaluation of safety being carried out for various risk factors of prevents for nuclear power plant accident. In general, an evaluation of the structural integrity was performed about seismic risk. In recent years, an assessment of integrity of internal equipment being carried out for earthquake loads owing to the possibility of severe accidents caused by the destruction of internal equipment or a blackout. Floor response spectra of the structure should be sought for evaluating of the integrity of internal equipment. The floor response spectra depends on the characteristics of seismic base isolation system such as the natural frequency, damping ratio, and height of the floor of the structure. An evaluation of the structural integrity using the equivalent stiffness of the seismic base isolation system was satisfactory. In this study, the effect of the non-linearity of isolated system in the floor response spectrum of the structure is analyzed. In this study, the floor response spectrum of the seismic base isolation system by the non-linear effect of the rubber isolator was analyzed. As a result, the influence of the non-linear isolated system was increased in hi-frequency domain. In addition, each floor exhibited a more different of responses compared with the equivalent linear model of the isolated structure. The non-linearity of the isolation system of the structure was considered, because of a more reliable assessment of integrity of equipment at each floor of seismic base the isolation system.

  3. Nonlinear normal modes and their application in structural dynamics

    Directory of Open Access Journals (Sweden)


    Full Text Available Recent progress in the area of nonlinear modal analysis for structural systems is reported. Systematic methods are developed for generating minimally sized reduced-order models that accurately describe the vibrations of large-scale nonlinear engineering structures. The general approach makes use of nonlinear normal modes that are defined in terms of invariant manifolds in the phase space of the system model. An efficient Galerkin projection method is developed, which allows for the construction of nonlinear modes that are accurate out to large amplitudes of vibration. This approach is successfully extended to the generation of nonlinear modes for systems that are internally resonant and for systems subject to external excitation. The effectiveness of the Galerkin-based construction of the nonlinear normal modes is also demonstrated for a realistic model of a rotating beam.

  4. Multiaxial nonlinear viscoelastic characterization and modeling of a structural adhesive

    Energy Technology Data Exchange (ETDEWEB)

    Popelar, C.F.; Liechti, K.M. [Univ. of Texas, Austin, TX (United States)


    Many polymeric materials, including structural adhesives, exhibit a nonlinear viscoelastic response. The nonlinear free volume approach is based on the Doolittle concept that the free volume controls the mobility of polymer molecules and, thus, the inherent time scale of the material. It then follows that factors such as temperature and moisture, which change the free volume, will influence the time scale. Furthermore, stress-induced dilatation will also affect the free volume and, hence, the time scale. However, during this investigation dilatational effects alone were found to be insufficient in describing the response of near pure shear tests performed on a bisphenol A epoxy with an amido amine hardener. Thus, the free volume approach presented here has been modified to include distortional effects in the inherent time scale of the material. In addition to predicting the global response under a variety of multiaxial stress states, the modified free volume theory also accurately predicts the local displacement fields, including those associated with a localized region, as determined from geometric moire measurements at various stages of deformation.

  5. Stability analysis and non-linear behaviour of structural systems using the complex non-linear modal analysis (CNLMA)


    Sinou, Jean-Jacques; Thouverez, Fabrice; Jezequel, Louis


    International audience; Herein, a novel non-linear procedure for producing non-linear behaviour and stable limit cycle amplitudes of non-linear systems subjected to super-critical Hopf bifurcation point is presented. This approach, called Complex Non-Linear Modal Analysis (CNLMA), makes use of the non-linear unstable mode which governs the non-linear dynamic of structural systems in unstable areas. In this study, the computational methodology of CNLMA is presented for the systematic estimatio...

  6. Extreme value distribution and reliability of nonlinear stochastic structures

    Institute of Scientific and Technical Information of China (English)

    Chen Jianbing; Li Jie


    A new approach to evaluate the extreme value distribution (EVD) of the response and reliability of general multi-DOF nonlinear stochastic structures is proposed. The approach is based on the recently developed probability density evolution method, which enables the instantaneous probability density functions of the stochastic responses to be captured.In the proposed method, a virtual stochastic process is first constructed to satisfy the condition that the extreme value of the response equals the value of the constructed process at a certain instant of time. The probability density evolution method is then applied to evaluate the instantaneous probability density function of the response, yielding the EVD. The reliability is therefore available through a simple integration over the safe domain. A numerical algorithm is developed using the Number Theoretical Method to select the discretized representative points. Further, a hyper-ball is imposed to sieve the points from the preceding point set in the hypercube. In the numerical examples, the EVD of random variables is evaluated and compared with the analytical solution. A frame structure is analyzed to capture the EVD of the response and the dynamic reliability. The investigations indicate that the proposed approach provides reasonable accuracy and efficiency.

  7. Prolongation Structure of Semi-discrete Nonlinear Evolution Equations

    Institute of Scientific and Technical Information of China (English)


    Based on noncommutative differential calculus, we present a theory of prolongation structure for semi-discrete nonlinear evolution equations. As an illustrative example, a semi-discrete model of the nonlinear Schr(o)dinger equation is discussed in terms of this theory and the corresponding Lax pairs are also given.

  8. Non-linear finite element analysis in structural mechanics

    CERN Document Server

    Rust, Wilhelm


    This monograph describes the numerical analysis of non-linearities in structural mechanics, i.e. large rotations, large strain (geometric non-linearities), non-linear material behaviour, in particular elasto-plasticity as well as time-dependent behaviour, and contact. Based on that, the book treats stability problems and limit-load analyses, as well as non-linear equations of a large number of variables. Moreover, the author presents a wide range of problem sets and their solutions. The target audience primarily comprises advanced undergraduate and graduate students of mechanical and civil engineering, but the book may also be beneficial for practising engineers in industry.

  9. Nonlinear phononics and structural control of strongly correlated materials

    Energy Technology Data Exchange (ETDEWEB)

    Mankowsky, Roman


    Mid-infrared light pulses can be used to resonantly excite infrared-active vibrational modes for the phase control of strongly correlated materials on subpicosecond timescales. As the energy is transferred directly into atomic motions, dissipation into the electronic system is reduced, allowing for the emergence of unusual low energy collective properties. Light-induced superconductivity, insulator-metal transitions and melting of magnetic order demonstrate the potential of this method. An understanding of the mechanism, by which these transitions are driven, is however missing. The aim of this work is to uncover this process by investigating the nonlinear lattice dynamics induced by the excitation and to elucidate their contribution to the modulation of collective properties of strongly correlated materials. The first signature of nonlinear lattice dynamics was reported in the observation of coherent phonon oscillations, resonant with the excitation of an infrared-active phonon mode in a manganite. This nonlinear phononic coupling can be described within a model, which predicts not only oscillatory coherent phonons dynamics but also directional atomic displacements along the coupled modes on average, which could cause the previously observed transitions. We verified this directional response and quantified the anharmonic coupling constant by tracing the atomic motions in a time-resolved hard X-ray diffraction experiment with sub-picometer spatial and femtosecond temporal resolution. In a subsequent study, we investigated the role of nonlinear lattice dynamics in the emergence of superconductivity far above the equilibrium transition temperature, an intriguing effect found to follow lattice excitation of YBa{sub 2}Cu{sub 3}O{sub 6+x}. By combining density functional theory (DFT) calculations of the anharmonic coupling constants with time-resolved X-ray diffraction experiments, we identified a structural rearrangement, which appears and decays with the same temporal

  10. Towards homoscedastic nonlinear cointegration for structural health monitoring (United States)

    Zolna, Konrad; Dao, Phong B.; Staszewski, Wieslaw J.; Barszcz, Tomasz


    The paper presents the homoscedastic nonlinear cointegration. The method leads to stable variances in nonlinear cointegration residuals. The adapted Breusch-Pagan test procedure is developed to test for the presence of heteroscedasticity (or homoscedasticity) in the cointegration residuals obtained from the nonlinear cointegration analysis. Three different time series - i.e. one with a nonlinear quadratic deterministic trend, simulated vibration data and experimental wind turbine data - are used to illustrate the application of the proposed method. The proposed approach can be used for effective removal of nonlinear trends from various types of data and for reliable structural damage detection based on data that are corrupted by environmental and/or operational nonlinear trends.

  11. Modeling of the nonlinear resonant response in sedimentary rocks

    Energy Technology Data Exchange (ETDEWEB)

    Ten Cate, James A [Los Alamos National Laboratory; Shankland, Thomas J [Los Alamos National Laboratory; Vakhnenko, Vyacheslav O [NON LANL; Vakhnenko, Oleksiy [NON LANL


    We suggest a model for describing a wide class of nonlinear and hysteretic effects in sedimentary rocks at longitudinal bar resonance. In particular, we explain: hysteretic behaviour of a resonance curve on both its upward and downward slopes; linear softening of resonant frequency with increase of driving level; gradual (almost logarithmic) recovery of resonant frequency after large dynamical strains; and temporal relaxation of response amplitude at fixed frequency. Starting with a suggested model, we predict the dynamical realization of end-point memory in resonating bar experiments with a cyclic frequency protocol. These theoretical findings were confirmed experimentally at Los Alamos National Laboratory. Sedimentary rocks, particularly sandstones, are distinguished by their grain structure in which each grain is much harder than the intergrain cementation material. The peculiarities of grain and pore structures give rise to a variety of remarkable nonlinear mechanical properties demonstrated by rocks, both at quasistatic and alternating dynamic loading. Thus, the hysteresis earlier established for the stress-strain relation in samples subjected to quasistatic loading-unloading cycles has also been discovered for the relation between acceleration amplitude and driving frequency in bar-shaped samples subjected to an alternating external drive that is frequency-swept through resonance. At strong drive levels there is an unusual, almost linear decrease of resonant frequency with strain amplitude, and there are long-term relaxation phenomena such as nearly logarithmic recovery (increase) of resonant frequency after the large conditioning drive has been removed. In this report we present a short sketch of a model for explaining numerous experimental observations seen in forced longitudinal oscillations of sandstone bars. According to our theory a broad set of experimental data can be understood as various aspects of the same internally consistent pattern. Furthermore

  12. Nonlinear and stochastic dynamics of coherent structures

    DEFF Research Database (Denmark)

    Rasmussen, Kim


    system described by a tight-binding Hamiltonian and a harmonic lattice coupled b y a deformation-type potential. This derivation results in a two-dimensional nonline ar Schrödinger model, and considering the harmonic lattice to be in thermal contact with a heat bath w e show that the nonlinear...... phenomenon. We find numerically and analytically that the collapse can be delayed and ultimatively arrested by the fluctuations. Allowing the system to reach thermal equilibrium we further augment the model by a nonlineardamping term and find that this prohibits collapse in the strict mathematical se nse....... However a collapse like behavior still persists in the presence of the nonlinear damping . Apart from the absence of the collapse in the strict mathematical sense we find that the nonlinear damping term has rather weak influence on the interplay between fluctuations and self-focusing. The study...


    Institute of Scientific and Technical Information of China (English)


    A numerical scheme for the nonlinear behavior of structure under wind excitation is investigated. With the white noise filter of turbulent-wind fluctuations, the nonlinear motion equation of structures subjected to wind load was modeled as the Ito' s stochastic differential equation. The state vector associated with such a model is a diffusion process. A continuous linearization strategy in the time-domain was adopted.Based on the solution series of its stochastic linearization equations, the formal probabilistic density of the structure response was developed by the path integral technique. It is shown by the numerical example of a guyed mast that compared with the frequency-domain method and the time-domain nonlinear analysis, the proposed approach is highlighted by high accuracy and effectiveness. The influence of the structure non-linearity on the dynamic reliability assessment is also analyzed in the example.

  14. Nonlinear Phononic Periodic Structures and Granular Crystals (United States)


    of the advanced delay equation (13) and they compared the numerically obtained solutions with those of approximated PDEs. Recently, Starosvetsky... KdV ), a nonlinear partial differential equation , and have been discovered in myriad systems and discrete nonlinear lattices of all the above types...granular chain, and derived the following KdV equation : t 0 0 1/2 2 2 2 2 0 0 0 0 0 0, 2 6 , , . 6 xx x xc uc A R c R c Rc m σξ ξ γξ ξξ ξ δ γ σ δ

  15. Crystalline structure and symmetry dependence of acoustic nonlinearity parameters (United States)

    Cantrell, John H.


    A quantitative measure of elastic wave nonlinearity in crystals is provided by the acoustic nonlinearity parameters. The nonlinearity parameters are defined for arbitrary propagation modes for solids of arbitrary crystalline symmetry and are determined along the pure mode propagation directions for 33 crystals of cubic symmetry from data reported in the literature. The magnitudes of the nonlinearity parameters are found to exhibit a strong dependence on the crystalline structure and symmetries associated with the modal direction in the solid. Calculations based on the Born-Mayer potential for crystals having a dominant repulsive contribution to the elastic constants from the interatomic pair potential suggest that the origin of the structure dependence is associated with the shape rather than the strength of the potential. Considerations based on variations in crystal symmetry during loading along pure mode propagation directions of face-centered-cubic solids provide a qualitative explanation for the dependence of the acoustic nonlinearity parameters on modal direction.

  16. Parametric characteristic of the random vibration response of nonlinear systems

    Institute of Scientific and Technical Information of China (English)

    Xing-Jian Dong; Zhi-Ke Peng; Wen-Ming Zhang; Guang Meng; Fu-Lei Chu


    Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of non-linear engineering systems and structures that can be represented by a Volterra series model.In the present study,the random vibration of nonlinear systems is investigated using Volterra series.Analytical expressions were derived for the calculation of the output power spectral density (PSD) and input-output cross-PSD for nonlinear systems subjected to Gaussian excitation.Based on these expressions,it was revealed that both the output PSD and the input-output crossPSD can be expressed as polynomial functions of the nonlinear characteristic parameters or the input intensity.Numerical studies were carried out to verify the theoretical analysis result and to demonstrate the effectiveness of the derived relationship.The results reached in this study are of significance to the analysis and design of the nonlinear engineering systems and structures which can be represented by a Volterra series model.

  17. Coupled parametric processes in binary nonlinear photonic structures

    CERN Document Server

    Saygin, M Yu


    We study parametric interactions in a new type of nonlinear photonic structures, which is realized in the vicinity of a pair of nonlinear crystals. In this kind of structure, which we call binary, multiple nonlinear optical processes can be implemented simultaneously, owing to multiple phase-matching conditions, fulfilled separately in the constituent crystals. The coupling between the nonlinear processes by means of modes sharing similar frequency is attained by the spatially-broadband nature of the parametric fields. We investigate the spatial properties of the fields generated in the binary structure constructed from periodically poled crystals for the two examples: 1) single parametric down-conversion, and 2) coupled parametric down-conversion and up-conversion processes. The efficacy of the fields' generation in these examples is analyzed through comparison with the cases of traditional single periodically poled crystal and aperiodic photonic structure, respectively. It has been shown that the relative s...

  18. International Conference on Structural Nonlinear Dynamics and Diagnosis

    CERN Document Server

    CSNDD 2012; CSNDD 2014


    This book, which presents the peer-reviewed post-proceedings of CSNDD 2012 and CSNDD 2014, addresses the important role that relevant concepts and tools from nonlinear and complex dynamics could play in present and future engineering applications. It includes 22 chapters contributed by outstanding researchers and covering various aspects of applications, including: structural health monitoring, diagnosis and damage detection, experimental methodologies, active vibration control and smart structures, passive control of structures using nonlinear energy sinks, vibro-impact dynamic MEMS/NEMS/AFM, energy-harvesting materials and structures, and time-delayed feedback control, as well as aspects of deterministic versus stochastic dynamics and control of nonlinear phenomena in physics.  Researchers and engineers interested in the challenges posed and opportunities offered by nonlinearities in the development of passive and active control strategies, energy harvesting, novel design criteria, modeling and characteriz...

  19. Multiwave nonlinear couplings in elastic structures

    Directory of Open Access Journals (Sweden)


    Full Text Available This short contribution considers the essentials of nonlinear wave properties in typical mechanical systems such as an infinite straight bar, a circular ring, and a flat plate. It is found that nonlinear resonance is experienced in all the systems exhibiting continuous and discrete spectra, respectively. Multiwave interactions and the stability of coupled modes with respect to small perturbations are discussed. The emphasis is placed on mechanical phenomena, for example, stress amplification, although some analogies with some nonlinear optical systems are also obvious. The nonlinear resonance coupling in a plate within the Kirchhoff-Love approximation is selected as a two-dimensional example exhibiting a rich range of resonant wave phenomena. This is originally examined by use of Whitham's averaged Lagrangian method. In particular, the existence of three basic resonant triads between longitudinal, shear, and bending modes is shown. Some of these necessarily enter cascade wave processes related to the instability of some mode components of the triad under small perturbations.


    Institute of Scientific and Technical Information of China (English)

    ZhaoYan; LinJiahao; ZhangYahui; AnWei


    A nonlinear seismic analysis method for complex frame structures subjected to stationary random ground excitations is proposed. The nonlinear elasto-plastic behaviors may take place only on a small part of the structure. The Bouc-Wen differential equation model is used to model the hysteretic characteristics of the nonlinear components. The Pseudo Excitation Method (PEM) is used in solving the linearized random differential equations to replace the solution of the less efficient Lyapunov equation. Numerical results of a real bridge show that .the method proposed is effective for practical engineering analysis.

  1. Response bounds for complex systems with a localised and uncertain nonlinearity (United States)

    Butlin, T.


    Predicting the vibration response of complex nonlinear structures is a significant challenge: the response may involve many modes of the structure; nonlinearity precludes the use of efficient techniques developed for linear systems; and there is often uncertainty associated with the nonlinear law, even to the extent that its functional form is not always known. This paper builds on a recently developed method for handling this class of problem in a novel way. The method exploits the fact that nonlinearities are often spatially localised, and seeks the best- and worst-case system response with respect to a chosen metric by regarding the internal nonlinear force as an independent excitation to the underlying linear system. Constraints are used to capture what is thought to be known about the nonlinearity without needing to specify a particular law. This paper focuses on the case of systems with a single point nonlinearity but with arbitrarily complex underlying linear dynamics, driven by a sinusoidal force excitation. Semi-analytic upper and lower bounds are proposed for root-mean-square response metrics subject to constraints which specify that the nonlinearity should be a combination of (A) passive, (B) displacement-limited, and / or (C) force-saturating. The concept of 'equivalent linear bounds' is also introduced for cases where the response metric is thought to be dominated by the same frequency as the input. The bounds corresponding to a passive and displacement-limited nonlinearity are compared with Monte Carlo experimental and numerical results from an impacting beam test rig. The bounds corresponding to a passive and force-saturating nonlinearity are compared with numerical results for a friction-damped beam. The global upper and lower bounds are satisfied for all input frequencies but are generally found to be rather conservative. The 'equivalent linear bounds' show remarkably good agreement for predicting the range of root-mean-square velocity responses

  2. Localization and identification of structural nonlinearities using cascaded optimization and neural networks (United States)

    Koyuncu, A.; Cigeroglu, E.; Özgüven, H. N.


    In this study, a new approach is proposed for identification of structural nonlinearities by employing cascaded optimization and neural networks. Linear finite element model of the system and frequency response functions measured at arbitrary locations of the system are used in this approach. Using the finite element model, a training data set is created, which appropriately spans the possible nonlinear configurations space of the system. A classification neural network trained on these data sets then localizes and determines the types of all nonlinearities associated with the nonlinear degrees of freedom in the system. A new training data set spanning the parametric space associated with the determined nonlinearities is created to facilitate parametric identification. Utilizing this data set, initially, a feed forward regression neural network is trained, which parametrically identifies the classified nonlinearities. Then, the results obtained are further improved by carrying out an optimization which uses network identified values as starting points. Unlike identification methods available in literature, the proposed approach does not require data collection from the degrees of freedoms where nonlinear elements are attached, and furthermore, it is sufficiently accurate even in the presence of measurement noise. The application of the proposed approach is demonstrated on an example system with nonlinear elements and on a real life experimental setup with a local nonlinearity.

  3. Parametric localized modes in quadratic nonlinear photonic structures

    DEFF Research Database (Denmark)

    Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole;


    We analyze two-color spatially localized nonlinear modes formed by parametrically coupled fundamental and second-harmonic fields excited at quadratic (or chi2) nonlinear interfaces embedded in a linear layered structure-a quadratic nonlinear photonic crystal. For a periodic lattice of nonlinear...... interfaces, we derive an effective discrete model for the amplitudes of the fundamental and second-harmonic waves at the interfaces (the so-called discrete chi2 equations) and find, numerically and analytically, the spatially localized solutions-discrete gap solitons. For a single nonlinear interface...... in a linear superlattice, we study the properties of two-color localized modes, and describe both similarities to and differences from quadratic solitons in homogeneous media....

  4. Nonlinear structure formation in the Cubic Galileon gravity model

    CERN Document Server

    Barreira, Alexandre; Hellwing, Wojciech A; Baugh, Carlton M; Pascoli, Silvia


    We model the linear and nonlinear growth of large scale structure in the Cubic Galileon gravity model, by running a suite of N-body cosmological simulations using the {\\tt ECOSMOG} code. Our simulations include the Vainshtein screening effect, which reconciles the Cubic Galileon model with local tests of gravity. In the linear regime, the amplitude of the matter power spectrum increases by $\\sim 25%$ with respect to the standard $\\Lambda$CDM model today. The modified expansion rate accounts for $\\sim 20%$ of this enhancement, while the fifth force is responsible for only $\\sim 5%$. This is because the effective unscreened gravitational strength deviates from standard gravity only at late times, even though it can be twice as large today. In the nonlinear regime ($k \\gtrsim 0.1 h\\rm{Mpc}^{-1}$), the fifth force leads to only a modest increase ($\\lesssim 8%$) in the clustering power on all scales due to the very efficient operation of the Vainshtein mechanism. Such a strong effect is typically not seen in other...

  5. Nonlinear Response of Cantilever Beams to Combination and Subcombination Resonances

    Directory of Open Access Journals (Sweden)

    Ali H. Nayfeh


    Full Text Available The nonlinear planar response of cantilever metallic beams to combination parametric and external subcombination resonances is investigated, taking into account the effects of cubic geometric and inertia nonlinearities. The beams considered here are assumed to have large length-to-width aspect ratios and thin rectangular cross sections. Hence, the effects of shear deformations and rotatory inertia are neglected. For the case of combination parametric resonance, a two-mode Galerkin discretization along with Hamilton’s extended principle is used to obtain two second-order nonlinear ordinary-differential equations of motion and associated boundary conditions. Then, the method of multiple scales is applied to obtain a set of four first-order nonlinear ordinary-differential equations governing the modulation of the amplitudes and phases of the two excited modes. For the case of subcombination resonance, the method of multiple scales is applied directly to the Lagrangian and virtual-work term. Then using Hamilton’s extended principle, we obtain a set of four first-order nonlinear ordinary-differential equations governing the amplitudes and phases of the two excited modes. In both cases, the modulation equations are used to generate frequency- and force-response curves. We found that the trivial solution exhibits a jump as it undergoes a subcritical pitchfork bifurcation. Similarly, the nontrivial solutions also exhibit jumps as they undergo saddle-node bifurcations.

  6. Modeling and non-linear responses of MEMS capacitive accelerometer

    Directory of Open Access Journals (Sweden)

    Sri Harsha C.


    Full Text Available A theoretical investigation of an electrically actuated beam has been illustrated when the electrostatic-ally actuated micro-cantilever beam is separated from the electrode by a moderately large gap for two distinct types of geometric configurations of MEMS accelerometer. Higher order nonlinear terms have been taken into account for studying the pull in voltage analysis. A nonlinear model of gas film squeezing damping, another source of nonlinearity in MEMS devices is included in obtaining the dynamic responses. Moreover, in the present work, the possible source of nonlinearities while formulating the mathematical model of a MEMS accelerometer and their influences on the dynamic responses have been investigated. The theoretical results obtained by using MATLAB has been verified with the results obtained in FE software and has been found in good agreement. Criterion towards stable micro size accelerometer for each configuration has been investigated. This investigation clearly provides an understanding of nonlinear static and dynamics characteristics of electrostatically micro cantilever based device in MEMS.

  7. Measurement of Localized Nonlinear Microwave Response of Superconductors (United States)

    Lee, Sheng-Chiang; Palmer, Benjamin; Maiorov, B.


    We measure the local harmonic generation from superconducting thin films at microwave frequencies to investigate the intrinsic nonlinear Meissner effect near T/c in zero magnetic field. Both second and third harmonic generation are measured to identify time-reversal symmetry breaking (TRSB) and time-reversal symmetric (TRS) nonlinearities. The microscope can measure the local nonlinear response of a bicrystal grain boundary [Sheng-Chiang Lee and Steven M. Anlage, Physica C 408-410, 324 (2004); cond-mat/0408170]. We also performed a systematic doping-dependent study of the nonlinear response and find that the TRS characteristic nonlinearity current density scale follows the doping dependence of the de-pairing critical current density [cond-mat/0405595]. We extract a spontaneous TRSB characteristic current density scale that onsets at T/c, grows with decreasing temperature, and systematically decreases in magnitude (at fixed T/T/c) with under-doping. The origin of this current scale could be Josephson circulating currents or the spontaneous magnetization associated with a TRSB order parameter.

  8. Nonlinear magneto-electric response of a giant magnetostrictive/piezoelectric composite cylinder

    Institute of Scientific and Technical Information of China (English)

    Yuan-Wen Gao; Juan-Juan Zhang


    In this study,we investigate the nonlinear coupling magneto-electric (ME) effect of a giant magnetostrictive/piezoelectric composite cylinder.The nonlinear constitutive relations of the ME material are taken into account,and the influences of the nonlinear material properties on the ME effect are investigated for the static and dynamic cases,respectively.The influences of different constraint conditions on the ME effect are discussed.In the dynamic case considering nonlinear material properties,the double frequency ME response (The response frequency is twice the applied magnetic frequency) is obtained and discussed,which can be used to explain the experiment phenomenon in which the input signal with frequency f is converted to the output signal with 2f in ME laminated structures.Some calculations on nonlinear ME effect are conducted.The obtained results indicate that the nonlinear material properties affect not only the magnitude of the ME effect in the static case but also the ME response frequency in the dynamic case.

  9. Nonlinear vibration with control for flexible and adaptive structures

    CERN Document Server

    Wagg, David


    This book provides a comprehensive discussion of nonlinear multi-modal structural vibration problems, and shows how vibration suppression can be applied to such systems by considering a sample set of relevant control techniques. It covers the basic principles of nonlinear vibrations that occur in flexible and/or adaptive structures, with an emphasis on engineering analysis and relevant control techniques. Understanding nonlinear vibrations is becoming increasingly important in a range of engineering applications, particularly in the design of flexible structures such as aircraft, satellites, bridges, and sports stadia. There is an increasing trend towards lighter structures, with increased slenderness, often made of new composite materials and requiring some form of deployment and/or active vibration control. There are also applications in the areas of robotics, mechatronics, micro electrical mechanical systems, non-destructive testing and related disciplines such as structural health monitoring. Two broader ...

  10. Nonlinear microwave switching response of BSCCO single crystals

    Energy Technology Data Exchange (ETDEWEB)

    Jacobs, T.; Sridhar, S. [Northeastern Univ., Boston, MA (United States). Dept. of Physics; Willemsen, B.A. [Northeastern Univ., Boston, MA (United States). Dept. of Physics]|[Rome Lab., Hanscom AFB, MA (United States); Li, Qiang [Brookhaven National Lab., Upton, NY (United States); Gu, G.D.; Koshizuka, N. [Superconductivity Research Lab., Tokyo (Japan)


    Measurements of the surface impedance in Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+{delta}} single crystal with microwave currents flowing along the {cflx c} axis show clear evidence of a step-like nonlinearity. The surface resistance switches between apparently quantized levels for microwave field strength changes < 1 mG. This nonlinear response can arise from the presence of intrinsic Josephson junctions along the {cflx c} axis of these samples driven by the microwave current.

  11. Nonlinear THz response of metallic armchair graphene nanoribbon superlattices (United States)

    Wang, Yichao; Andersen, David R.


    We study the third order THz nonlinear response of metallic armchair graphene nanoribbon superlattices in the presence of an elliptically-polarized excitation field using the time dependent perturbation theory. For a one-dimensional Kronig-Penney potential of infinite length, the nonlinear response can be described perturbatively by a low energy \\mathbf{k}\\centerdot \\mathbf{p} N-photon coupling model. Remarkably, as shown by Burset et al the energy dispersion of the metallic band in the direction parallel to the superlattice wavevector is independent of the applied superlattice potential while the energy dispersion in the direction perpendicular to the superlattice wavevector depends strongly on the superlattice parameters. As a result, we predict novel behavior for the nonlinear response of single layer metallic acGNR superlattices to an applied elliptically-polarized electric field. Our work shows that the superlattice potential, periodicity, Fermi level, excitation field polarization state, and temperature all play a significant role in the resulting THz nonlinear conductances.

  12. Observability and Information Structure of Nonlinear Systems, (United States)


    defined by Shannon and used as a measure of mut.:al infor-mation between event x. and y4. If p(x.l IY.) I I(x., y.) xil -in (1/p(x.)) =- JInp (x.) (2...entropy H(x,y) in a similar way as H(x,y) = - fx,yp(xiy)lnp(x,y)cdlY, = -E[ JInp (x,y)]. (3-13) With the above definitions, mutual information between x...Observabiity of Nonlinear Systems, Eng. Cybernetics, Volume 1, pp 338-345, 1972. 18. Sen , P., Chidambara, M.R., Observability of a Class of Nonli-.ear

  13. Nonlinear Quantum Optics in Artificially Structured Media (United States)

    Helt, Lukas Gordon

    This thesis presents an analysis of photon pairs generated via either spontaneous parametric downconversion or spontaneous four-wave mixing in channel waveguides as well as in microring resonators side-coupled to channel waveguides. The state of photons exiting a particular device is calculated within a general Hamiltonian formalism that simplifies the link between quantum nonlinear optics experiments and classical nonlinear optics experiments. This state contains information regarding photon pair production efficiency as well as modal and spectral correlations between the two photons, characterized by a two-dimensional spectral distribution function called the biphoton wave function. In the limit of a low probability of pair production, photon pair production efficiencies are cast into forms resembling corresponding well-known classical nonlinear optical frequency conversion efficiencies, making it easy to see what plays the role of a classical "seed" field in an un-seeded (quantum) process. This also allows photon pair production efficiencies to be calculated based on the results of classical nonlinear optical experiments. It is further calculated that, unless generated photons are collected over a very narrow frequency range, their generation efficiency does not scale the same way with device length in a channel waveguide, or resonance quality factor in a microring resonator, as might be expected from the corresponding classical frequency conversion efficiency. Although calculations do not include self- or cross-phase modulation, nor two-photon absorption or free-carrier absorption, it is calculated that their neglect is justified in the low pair production probability limit. Linear (scattering) loss is also neglected, though partially addressed in the final chapter of this thesis. Biphoton wave functions are calculated explicitly, such that their shape and orientation, including approximate analytic expressions for their widths, can easily be determined. This

  14. Nonlinear Structure Formation with the Environmentally Dependent Dilaton

    CERN Document Server

    Brax, Phil; Davis, Anne-C; Li, Baojiu; Shaw, Douglas J


    We have studied the nonlinear structure formation of the environmentally dependent dilaton model using $N$-body simulations. We find that the mechanism of suppressing the scalar fifth force in high-density regions works very well. Within the parameter space allowed by the solar system tests, the dilaton model predicts small deviations of the matter power spectrum and the mass function from their $\\Lambda$CDM counterparts. The importance of taking full account of the nonlinearity of the model is also emphasized.

  15. Time-domain seismic reliability of nonlinear structures

    Indian Academy of Sciences (India)

    Achintya Haldar; Jungwon Huh; Ali Mehrabian


    A novel reliability analysis technique is presented to estimate the reliability of real structural systems. Its unique feature is that the dynamic loadings can be applied in time domain. It is a nonlinear stochastic finite element logarithm combined with the response surface method (RSM). It generates the response surface around the most probable failure point and incorporates information of the distribution of the random variables in the RSM formulation. It is verified using the Monte Carlo simulation technique, and is found to be very efficient and accurate. Most sources of nonlinearlity and uncertainty can be explicitly incorporated in the formulation. The flexibility of connections, represented by moment-relative rotation $(M–\\theta )$ curves, is addressed. After the Northridge earthquake of 1994, several improved steel connections were proposed. Structural Sesimic Design Associates (SSDA) tested several full-scale proprietory slotted web beam–column connections. The authors suggested $(M–\\theta )$ curves for this connection using actual test data. Behaviours of steel frames, assuming the connections are fully restrained, partially restrained, consisting of pre- and post-Northridge connections are evaluated and compared. Desirable features of the post-Northridge connections observed during testing are analytically confirmed. Laterally weak steel frame is then strengthened with concrete shear walls. Capabilities and the advanced nature of the method are demonstrated with the help of realistic examples.

  16. Predicting the nonlinear optical response in the resonant region from the linear characterization: a self-consistent theory for the first-, second-, and third-order (non)linear optical response (United States)

    Pérez-Moreno, Javier; Clays, Koen; Kuzyk, Mark G.


    We introduce a self-consistent theory for the description of the optical linear and nonlinear response of molecules that is based strictly on the results of the experimental characterization. We show how the Thomas-Kuhn sum-rules can be used to eliminate the dependence of the nonlinear response on parameters that are not directly measurable. Our approach leads to the successful modeling of the dispersion of the nonlinear response of complex molecular structures with different geometries (dipolar and octupolar), and can be used as a guide towards the modeling in terms of fundamental physical parameters.

  17. Nonlinear Structured Illumination Using a Fluorescent Protein Activating at the Readout Wavelength (United States)

    Hou, Wenya; Kielhorn, Martin; Arai, Yoshiyuki; Nagai, Takeharu; Kessels, Michael M.; Qualmann, Britta; Heintzmann, Rainer


    Structured illumination microscopy (SIM) is a wide-field technique in fluorescence microscopy that provides fast data acquisition and two-fold resolution improvement beyond the Abbe limit. We observed a further resolution improvement using the nonlinear emission response of a fluorescent protein. We demonstrated a two-beam nonlinear structured illumination microscope by introducing only a minor change into the system used for linear SIM (LSIM). To achieve the required nonlinear dependence in nonlinear SIM (NL-SIM) we exploited the photoswitching of the recently introduced fluorophore Kohinoor. It is particularly suitable due to its positive contrast photoswitching characteristics. Contrary to other reversibly photoswitchable fluorescent proteins which only have high photostability in living cells, Kohinoor additionally showed little degradation in fixed cells over many switching cycles. PMID:27783656

  18. Full Hydrodynamic Model of Nonlinear Electromagnetic Response in Metallic Metamaterials

    CERN Document Server

    Fang, Ming; Sha, Wei E I; Xiong, Xiaoyan Y Z; Wu, Xianliang


    Applications of metallic metamaterials have generated significant interest in recent years. Electromagnetic behavior of metamaterials in the optical range is usually characterized by a local-linear response. In this article, we develop a finite-difference time-domain (FDTD) solution of the hydrodynamic model that describes a free electron gas in metals. Extending beyond the local-linear response, the hydrodynamic model enables numerical investigation of nonlocal and nonlinear interactions between electromagnetic waves and metallic metamaterials. By explicitly imposing the current continuity constraint, the proposed model is solved in a self-consistent manner. Charge, energy and angular momentum conservation laws of high-order harmonic generation have been demonstrated for the first time by the Maxwell-hydrodynamic FDTD model. The model yields nonlinear optical responses for complex metallic metamaterials irradiated by a variety of waveforms. Consequently, the multiphysics model opens up unique opportunities f...

  19. Non-linear dynamic response of a wind turbine blade (United States)

    Chopra, I.; Dugundji, J.


    The paper outlines the nonlinear dynamic analysis of an isolated three-degree flap-lag-feather wind turbine blade under a gravity field and with shear flow. Lagrangian equations are used to derive the nonlinear equations of motion of blade for arbitrarily large angular deflections. The limit cycle analysis for forced oscillations and the determination of the principal parametric resonance of the blade due to periodic forces from the gravity field and wind shear are performed using the harmonic balance method. Results are obtained first for a two-degree flap-lag blade, then the effect of the third degree of freedom (feather) is studied. The self-excited flutter solutions are obtained for a uniform wind and with gravity forces neglected. The effects of several parameters on the blade stability are examined, including coning angle, structural damping, Lock number, and feather frequency. The limit cycle flutter solution of a typical configuration shows a substantial nonlinear softening spring behavior.

  20. Evaluation of Floor Response Spectrum considering Ductility of Structure

    Energy Technology Data Exchange (ETDEWEB)

    Park, Junhee; Choi, In-Kil [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)


    The FRS (floor response spectrum) is directly influenced by the behavior of structure under the seismic load. If the structure is nonlinear range, the energy dissipation will be occurred by the damage of structure and the maximum force will be reduced. In Zion method, the inelastic energy abortion factor has been used to consider the nonlinearity of structure. This factor was used for the seismic fragility of structure. For the seismic fragility of equipment, the uncertainty of this factor was used differently according to the story level. But this method is not warranted under the strong earthquake leads to the structural damage. Therefore it is needed to evaluate the FRS considering the nonlinear behavior of structure and to assessment the conservatism related to nonlinear behavior of structure in FRS. In this study, the nonlinear analysis was performed for the conservatism of FRS under the damage of structure. The conservatism of FRS by the nonlinear analysis was compared by that proposed by the Zion method. The conservatism of floor acceleration response for the equipment was evaluated by performing the nonlinear analysis. From the nonlinear analysis results, it was showed that the median and β{sub c} of FRSR was increased with the ductility of structure and the response of equipment had the resonance effect between the frequency of equipment and structure. The seismic capacity of equipment by the Zion method can be different from the real seismic capacity of equipment because the inelastic structure response factor has nothing to do with the ductility of structure. Therefore the median and COV for FRSR should be defined considering the ductility of structure and the frequency of equipment for more exactly evaluating the seismic capacity of equipment.

  1. Adhesive nonlinearity in Lamb-wave-based structural health monitoring systems (United States)

    Shan, Shengbo; Cheng, Li; Li, Peng


    Structural health monitoring (SHM) techniques with nonlinear Lamb waves have gained wide popularity due to their high sensitivity to microstructural changes for the detection of damage precursors. Despite the significant progress made, various unavoidable nonlinear sources in a practical SHM system, as well as their impact on the detection, have not been fully assessed and understood. For the real-time and online monitoring, transducers are usually permanently bonded on the structure under inspection. In this case, the inherent material nonlinear properties of the bonding layer, referred to as adhesive nonlinearity (AN), may create undesired interference to the SHM system, or even jeopardize the damage diagnosis if they become serious. In this paper, a nonlinear theoretical framework is developed, covering the process of wave generation, propagation and sensing, with the aim of investigating the mechanism and characteristics of AN-induced Lamb waves in plates, which potentially allows for further system optimization to minimize the influence of AN. The model shows that an equivalent nonlinear normal stress is generated in the bonding layer due to its nonlinear material behavior, which, through its coupling with the system, is responsible for the generation of second harmonic Lamb waves in the plate, subsequently resulting in the nonlinear responses in the captured signals. With the aid of the finite element (FE) modeling and a superposition method for nonlinear feature extraction, the theoretical model is validated in terms of generation mechanism of the AN-induced wave components as well as their propagating characteristics. Meanwhile, the influence of the AN is evaluated by comparing the AN-induced nonlinear responses with those caused by the material nonlinearity of the plate, showing that AN should be considered as a non-negligible nonlinear source in a typical nonlinear Lamb-wave-based SHM system. In addition, the theoretical model is also experimentally

  2. Dissipative nonlinear structures in tokamak plasmas

    Directory of Open Access Journals (Sweden)

    K. A. Razumova


    Full Text Available A lot of different kinds of instabilities may be developed in high temperature plasma located in a strong toroidal magnetic field (tokamak plasma. Nonlinear effects in the instability development result in plasma self-organization. Such plasma has a geometrically complicated configuration, consisting of the magnetic surfaces imbedded into each other and split into islands with various characteristic numbers of helical twisting. The self-consistency of the processes means that the transport coefficients in plasma do not depend just on the local parameters, being a function of the whole plasma configuration and of the forces affecting it. By disrupting the bonds between separate magnetic surfaces filled with islands, one can produce zones of reduced transport in the plasma, i.e. “internal thermal barriers”, allowing one essentially to increase the plasma temperature and density.

  3. Damage detection in structures through nonlinear excitation and system identification (United States)

    Hajj, Muhammad R.; Bordonaro, Giancarlo G.; Nayfeh, Ali H.; Duke, John C., Jr.


    Variations in parameters representing natural frequency, damping and effective nonlinearities before and after damage initiation in a beam carrying a lumped mass are assessed. The identification of these parameters is performed by exploiting and modeling nonlinear behavior of the beam-mass system and matching an approximate solution of the representative model with quantities obtained from spectral analysis of measured vibrations. The representative model and identified coefficients are validated through comparison of measured and predicted responses. Percentage variations of the identified parameters before and after damage initiation are determined to establish their sensitivities to the state of damage of the beam. The results show that damping and effective nonlinearity parameters are more sensitive to damage initiation than the system's natural frequency. Moreover, the sensitivity of nonlinear parameters to damage is better established using a physically-derived parameter rather than spectral amplitudes of harmonic components.

  4. Nonlinear Aerodynamic ROM-Structural ROM Methodology for Inflatable Aeroelasticity in Hypersonic Atmospheric Entry Project (United States)

    National Aeronautics and Space Administration — ZONA Technology proposes to develop an innovative nonlinear structural reduced order model (ROM) - nonlinear aerodynamic ROM methodology for the inflatable...

  5. Nonlinear Kalman Filtering in Affine Term Structure Models

    DEFF Research Database (Denmark)

    Christoffersen, Peter; Dorion, Christian; Jacobs, Kris;

    When the relationship between security prices and state variables in dynamic term structure models is nonlinear, existing studies usually linearize this relationship because nonlinear fi…ltering is computationally demanding. We conduct an extensive investigation of this linearization and analyze...... Monte Carlo experiment demonstrates that the unscented Kalman fi…lter is much more accurate than its extended counterpart in fi…ltering the states and forecasting swap rates and caps. Our fi…ndings suggest that the unscented Kalman fi…lter may prove to be a good approach for a number of other problems...... in fi…xed income pricing with nonlinear relationships between the state vector and the observations, such as the estimation of term structure models using coupon bonds and the estimation of quadratic term structure models....

  6. Variable structure control of nonlinear systems through simplified uncertain models (United States)

    Sira-Ramirez, Hebertt


    A variable structure control approach is presented for the robust stabilization of feedback equivalent nonlinear systems whose proposed model lies in the same structural orbit of a linear system in Brunovsky's canonical form. An attempt to linearize exactly the nonlinear plant on the basis of the feedback control law derived for the available model results in a nonlinearly perturbed canonical system for the expanded class of possible equivalent control functions. Conservatism tends to grow as modeling errors become larger. In order to preserve the internal controllability structure of the plant, it is proposed that model simplification be carried out on the open-loop-transformed system. As an example, a controller is developed for a single link manipulator with an elastic joint.

  7. A new topology optimization scheme for nonlinear structures

    Energy Technology Data Exchange (ETDEWEB)

    Eim, Young Sup; Han, Seog Young [Hanyang University, Seoul (Korea, Republic of)


    A new topology optimization algorithm based on artificial bee colony algorithm (ABCA) was developed and applied to geometrically nonlinear structures. A finite element method and the Newton-Raphson technique were adopted for the nonlinear topology optimization. The distribution of material is expressed by the density of each element and a filter scheme was implemented to prevent a checkerboard pattern in the optimized layouts. In the application of ABCA for long structures or structures with small volume constraints, optimized topologies may be obtained differently for the same problem at each trial. The calculation speed is also very slow since topology optimization based on the roulette-wheel method requires many finite element analyses. To improve the calculation speed and stability of ABCA, a rank-based method was used. By optimizing several examples, it was verified that the developed topology scheme based on ABCA is very effective and applicable in geometrically nonlinear topology optimization problems.

  8. Generation of High Frequency Response in a Dynamically Loaded, Nonlinear Soil Column

    Energy Technology Data Exchange (ETDEWEB)

    Spears, Robert Edward [Idaho National Laboratory; Coleman, Justin Leigh [Idaho National Laboratory


    Detailed guidance on linear seismic analysis of soil columns is provided in “Seismic Analysis of Safety-Related Nuclear Structures and Commentary (ASCE 4, 1998),” which is currently under revision. A new Appendix in ASCE 4-2014 (draft) is being added to provide guidance for nonlinear time domain analysis which includes evaluation of soil columns. When performing linear analysis, a given soil column is typically evaluated with a linear, viscous damped constitutive model. When submitted to a sine wave motion, this constitutive model produces a smooth hysteresis loop. For nonlinear analysis, the soil column can be modelled with an appropriate nonlinear hysteretic soil model. For the model in this paper, the stiffness and energy absorption result from a defined post yielding shear stress versus shear strain curve. This curve is input with tabular data points. When submitted to a sine wave motion, this constitutive model produces a hysteresis loop that looks similar in shape to the input tabular data points on the sides with discontinuous, pointed ends. This paper compares linear and nonlinear soil column results. The results show that the nonlinear analysis produces additional high frequency response. The paper provides additional study to establish what portion of the high frequency response is due to numerical noise associated with the tabular input curve and what portion is accurately caused by the pointed ends of the hysteresis loop. Finally, the paper shows how the results are changed when a significant structural mass is added to the top of the soil column.

  9. 脉冲地震动缩放水平对结构非线性位移反应影响的分析%Effects of scaled pulse-like ground motion records on nonlinear structural displacement response

    Institute of Scientific and Technical Information of China (English)

    周靖; 陈凯亮; 黄靓


    Nonlinear displacement biases in response of a single-degree-of-freedom (SDOF) systems were studied,they were induced by scaled pulse-like ground motion velocity records. Based on response time-history analysis of a SDOF system subjected to 30 pulse-like ground motions, the variation laws of the nonlinear displacement biases versus the structural vibration period (T) and the strength reduction factor (R) with scaling the earthquake records to the levels of target spectral acceleration ( Sa ), peak ground acceleration ( PGA ), peak ground velocity ( PGV ), and peak ground displacement (PGD) were studied. The variation trends of the displacement biases were determined with log-linear regression of scattered points, and the stability of the biases under the condition of scaling different ground motion intensities was comparatively analyzed. The results demonstrated that the amount of the displacement biases greatly depends on the scaling factor, the first modal period of the vibration, and the overall strength of the structure; reasonably selecting the scaling factor and the ground motion intensity presenting parameter of the pulse-like ground motion velocity records can reduce the displacement bias in structural seismic responses.%研究缩放速度脉冲型地震动强度水平引起的单自由度(SDOF)体系非线性位移反应的偏差.采用30条速度脉冲地震记录,通过SDOF的体系动力时程分析,分析了速度脉冲型地震动分别缩放到不同目标谱加速度(Sα)、峰值加速度(PGA)、峰值速度(PGV)、峰值位移(PGD)水平时,SDOF体系非线性位移反应偏差随系统自振周期和强度折减系数变化的规律;通过对散点数据的对数线性回归确定了位移反应偏差的变化趋势,并比较了不同地面运动强度表征参数下位移偏差的稳定性.分析结果表明:位移偏差对地震动缩放系数、系统的基阶自振周期和系统的强度有一定的依赖性,合理选

  10. Diagnosing nonlinearities in the local and remote responses to partial Amazon deforestation (United States)

    Badger, Andrew M.; Dirmeyer, Paul A.


    Using a set of fully coupled climate model simulations, the response to partial deforestation over the Amazon due to agricultural expansion has been analyzed. Three variations of 50% deforestation (all of western half, all of eastern half, and half of each grid box) were compared with total deforestation to determine the degree and character of nonlinearity of the climate response to partial deforestation. A metric is developed to quantify the degree and distribution of nonlinearity in the response, applicable to any variable. The metric also quantifies whether the response is saturating or accelerating, meaning significantly either more or less than 50% of the simulated response to total deforestation is attained at 50% deforestation. The spatial structure of the atmospheric response to Amazon deforestation reveals large areas across the tropics that exhibit a significant nonlinear component, particularly for temperature and geopotential height. Over the domain between 45°S and 45°N across all longitudes, 50% deforestation generally provides less than half of the total response to deforestation over oceans, indicating the marine portion of climate system is somewhat resilient to progressive deforestation. However, over continents there are both accelerating and saturating responses to 50% Amazon deforestation, and the response is different depending on whether the eastern or western half of Amazonia is deforested or half of the forest is removed uniformly across the region.


    Institute of Scientific and Technical Information of China (English)

    LIN Li-ming; LING Guo-can; WU Ying-xiang; ZENG Xiao-hui


    A Nonlinear Fluid Damping(NFD)in the form of the square-velocity is applied in the response analysis of Vortex-Induced Vibrations(VIV).Its nonlinear hydrodynamic effects on the coupled wake and structure oscillators are investigated.A comparison between the coupled systems with the linear and nonlinear fluid dampings and experiments shows that the NFD model can well describe response characteristics,such as the amplification of body displacement at lock-in and frequency lock-in,both at high and low mass ratios.Particularly,the predicted peak amplitude of the body in the Griffin plot is in good agreement with experimental data and empirical equation,indicating the significant effect of the NFD on the structure motion.

  12. Nonlinear analysis and dynamic structure in the energy market (United States)

    Aghababa, Hajar

    This research assesses the dynamic structure of the energy sector of the aggregate economy in the context of nonlinear mechanisms. Earlier studies have focused mainly on the price of the energy products when detecting nonlinearities in time series data of the energy market, and there is little mention of the production side of the market. Moreover, there is a lack of exploration about the implication of high dimensionality and time aggregation when analyzing the market's fundamentals. This research will address these gaps by including the quantity side of the market in addition to the price and by systematically incorporating various frequencies for sample sizes in three essays. The goal of this research is to provide an inclusive and exhaustive examination of the dynamics in the energy markets. The first essay begins with the application of statistical techniques, and it incorporates the most well-known univariate tests for nonlinearity with distinct power functions over alternatives and tests different null hypotheses. It utilizes the daily spot price observations on five major products in the energy market. The results suggest that the time series daily spot prices of the energy products are highly nonlinear in their nature. They demonstrate apparent evidence of general nonlinear serial dependence in each individual series, as well as nonlinearity in the first, second, and third moments of the series. The second essay examines the underlying mechanism of crude oil production and identifies the nonlinear structure of the production market by utilizing various monthly time series observations of crude oil production: the U.S. field, Organization of the Petroleum Exporting Countries (OPEC), non-OPEC, and the world production of crude oil. The finding implies that the time series data of the U.S. field, OPEC, and the world production of crude oil exhibit deep nonlinearity in their structure and are generated by nonlinear mechanisms. However, the dynamics of the non

  13. Fractal structures in nonlinear plasma physics. (United States)

    Viana, R L; da Silva, E C; Kroetz, T; Caldas, I L; Roberto, M; Sanjuán, M A F


    Fractal structures appear in many situations related to the dynamics of conservative as well as dissipative dynamical systems, being a manifestation of chaotic behaviour. In open area-preserving discrete dynamical systems we can find fractal structures in the form of fractal boundaries, associated to escape basins, and even possessing the more general property of Wada. Such systems appear in certain applications in plasma physics, like the magnetic field line behaviour in tokamaks with ergodic limiters. The main purpose of this paper is to show how such fractal structures have observable consequences in terms of the transport properties in the plasma edge of tokamaks, some of which have been experimentally verified. We emphasize the role of the fractal structures in the understanding of mesoscale phenomena in plasmas, such as electromagnetic turbulence.

  14. Nonlinear Aerodynamic and Nonlinear Structures Interations (NANSI) Methodology for Ballute/Inflatable Aeroelasticity in Hypersonic Atmospheric Entry Project (United States)

    National Aeronautics and Space Administration — ZONA proposes a phase II effort to fully develop a comprehensive methodology for aeroelastic predictions of the nonlinear aerodynamic/aerothermodynamic - structure...

  15. Effect of nonlinearity of restrainer and supports on the elasto-plastic seismic response of continuous girder bridge

    Directory of Open Access Journals (Sweden)

    Wang Changfeng


    Full Text Available During an earthquake, the nonlinearity of the bridge structure mainly occurs at the supports, bridge piers and restrainers. When entering nonlinear stage, members of the bridge structure affect the elasto-plastic seismic response of the whole structure to a certain extent; for multi-span continuous bridges, longitudinal restrainers can be installed on the movable piers to optimise the distribution of seismic force and enable the movable piers to bear a certain amount of seismic effect. In order to evaluate the effect of nonlinearity of restrainer and supports on the elasto-plastic seismic response of continuous girder bridge, analytical models of continuous girder bridge structure considering the nonlinearity of movable supports, restrainers and bridge piers were built and the nonlinear time history analysis was conducted to evaluate the effect of nonlinearity of restraining devices and supports on the elasto-plastic seismic response of continuous girder bridge. Relevant structural measures and recommendation were made to reduce the seismic response of the fixed piers of the continuous girder bridge.

  16. Estimations of non-linearities in structural vibrations of string musical instruments

    CERN Document Server

    Ege, Kerem; Boutillon, Xavier


    Under the excitation of strings, the wooden structure of string instruments is generally assumed to undergo linear vibrations. As an alternative to the direct measurement of the distortion rate at several vibration levels and frequencies, we characterise weak non-linearities by a signal-model approach based on cascade of Hammerstein models. In this approach, in a chain of two non-linear systems, two measurements are sufficient to estimate the non-linear contribution of the second (sub-)system which cannot be directly linearly driven, as a function of the exciting frequency. The experiment consists in exciting the instrument acoustically. The linear and non-linear contributions to the response of (a) the loudspeaker coupled to the room, (b) the instrument can be separated. Some methodological issues will be discussed. Findings pertaining to several instruments - one piano, two guitars, one violin - will be presented.

  17. Resonances in nonlinear structure vibrations under multifrequency excitations

    Energy Technology Data Exchange (ETDEWEB)

    El-Bassiouny, A F [Faculty of Science, Mathematics Department, Benha University, Benha 1358 (Egypt); El-Latif, G M Abd [Faculty of Science, Mathematics Department, Sohag University, Sohag (Egypt)


    The response of a single-degree-of-freedom system with quadratic, cubic and quartic nonlinearities subjected to a sinusoidal excitation that involves multiple frequencies is considered. The method of multiple scales is used to construct a first order uniform expansion yielding two first-order nonlinear ordinary differential equations that are derived for the evolution of the amplitude and phase. These oscillations involve a subharmonic oscillation of order one-fourth and superharmonic oscillation of order two. Steady state responses and their stability are computed for selected values of the system parameters. The effects of these (quadratic, cubic, and quartic) nonlinearities on these oscillations are specifically investigated. With this study, it has been verified that the qualitative effects of these nonlinearities are different. Regions of hardening (softening) behaviour of the system exist for the case of subharmonic resonance. The response curve is not affected by decreasing the damping factor for the case of superharmonic resonance. It is shown that the response curve contracts or expands as the parameters vary. The multivalued region increases or decreases when some parameters vary.

  18. Nonlinear analysis of a structure loaded by a stochastic excitation

    Institute of Scientific and Technical Information of China (English)


    For a non-linear system excited by a stochastic load which is expressed as a time series, a recursive method based on the Z-transform is presented. To identify the obtained response time series, a discrete wavelet transform (DWT) technique is proposed.

  19. Output-only identification of civil structures using nonlinear finite element model updating (United States)

    Ebrahimian, Hamed; Astroza, Rodrigo; Conte, Joel P.


    This paper presents a novel approach for output-only nonlinear system identification of structures using data recorded during earthquake events. In this approach, state-of-the-art nonlinear structural FE modeling and analysis techniques are combined with Bayesian Inference method to estimate (i) time-invariant parameters governing the nonlinear hysteretic material constitutive models used in the FE model of the structure, and (ii) the time history of the earthquake ground motion. To validate the performance of the proposed framework, the simulated responses of a bridge pier to an earthquake ground motion is polluted with artificial output measurement noise and used to jointly estimate the unknown material parameters and the time history of the earthquake ground motion. This proof-of-concept example illustrates the successful performance of the proposed approach even in the presence of high measurement noise.

  20. Control Lyapunov Stabilization of Nonlinear Systems with Structural Uncertainty

    Institute of Scientific and Technical Information of China (English)

    CAI Xiu-shan; HAN Zheng-zhi; TANG Hou-jun


    This paper deals with global stabilization problem for the nonlinear systems with structural uncertainty.Based on control Lyapunov function, a sufficient and necessary condition for the globally and asymptotically stabilizing the equailibrium of the closed system is given. Moreovery, an almost smooth state feedback control law is constructed. The simulation shows the effectiveness of the method.

  1. Stable Solution of Nonlinear Age-structuredForest Evolution System

    Institute of Scientific and Technical Information of China (English)

    WANGDing-jiang; ZHAOTing-fang


    This paper studies the dynamical behavior of a class of total area dependent nonlinear age-structured forest evolution model. We give the problem of equal value for the forest system, and discuss the stable solution of system. We obtained the necessary and sufficient conditions for there exists the stable solution.

  2. Maximum Likelihood Estimation of Nonlinear Structural Equation Models. (United States)

    Lee, Sik-Yum; Zhu, Hong-Tu


    Developed an EM type algorithm for maximum likelihood estimation of a general nonlinear structural equation model in which the E-step is completed by a Metropolis-Hastings algorithm. Illustrated the methodology with results from a simulation study and two real examples using data from previous studies. (SLD)

  3. Case-Deletion Diagnostics for Nonlinear Structural Equation Models (United States)

    Lee, Sik-Yum; Lu, Bin


    In this article, a case-deletion procedure is proposed to detect influential observations in a nonlinear structural equation model. The key idea is to develop the diagnostic measures based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm. An one-step pseudo approximation is proposed to reduce the…

  4. Local Influence Analysis of Nonlinear Structural Equation Models (United States)

    Lee, Sik-Yum; Tang, Nian-Sheng


    By regarding the latent random vectors as hypothetical missing data and based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm, we investigate assessment of local influence of various perturbation schemes in a nonlinear structural equation model. The basic building blocks of local influence analysis…

  5. Structure of Dirac matrices and invariants for nonlinear Dirac equations



    We present invariants for nonlinear Dirac equations in space-time ${\\mathbb R}^{n+1}$, by which we prove that a special choice of the Cauchy data yields free solutions. Our argument works for Klein-Gordon-Dirac equations with Yukawa coupling as well. Related problems on the structure of Dirac matrices are studied.

  6. A FORTRAN program for calculating nonlinear seismic ground response (United States)

    Joyner, William B.


    The program described here was designed for calculating the nonlinear seismic response of a system of horizontal soil layers underlain by a semi-infinite elastic medium representing bedrock. Excitation is a vertically incident shear wave in the underlying medium. The nonlinear hysteretic behavior of the soil is represented by a model consisting of simple linear springs and Coulomb friction elements arranged as shown. A boundary condition is used which takes account of finite rigidity in the elastic substratum. The computations are performed by an explicit finite-difference scheme that proceeds step by step in space and time. A brief program description is provided here with instructions for preparing the input and a source listing. A more detailed discussion of the method is presented elsewhere as is the description of a different program employing implicit integration.

  7. Effects of Particle Shape and Microstructure on Effective Nonlinear Response

    Institute of Scientific and Technical Information of China (English)

    HUANG Ji-Ping; LI Zhen-Ya


    We consider a binary granular composite medium, in which two materials have high-order nonlinearities.The effect of particle shape on effective nonlinear response (ENR) is investigated by assuming all the particles to be shaped as uniaxial ellipsoid. We discuss two types of arrangements of particles: 1) parallel axes (Case I); 2) random axes (Case II). During the process of numerical calculation, one component material is assumed to be linear, and two kinds of conductors are assumed to be at high conducting contrast. We find that: 1) the shape effect on ENR is possibly strong; 2) the enhanced ENR can even be obtained by choosing particles of appropriate ellipsoidal shapes; 3) the ENR enhancement predicted by Case I is much stronger than that by Case II.``

  8. Strong nonlinear photonic responses from microbiologically synthesized tellurium nanocomposites (United States)

    Liao, K.-S.; Wang, Jingyuan; Dias, S.; Dewald, J.; Alley, N.J.; Baesman, S.M.; Oremland, R.S.; Blau, W.J.; Curran, S.A.


    A new class of nanomaterials, namely microbiologically-formed nanorods composed of elemental tellurium [Te(0)] that forms unusual nanocomposites when combined with poly(m-phenylenevinylene-co-2,5-dioctoxy-phenylenevinylene) (PmPV) is described. These bio-nanocomposites exhibit excellent broadband optical limiting at 532 and 1064 nm. Nonlinear scattering, originating from the laser induced solvent bubbles and microplasmas, is responsible for this nonlinear behavior. The use of bacterially-formed Te(0) when combined with an organic chemical host (e.g., PmPV) is a new green method of nanoparticle syntheses. This opens the possibilities of using unique, biologically synthesized materials to advance future nanoelectronic and nanophotonic applications. ?? 2009 Elsevier B.V. All rights reserved.

  9. The Effect of Nonlinearities on Flexible Structures. (United States)


    No. 87- 0777-CP, 1987. 4. Nayfeh, A. H. and Sanchez, N. E., ’Global Bifurcations Including Escape for a Softening Duffing Oscillator ", submitted for...biock number FIELD GROUP SUB. GR. _ ?onlinear Oscillations , Flexible structures, Resonances, Attractors, Bifurcations 19. 4 TACT jnt nue on r,.erse it...Excitation of Two Internally Resonant Oscillators ", Journal of Sound and Vibration, Vol. 119, No. 2, 1987. 3 4 2. Zavodney, L D. and Nayfeh, A. H., NThe

  10. Nonlinear feature identification of impedance-based structural health monitoring

    Energy Technology Data Exchange (ETDEWEB)

    Rutherford, A. C. (Amanda C.); Park, G. H. (Gyu Hae); Sohn, H. (Hoon); Farrar, C. R. (Charles R.)


    The impedance-based structural health monitoring technique, which utilizes electromechanical coupling properties of piezoelectric materials, has shown feasibility for use in a variety of structural health monitoring applications. Relying on high frequency local excitations (typically > 30 kHz), this technique is very sensitive to minor changes in structural integrity in the near field of piezoelectric sensors. Several damage sensitive features have been identified and used coupled with the impedance methods. Most of these methods are, however, limited to linearity assumptions of a structure. This paper presents the use of experimentally identified nonlinear features, combined with impedance methods, for structural health monitoring. Their applicability to damage detection in various frequency ranges is demonstrated using actual impedance signals measured from a portal frame structure. The performance of the nonlinear feature is compared with those of conventional impedance methods. This paper reinforces the utility of nonlinear features in structural health monitoring and suggests that their varying sensitivity in different frequency ranges may be leveraged for certain applications.

  11. Nonlinear Finite Element Analysis of a Composite Non-Cylindrical Pressurized Aircraft Fuselage Structure (United States)

    Przekop, Adam; Wu, Hsi-Yung T.; Shaw, Peter


    The Environmentally Responsible Aviation Project aims to develop aircraft technologies enabling significant fuel burn and community noise reductions. Small incremental changes to the conventional metallic alloy-based 'tube and wing' configuration are not sufficient to achieve the desired metrics. One of the airframe concepts that might dramatically improve aircraft performance is a composite-based hybrid wing body configuration. Such a concept, however, presents inherent challenges stemming from, among other factors, the necessity to transfer wing loads through the entire center fuselage section which accommodates a pressurized cabin confined by flat or nearly flat panels. This paper discusses a nonlinear finite element analysis of a large-scale test article being developed to demonstrate that the Pultruded Rod Stitched Efficient Unitized Structure concept can meet these challenging demands of the next generation airframes. There are specific reasons why geometrically nonlinear analysis may be warranted for the hybrid wing body flat panel structure. In general, for sufficiently high internal pressure and/or mechanical loading, energy related to the in-plane strain may become significant relative to the bending strain energy, particularly in thin-walled areas such as the minimum gage skin extensively used in the structure under analysis. To account for this effect, a geometrically nonlinear strain-displacement relationship is needed to properly couple large out-of-plane and in-plane deformations. Depending on the loading, this nonlinear coupling mechanism manifests itself in a distinct manner in compression- and tension-dominated sections of the structure. Under significant compression, nonlinear analysis is needed to accurately predict loss of stability and postbuckled deformation. Under significant tension, the nonlinear effects account for suppression of the out-of-plane deformation due to in-plane stretching. By comparing the present results with the previously

  12. Practical Soil-Shallow Foundation Model for Nonlinear Structural Analysis

    Directory of Open Access Journals (Sweden)

    Moussa Leblouba


    Full Text Available Soil-shallow foundation interaction models that are incorporated into most structural analysis programs generally lack accuracy and efficiency or neglect some aspects of foundation behavior. For instance, soil-shallow foundation systems have been observed to show both small and large loops under increasing amplitude load reversals. This paper presents a practical macroelement model for soil-shallow foundation system and its stability under simultaneous horizontal and vertical loads. The model comprises three spring elements: nonlinear horizontal, nonlinear rotational, and linear vertical springs. The proposed macroelement model was verified using experimental test results from large-scale model foundations subjected to small and large cyclic loading cases.

  13. Models of the delayed nonlinear Raman response in diatomic gases (United States)

    Palastro, J. P.; Antonsen, T. M., Jr.; Pearson, A.


    We examine the delayed response of a diatomic gas to a polarizing laser field with the goal of obtaining computationally efficient methods for use with laser pulse propagation simulations. We demonstrate that for broadband pulses, heavy molecules such as O2 and N2, and typical atmospheric temperatures, the initial delayed response requires only classical physics. The linear kinetic Green's function is derived from the Boltzmann equation and shown to be in excellent agreement with full density-matrix calculations. A straightforward perturbation approach for the fully nonlinear, kinetic impulse response is also presented. With the kinetic theory a reduced fluid model of the diatomic gas’ orientation is derived. Transport coefficients are introduced to model the kinetic phase mixing of the delayed response. In addition to computational rapidity, the fluid model provides intuition through the use of familiar macroscopic quantities. Both the kinetic and the fluid descriptions predict a nonlinear steady-state alignment after passage of the laser pulse, which in the fluid model is interpreted as an anisotropic temperature of the diatomic fluid with respect to motion about the polarization axis.

  14. Beyond the effective mass approximation: predictive theory of the nonlinear optical response of conduction electrons

    CERN Document Server

    Yu, Shukai; Talbayev, Diyar


    We present an experimental and computational study of the nonlinear optical response of conduction electrons to intense terahertz (THz) electric field. Our observations (saturable absorption and an amplitude-dependent group refractive index) can be understood on the qualitative level as the breakdown of the effective mass approximation. However, a predictive theoretical description of the nonlinearity has been missing. We propose a model based on the semiclassical electron dynamics, a realistic band structure, and the free electron Drude parameters to accurately calculate the experimental observables in InSb. Our results open a path to predictive modeling of the conduction-electron optical nonlinearity in semiconductors, metamaterials, as well as high-field effects in THz plasmonics.

  15. A Nonlinear Theory for Smart Composite Structures (United States)

    Chattopadhyay, Aditi


    The paper discusses the following: (1) Development of a completely coupled thermo-piezoelectric-mechanical theory for the analysis of composite shells with segmented and distributed piezoelectric sensor/actuators and shape memory alloys. The higher order displacement theory will be used to capture the transverse shear effects in anisotropic composites. The original theory will be modified to satisfy the stress continuity at ply interfaces. (2) Development of a finite element technique to implement the mathematical model. (3) Investigation of the coupled structures/controls interaction problem to study the complex trade-offs associated with the coupled problem.

  16. Do horizontal propulsive forces influence the nonlinear structure of locomotion?

    Directory of Open Access Journals (Sweden)

    Stergiou Nicholas


    Full Text Available Abstract Background Several investigations have suggested that changes in the nonlinear gait dynamics are related to the neural control of locomotion. However, no investigations have provided insight on how neural control of the locomotive pattern may be directly reflected in changes in the nonlinear gait dynamics. Our simulations with a passive dynamic walking model predicted that toe-off impulses that assist the forward motion of the center of mass influence the nonlinear gait dynamics. Here we tested this prediction in humans as they walked on the treadmill while the forward progression of the center of mass was assisted by a custom built mechanical horizontal actuator. Methods Nineteen participants walked for two minutes on a motorized treadmill as a horizontal actuator assisted the forward translation of the center of mass during the stance phase. All subjects walked at a self-select speed that had a medium-high velocity. The actuator provided assistive forces equal to 0, 3, 6 and 9 percent of the participant's body weight. The largest Lyapunov exponent, which measures the nonlinear structure, was calculated for the hip, knee and ankle joint time series. A repeated measures one-way analysis of variance with a t-test post hoc was used to determine significant differences in the nonlinear gait dynamics. Results The magnitude of the largest Lyapunov exponent systematically increased as the percent assistance provided by the mechanical actuator was increased. Conclusion These results support our model's prediction that control of the forward progression of the center of mass influences the nonlinear gait dynamics. The inability to control the forward progression of the center of mass during the stance phase may be the reason the nonlinear gait dynamics are altered in pathological populations. However, these conclusions need to be further explored at a range of walking speeds.

  17. Dynamic structural correlation via nonlinear programming techniques (United States)

    Ting, T.; Ojalvo, I. U.


    A solution to the correlation between structural dynamic test results and finite element analyses of the same components is presented in this paper. Basically, the method can be categorized as a Levenberg-Marquardt type Gauss-Newton method which requires only the differences between FE modal analyses and test results and their first derivatives with respect to preassigned design variables. With proper variable normalization and equation scaling, the method has been made numerically better-conditioned and the inclusion of the Levenberg-Marquardt technique overcomes any remaining difficulty encountered in inverting singular or near-singular matrices. An important feature is that each iteration requires only one function evaluation along with the associated design sensitivity analysis and so the procedure is computationally efficient.

  18. Nonlinear Time Domain Seismic Soil-Structure Interaction (SSI) Deep Soil Site Methodology Development

    Energy Technology Data Exchange (ETDEWEB)

    Spears, Robert Edward [Idaho National Lab. (INL), Idaho Falls, ID (United States); Coleman, Justin Leigh [Idaho National Lab. (INL), Idaho Falls, ID (United States)


    Currently the Department of Energy (DOE) and the nuclear industry perform seismic soil-structure interaction (SSI) analysis using equivalent linear numerical analysis tools. For lower levels of ground motion, these tools should produce reasonable in-structure response values for evaluation of existing and new facilities. For larger levels of ground motion these tools likely overestimate the in-structure response (and therefore structural demand) since they do not consider geometric nonlinearities (such as gaping and sliding between the soil and structure) and are limited in the ability to model nonlinear soil behavior. The current equivalent linear SSI (SASSI) analysis approach either joins the soil and structure together in both tension and compression or releases the soil from the structure for both tension and compression. It also makes linear approximations for material nonlinearities and generalizes energy absorption with viscous damping. This produces the potential for inaccurately establishing where the structural concerns exist and/or inaccurately establishing the amplitude of the in-structure responses. Seismic hazard curves at nuclear facilities have continued to increase over the years as more information has been developed on seismic sources (i.e. faults), additional information gathered on seismic events, and additional research performed to determine local site effects. Seismic hazard curves are used to develop design basis earthquakes (DBE) that are used to evaluate nuclear facility response. As the seismic hazard curves increase, the input ground motions (DBE’s) used to numerically evaluation nuclear facility response increase causing larger in-structure response. As ground motions increase so does the importance of including nonlinear effects in numerical SSI models. To include material nonlinearity in the soil and geometric nonlinearity using contact (gaping and sliding) it is necessary to develop a nonlinear time domain methodology. This

  19. Identification of nonlinear vibrating structures by polynomial expansion in the z-domain (United States)

    Fasana, Alessandro; Garibaldi, Luigi; Marchesiello, Stefano


    A new method in the frequency domain for the identification of nonlinear vibrating structures is described, by adopting the perspective of nonlinearities as internal feedback forces. The technique is based on a polynomial expansion representation of the frequency response function of the underlying linear system, relying on a z-domain formulation. A least squares approach is adopted to take into account the information of all the frequency response functions but, when large data sets are used, the solution of the resulting system of algebraic linear equations can be a difficult task. A procedure to drastically reduce the matrix dimensions and consequently the computational cost - which largely depends on the number of spectral lines - is adopted, leading to a compact and well conditioned problem. The robustness and numerical performances of the method are demonstrated by its implementation on simulated data from single and two degree of freedom systems with typical nonlinear characteristics.

  20. Transient response of an active nonlinear sandwich piezolaminated plate (United States)

    Oveisi, Atta; Nestorović, Tamara


    In this paper, the dynamic modelling and active vibration control of a piezolaminated plate with geometrical nonlinearities are investigated using a semi-analytical approach. For active vibration control purposes, the core orthotropic elastic layer is assumed to be perfectly bonded with two piezo-layers on its top and bottom surfaces which act as sensor and actuator, respectively. In the modelling procedure, the piezo-layers are assumed to be connected via a proportional derivative (PD) feedback control law. Hamilton's principle is employed to acquire the strong form of the dynamic equation in terms of additional higher order strain expressions by means of von Karman strain-displacement correlation. The obtained nonlinear partial differential equation (NPDE) is converted to a system of nonlinear ordinary differential equations (NODEs) by engaging Galerkin method and using the orthogonality of shape functions for the simply supported boundary conditions. Then, the resulting system of NODEs is solved numerically by employing the built-in Mathematica function, "NDSolve". Next, the vibration attenuation performance is evaluated and sensitivity of the closed-loop system is investigated for several control parameters and the external disturbance parameters. The proposed solution in open loop configuration is validated by finite element (FE) package ABAQUS both in the spatial domain and for the time-/frequency-dependent response.

  1. Nonlinear electromechanical response of the ferroelectret ultrasonic transducers (United States)

    Döring, Joachim; Bovtun, Viktor; Bartusch, Jürgen; Erhard, Anton; Kreutzbruck, Marc; Yakymenko, Yuriy


    The ultrasonic transmission between two air-coupled polypropylene (PP) ferroelectret (FE) transducers in dependence on the amplitude of the high-voltage exciting pulse revealed a strongly nonlinear electromechanical response of the FE transmitter. This phenomenon is described by a linear increase of the inverse electromechanical transducer constant t_{33}^{(1)} of the PP FE film with an increase of the exciting electrical pulse amplitude. Enlargement of t_{33}^{(1)} by a factor of 4 was achieved by application of 3500 V exciting pulses. The electrostriction contribution to t_{33}^{(1)} can be attributed to the electrostatic force between electrodes and the Maxwell stress effect. The nonlinear electromechanical properties of the PP FE result in a strong increase of its air-coupled ultrasonic (ACUS) figure of merit ( FOM) under the high-voltage excitation, which exceeds results of the PP FE technological optimization. The FOM increase can be related to the increase of PP FE coupling factor and/or to the decrease of its acoustic impedance. A significant enhancement of the ACUS system transmission (12 dB) and signal-to-noise ratio (32 dB) was demonstrated by the increase of excitation voltage up to 3500 V. The nonlinear electromechanical properties of the PP FEs seem to be very important for their future applications.

  2. All-optical switching in subwavelength metallic grating structure containing nonlinear optical materials. (United States)

    Min, Changjun; Wang, Pei; Chen, Chunchong; Deng, Yan; Lu, Yonghua; Ming, Hai; Ning, Tingyin; Zhou, Yueliang; Yang, Guozhen


    All-optical switching based on a subwavelength metallic grating structure containing nonlinear optical materials has been proposed and numerically investigated. Metal-dielectric composite material is used in the switching for its larger third-order nonlinear susceptibility (approximately 10(-7)esu) and ultrafast response properties. The calculated dependence of the signal light intensity on the pump light intensity shows a bistable behavior, which results in a significant switch effect. It rests on a surface plasmon's enhanced intensity-dependent change of the effective dielectric constant of Kerr nonlinear media, corresponding to a transition of the far-field transmission from a low- to high-transmission state. The study of this switching structure shows great advantages of smaller size, lower requirement of pump light intensity, and shorter switching time at approximately the picosecond level.

  3. Nonlinear ultrasonic stimulated thermography for damage assessment in isotropic fatigued structures (United States)

    Fierro, Gian Piero Malfense; Calla', Danielle; Ginzburg, Dmitri; Ciampa, Francesco; Meo, Michele


    Traditional non-destructive evaluation (NDE) and structural health monitoring (SHM) systems are used to analyse that a structure is free of any harmful damage. However, these techniques still lack sensitivity to detect the presence of material micro-flaws in the form of fatigue damage and often require time-consuming procedures and expensive equipment. This research work presents a novel "nonlinear ultrasonic stimulated thermography" (NUST) method able to overcome some of the limitations of traditional linear ultrasonic/thermography NDE-SHM systems and to provide a reliable, rapid and cost effective estimation of fatigue damage in isotropic materials. Such a hybrid imaging approach combines the high sensitivity of nonlinear acoustic/ultrasonic techniques to detect micro-damage, with local defect frequency selection and infrared imaging. When exciting structures with an optimised frequency, nonlinear elastic waves are observed and higher frictional work at the fatigue damaged area is generated due to clapping and rubbing of the crack faces. This results in heat at cracked location that can be measured using an infrared camera. A Laser Vibrometer (LV) was used to evaluate the extent that individual frequency components contribute to the heating of the damage region by quantifying the out-of-plane velocity associated with the fundamental and second order harmonic responses. It was experimentally demonstrated the relationship between a nonlinear ultrasound parameter (βratio) of the material nonlinear response to the actual temperature rises near the crack. These results demonstrated that heat generation at damaged regions could be amplified by exciting at frequencies that provide nonlinear responses, thus improving the imaging of material damage and the reliability of NUST in a quick and reproducible manner.

  4. Linear and nonlinear optical response of spherical anisotropic semiconductor microcrystallites (United States)

    Ramaniah, Lavanya M.; Nair, Selvakumar V.; Rustagi, Kailash C.


    We present a phenomenological theory of the linear and nonlinear optical properties associated with the Fröhlich resonances of an optically anisotropic, spherical semiconductor crystallite. Using the Maxwell-Garnett approach, we calculate the effective dielectric function of a composite medium containing such crystallites. To study the effect of anisotropy, we take CdS and CdSe quantum dots as examples for the inclusions, and use a two-resonance model for the dielectric function. Even for randomly oriented inclusions, the Fröhlich resonances split as a result of anisotropic local-field corrections. At higher laser intensities, absorption saturation leads to bistability or tristability in the optical response of individual crystallites, while the response of the composite medium with randomly oriented inclusions shows multistability, with many intermediate branches. The nonlinear response of such a composite medium also exhibits a new kind of orientation-induced broadening of resonances. We also find that tristability is possible in another kind of inhomogeneous material, viz., a composite medium containing two types of isotropic spherical crystallites.

  5. Response of MDOF strongly nonlinear systems to fractional Gaussian noises (United States)

    Deng, Mao-Lin; Zhu, Wei-Qiu


    In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.

  6. Response of MDOF strongly nonlinear systems to fractional Gaussian noises

    Energy Technology Data Exchange (ETDEWEB)

    Deng, Mao-Lin; Zhu, Wei-Qiu, E-mail: [Department of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou 310027 (China)


    In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.

  7. Response of MDOF strongly nonlinear systems to fractional Gaussian noises. (United States)

    Deng, Mao-Lin; Zhu, Wei-Qiu


    In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.

  8. Vibration isolation by exploring bio-inspired structural nonlinearity. (United States)

    Wu, Zhijing; Jing, Xingjian; Bian, Jing; Li, Fengming; Allen, Robert


    Inspired by the limb structures of animals/insects in motion vibration control, a bio-inspired limb-like structure (LLS) is systematically studied for understanding and exploring its advantageous nonlinear function in passive vibration isolation. The bio-inspired system consists of asymmetric articulations (of different rod lengths) with inside vertical and horizontal springs (as animal muscle) of different linear stiffness. Mathematical modeling and analysis of the proposed LLS reveal that, (a) the system has very beneficial nonlinear stiffness which can provide flexible quasi-zero, zero and/or negative stiffness, and these nonlinear stiffness properties are adjustable or designable with structure parameters; (b) the asymmetric rod-length ratio and spring-stiffness ratio present very beneficial factors for tuning system equivalent stiffness; (c) the system loading capacity is also adjustable with the structure parameters which presents another flexible benefit in application. Experiments and comparisons with existing quasi-zero-stiffness isolators validate the advantageous features above, and some discussions are also given about how to select structural parameters for practical applications. The results would provide an innovative bio-inspired solution to passive vibration control in various engineering practice.

  9. Chiral Huygens metasurfaces for nonlinear structuring of linearly polarized light

    CERN Document Server

    Lesina, A Calà; Ramunno, L


    We report on a chiral nanostructure, which we term a "butterfly nanoantenna," that, when used in a metasurface, allows the direct conversion of a linearly polarized beam into a nonlinear optical far-field of arbitrary complexity. The butterfly nanoantenna exhibits field enhancement in its gap for every incident linear polarization, which can be exploited to drive nonlinear optical emitters within the gap, for the structuring of light within a frequency range not accessible by linear plasmonics. As the polarization, phase and amplitude of the field in the gap are highly controlled, nonlinear emitters within the gap behave as an idealized Huygens source. A general framework is thereby proposed wherein the butterfly nanoantennas can be arranged on a surface to produce a highly structured far-field nonlinear optical beam with high purity. A third harmonic Laguerre-Gauss beam carrying an optical orbital angular momentum of 41 is demonstrated as an example, through large-scale simulations on a high-performance comp...

  10. POD/MAC-Based Modal Basis Selection for a Reduced Order Nonlinear Response Analysis (United States)

    Rizzi, Stephen A.; Przekop, Adam


    A feasibility study was conducted to explore the applicability of a POD/MAC basis selection technique to a nonlinear structural response analysis. For the case studied the application of the POD/MAC technique resulted in a substantial improvement of the reduced order simulation when compared to a classic approach utilizing only low frequency modes present in the excitation bandwidth. Further studies are aimed to expand application of the presented technique to more complex structures including non-planar and two-dimensional configurations. For non-planar structures the separation of different displacement components may not be necessary or desirable.

  11. Constrained hierarchical least square nonlinear equation solvers. [for indefinite stiffness and large structural deformations (United States)

    Padovan, J.; Lackney, J.


    The current paper develops a constrained hierarchical least square nonlinear equation solver. The procedure can handle the response behavior of systems which possess indefinite tangent stiffness characteristics. Due to the generality of the scheme, this can be achieved at various hierarchical application levels. For instance, in the case of finite element simulations, various combinations of either degree of freedom, nodal, elemental, substructural, and global level iterations are possible. Overall, this enables a solution methodology which is highly stable and storage efficient. To demonstrate the capability of the constrained hierarchical least square methodology, benchmarking examples are presented which treat structure exhibiting highly nonlinear pre- and postbuckling behavior wherein several indefinite stiffness transitions occur.

  12. Confidence bounds for nonlinear dose-response relationships. (United States)

    Baayen, C; Hougaard, P


    An important aim of drug trials is to characterize the dose-response relationship of a new compound. Such a relationship can often be described by a parametric (nonlinear) function that is monotone in dose. If such a model is fitted, it is useful to know the uncertainty of the fitted curve. It is well known that Wald confidence intervals are based on linear approximations and are often unsatisfactory in nonlinear models. Apart from incorrect coverage rates, they can be unreasonable in the sense that the lower confidence limit of the difference to placebo can be negative, even when an overall test shows a significant positive effect. Bootstrap confidence intervals solve many of the problems of the Wald confidence intervals but are computationally intensive and prone to undercoverage for small sample sizes. In this work, we propose a profile likelihood approach to compute confidence intervals for the dose-response curve. These confidence bounds have better coverage than Wald intervals and are more precise and generally faster than bootstrap methods. Moreover, if monotonicity is assumed, the profile likelihood approach takes this automatically into account. The approach is illustrated using a public dataset and simulations based on the Emax and sigmoid Emax models. Copyright © 2015 John Wiley & Sons, Ltd.

  13. Stochastic response of nonlinear system in probability domain

    Indian Academy of Sciences (India)

    Deepak Kumar; T K Datta


    A stochastic averaging procedure for obtaining the probability density function (PDF) of the response for a strongly nonlinear single-degree-of-freedom system, subjected to both multiplicative and additive random excitations is presented. The procedure uses random Van Der Pol transformation, Ito’s equation of limiting diffusion process and stochastic averaging technique as outlined by Zhu and others. However, the equations are rederived in generalized form and arranged in such a way that the procedure lends itself to a numerical computational scheme using FFT. The main objective of the modification is to consider highly irregular nonlinear functions which cannot be integrated in closed form and also to solve problems where analytical expressions for probability density function cannot be obtained. The procedure is applied to obtain the PDF of the response of Duffing oscillator subjected to additive and multiplicative random excitations represented by rational power spectral density functions (PSDFs). The results are verified by digital simulation. It is shown that the procedure provides results which compare very well with those obtained from simulation analysis not only for wide-band excitations but also for very narrow-band excitations, which are weak (when normalized with respect to mass of the system).

  14. Structure-based control of complex networks with nonlinear dynamics

    CERN Document Server

    Zañudo, Jorge G T; Albert, Réka


    Given the network of interactions underlying a complex system, what can we learn about controlling such a system solely from its structure? Over a century of research in control theory has given us tools to answer this question, which were widely applied in science and engineering. Yet the current tools do not always consider the inherently nonlinear dynamics of real systems and the naturally occurring system states in their definition of "control", a term whose interpretation varies across disciplines. Here we use a new mathematical framework for structure-based control of networks governed by a broad class of nonlinear dynamics that includes the major dynamic models of biological, technological, and social processes. This framework provides realizable node overrides that steer a system towards any of its natural long term dynamic behaviors and which are guaranteed to be effective regardless of the dynamic details and parameters of the underlying system. We use this framework on several real networks, compar...

  15. Nonlinear Thermo-mechanical Finite Element Analysis of Polymer Foam Cored Sandwich Structures including Geometrical and Material Nonlinearity

    DEFF Research Database (Denmark)

    Palleti, Hara Naga Krishna Teja; Thomsen, Ole Thybo; Taher, Siavash Talebi;

    In this paper, polymer foam cored sandwich structures with fibre reinforced composite face sheets subjected to combined mechanical and thermal loads will be analysed using the commercial FE code ABAQUS® incorporating both material and geometrical nonlinearity. Large displacements and rotations ar...... are included in the analysis. The full nonlinear stress-strain curves up to failure will be considered for the polymer foams at different temperatures to study the effect of material nonlinearity in detail....

  16. Global stabilization of nonlinear systems with uncertain structure

    Institute of Scientific and Technical Information of China (English)


    The global stabilization problem of nonlinear systems with uncertain structure is dealt with. Based on control Lyapunov function (CLF), a sufficient and necessary condition for Lyapunov stabilization is given. From the condition,several simply sufficient conditions for the globally asymptotical stability are deduced. A state feedback control law is designed to globally asymptotically stabilize the equilibrium of the closed system. Last, a simulation shows the effectiveness of the method.

  17. Weakly nonlinear analysis and localised structures in nonlinear cavities with metamaterials (United States)

    Slimani, N.; Makhoute, A.; Tlidi, M.


    We consider an optical ring cavity filled with a metamaterial and with a Kerr medium. The cavity is driven by a coherent radiation beam. The modelling of this device leads to the well known Lugiato-Lefever equation with high order diffraction term. We assume that both left-handed and right-handed materials possess a Kerr focusing type of nonlinearity. We show that close to the zero-diffraction regime, high-order diffraction effect allows us to stabilise dark localised structures in this device. These structures consist of dips or holes in the transverse profile of the intracavity field and do not exist without high-order diffraction effects. We show that high order diffraction effects alter in depth the space-time dynamics of this device. A weakly nonlinear analysis in the vicinity of the first threshold associated with the Turing instability is performed. This analysis allows us to determine the parameter regime where the transition from super- to sub-critical bifurcation occurs. When the modulational instability appears subcritically, we show that bright localised structures of light may be generated in two-dimensional setting. Close to the second threshold associated with the Turing instability, dark localised structures are generated.

  18. Evaluation of model fit in nonlinear multilevel structural equation modeling

    Directory of Open Access Journals (Sweden)

    Karin eSchermelleh-Engel


    Full Text Available Evaluating model fit in nonlinear multilevel structural equation models (MSEM presents a challenge as no adequate test statistic is available. Nevertheless, using a product indicator approach a likelihood ratio test for linear models is provided which may also be useful for nonlinear MSEM. The main problem with nonlinear models is that product variables are nonnormally distributed. Although robust test statistics have been developed for linear SEM to ensure valid results under the condition of nonnormality, they were not yet investigated for nonlinear MSEM. In a Monte Carlo study, the performance of the robust likelihood ratio test was investigated for models with single-level latent interaction effects using the unconstrained product indicator approach. As overall model fit evaluation has a potential limitation in detecting the lack of fit at a single level even for linear models, level-specific model fit evaluation was also investigated using partially saturated models. Four population models were considered: a model with interaction effects at both levels, an interaction effect at the within-group level, an interaction effect at the between-group level, and a model with no interaction effects at both levels. For these models the number of groups, predictor correlation, and model misspecification was varied. The results indicate that the robust test statistic performed sufficiently well. Advantages of level-specific model fit evaluation for the detection of model misfit are demonstrated.

  19. Evaluation of model fit in nonlinear multilevel structural equation modeling. (United States)

    Schermelleh-Engel, Karin; Kerwer, Martin; Klein, Andreas G


    Evaluating model fit in nonlinear multilevel structural equation models (MSEM) presents a challenge as no adequate test statistic is available. Nevertheless, using a product indicator approach a likelihood ratio test for linear models is provided which may also be useful for nonlinear MSEM. The main problem with nonlinear models is that product variables are non-normally distributed. Although robust test statistics have been developed for linear SEM to ensure valid results under the condition of non-normality, they have not yet been investigated for nonlinear MSEM. In a Monte Carlo study, the performance of the robust likelihood ratio test was investigated for models with single-level latent interaction effects using the unconstrained product indicator approach. As overall model fit evaluation has a potential limitation in detecting the lack of fit at a single level even for linear models, level-specific model fit evaluation was also investigated using partially saturated models. Four population models were considered: a model with interaction effects at both levels, an interaction effect at the within-group level, an interaction effect at the between-group level, and a model with no interaction effects at both levels. For these models the number of groups, predictor correlation, and model misspecification was varied. The results indicate that the robust test statistic performed sufficiently well. Advantages of level-specific model fit evaluation for the detection of model misfit are demonstrated.

  20. Nonlinear optical response of the collagen triple helix and second harmonic microscopy of collagen liquid crystals (United States)

    Deniset-Besseau, A.; De Sa Peixoto, P.; Duboisset, J.; Loison, C.; Hache, F.; Benichou, E.; Brevet, P.-F.; Mosser, G.; Schanne-Klein, M.-C.


    Collagen is characterized by triple helical domains and plays a central role in the formation of fibrillar and microfibrillar networks, basement membranes, as well as other structures of the connective tissue. Remarkably, fibrillar collagen exhibits efficient Second Harmonic Generation (SHG) and SHG microscopy proved to be a sensitive tool to score fibrotic pathologies. However, the nonlinear optical response of fibrillar collagen is not fully characterized yet and quantitative data are required to further process SHG images. We therefore performed Hyper-Rayleigh Scattering (HRS) experiments and measured a second order hyperpolarisability of 1.25 10-27 esu for rat-tail type I collagen. This value is surprisingly large considering that collagen presents no strong harmonophore in its amino-acid sequence. In order to get insight into the physical origin of this nonlinear process, we performed HRS measurements after denaturation of the collagen triple helix and for a collagen-like short model peptide [(Pro-Pro-Gly)10]3. It showed that the collagen large nonlinear response originates in the tight alignment of a large number of weakly efficient harmonophores, presumably the peptide bonds, resulting in a coherent amplification of the nonlinear signal along the triple helix. To illustrate this mechanism, we successfully recorded SHG images in collagen liquid solutions by achieving liquid crystalline ordering of the collagen triple helices.

  1. A perturbation approach for geometrically nonlinear structural analysis using a general purpose finite element code

    NARCIS (Netherlands)

    Rahman, T.


    In this thesis, a finite element based perturbation approach is presented for geometrically nonlinear analysis of thin-walled structures. Geometrically nonlinear static and dynamic analyses are essential for this class of structures. Nowadays nonlinear analysis of thin-walled shell structures is oft

  2. Fluid transport due to nonlinear fluid-structure interaction

    DEFF Research Database (Denmark)

    Jensen, Jakob Søndergaard


    of the pipe. The behavior of the system in response to lateral resonant base excitation is analysed numerically and by the use of a perturbation method (multiple scales). Exciting the pipe in the fundamental mode of vibration seems to be most effective for transferring energy from the shaker to the fluid......, whereas higher modes of vibration can be used to transport fluid with pipe vibrations of smaller amplitude. The effect of the nonlinear geometrical terms is analysed and these terms are shown to affect the response for higher modes of vibration. Experimental investigations show good agreement...

  3. Structural Nonlinear Flutter Characteristics Analysis for an Actuator-fin System with Dynamic Stiffness

    Institute of Scientific and Technical Information of China (English)

    YANG Ning; WU Zhigang; YANG Chao


    The flutter characteristics of an actuator-fin system are investigated with structural nonlinearity and dynamic stiffness of the electric motor.The component mode substitution method is used to establish the nonlinear governing equations in time domain and frequency domain based on the fundamental dynamic equations of the electric motor and decelerator.The existing describing function method and a proposed iterative method are used to obtain the flutter characteristics containing preload freeplay nonlinearity when the control command is zero.A comparison between the results of frequency domain and those of time domain is studied.Simulations are carried out when the control command is not zero and further analysis is conducted when the freeplay angle is changed.The results show that structural nonlinearity and dynamic stiffness have a significant influence on the flutter characteristics.Limit cycle oscillations(LCOs)are observed within linear flutter boundary.The response of the actuator-fin system is related to the initial disturbance.In the nonlinear condition,the amplitude of the control command has an influence on the flutter characteristics.

  4. Residual mode correction in calibrating nonlinear damper for vibration control of flexible structures (United States)

    Sun, Limin; Chen, Lin


    Residual mode correction is found crucial in calibrating linear resonant absorbers for flexible structures. The classic modal representation augmented with stiffness and inertia correction terms accounting for non-resonant modes improves the calibration accuracy and meanwhile avoids complex modal analysis of the full system. This paper explores the augmented modal representation in calibrating control devices with nonlinearity, by studying a taut cable attached with a general viscous damper and its Equivalent Dynamic Systems (EDSs), i.e. the augmented modal representations connected to the same damper. As nonlinearity is concerned, Frequency Response Functions (FRFs) of the EDSs are investigated in detail for parameter calibration, using the harmonic balance method in combination with numerical continuation. The FRFs of the EDSs and corresponding calibration results are then compared with those of the full system documented in the literature for varied structural modes, damper locations and nonlinearity. General agreement is found and in particular the EDS with both stiffness and inertia corrections (quasi-dynamic correction) performs best among available approximate methods. This indicates that the augmented modal representation although derived from linear cases is applicable to a relatively wide range of damper nonlinearity. Calibration of nonlinear devices by this means still requires numerical analysis while the efficiency is largely improved owing to the system order reduction.

  5. Random vibration of linear and nonlinear structural systems with singular matrices: A frequency domain approach (United States)

    Kougioumtzoglou, I. A.; Fragkoulis, V. C.; Pantelous, A. A.; Pirrotta, A.


    A frequency domain methodology is developed for stochastic response determination of multi-degree-of-freedom (MDOF) linear and nonlinear structural systems with singular matrices. This system modeling can arise when a greater than the minimum number of coordinates/DOFs is utilized, and can be advantageous, for instance, in cases of complex multibody systems where the explicit formulation of the equations of motion can be a nontrivial task. In such cases, the introduction of additional/redundant DOFs can facilitate the formulation of the equations of motion in a less labor intensive manner. Specifically, relying on the generalized matrix inverse theory, a Moore-Penrose (M-P) based frequency response function (FRF) is determined for a linear structural system with singular matrices. Next, relying on the M-P FRF a spectral input-output (excitation-response) relationship is derived in the frequency domain for determining the linear system response power spectrum. Further, the above methodology is extended via statistical linearization to account for nonlinear systems. This leads to an iterative determination of the system response mean vector and covariance matrix. Furthermore, to account for singular matrices, the generalization of a widely utilized formula that facilitates the application of statistical linearization is proved as well. The formula relates to the expectation of the derivatives of the system nonlinear function and is based on a Gaussian response assumption. Several linear and nonlinear MDOF structural systems with singular matrices are considered as numerical examples for demonstrating the validity and applicability of the developed frequency domain methodology.

  6. Predicting nonlinear properties of metamaterials from the linear response. (United States)

    O'Brien, Kevin; Suchowski, Haim; Rho, Junsuk; Salandrino, Alessandro; Kante, Boubacar; Yin, Xiaobo; Zhang, Xiang


    The discovery of optical second harmonic generation in 1961 started modern nonlinear optics. Soon after, R. C. Miller found empirically that the nonlinear susceptibility could be predicted from the linear susceptibilities. This important relation, known as Miller's Rule, allows a rapid determination of nonlinear susceptibilities from linear properties. In recent years, metamaterials, artificial materials that exhibit intriguing linear optical properties not found in natural materials, have shown novel nonlinear properties such as phase-mismatch-free nonlinear generation, new quasi-phase matching capabilities and large nonlinear susceptibilities. However, the understanding of nonlinear metamaterials is still in its infancy, with no general conclusion on the relationship between linear and nonlinear properties. The key question is then whether one can determine the nonlinear behaviour of these artificial materials from their exotic linear behaviour. Here, we show that the nonlinear oscillator model does not apply in general to nonlinear metamaterials. We show, instead, that it is possible to predict the relative nonlinear susceptibility of large classes of metamaterials using a more comprehensive nonlinear scattering theory, which allows efficient design of metamaterials with strong nonlinearity for important applications such as coherent Raman sensing, entangled photon generation and frequency conversion.

  7. Nonlinear dynamic response of an electrically actuated imperfect microbeam resonator

    KAUST Repository

    Ruzziconi, Laura


    We present a study of the dynamic behavior of a MEMS device constituted of an imperfect clamped-clamped microbeam subjected to electrostatic and electrodynamic actuation. Our objective is to develop a theoretical analysis, which is able to describe and predict all the main relevant aspects of the experimental response. Extensive experimental investigation is conducted, where the main imperfections coming from microfabrication are detected and the nonlinear dynamics are explored at increasing values of electrodynamic excitation, in a neighborhood of the first symmetric resonance. The nonlinear behavior is highlighted, which includes ranges of multistability, where the non-resonant and the resonant branch coexist, and intervals where superharmonic resonances are clearly visible. Numerical simulations are performed. Initially, two single mode reduced-order models are considered. One is generated via the Galerkin technique, and the other one via the combined use of the Ritz method and the Padé approximation. Both of them are able to provide a satisfactory agreement with the experimental data. This occurs not only at low values of electrodynamic excitation, but also at higher ones. Their computational efficiency is discussed in detail, since this is an essential aspect for systematic local and global simulations. Finally, the theoretical analysis is further improved and a two-degree-of-freedom reduced-order model is developed, which is capable also to capture the measured second symmetric superharmonic resonance. Despite the apparent simplicity, it is shown that all the proposed reduced-order models are able to describe the experimental complex nonlinear dynamics of the device accurately and properly, which validates the proposed theoretical approach. Copyright © 2013 by ASME.

  8. Nonlinear Gust Response Analysis of Free Flexible Aircraft

    Directory of Open Access Journals (Sweden)

    Chen Shilu


    Full Text Available Gust response analysis plays a very important role in large aircraft design. This paper presents a methodology for calculating the flight dynamic characteristics and gust response of free flexible aircraft. A multidisciplinary coupled numerical tool is developed to simulate detailed aircraft models undergoing arbitrary free flight motion in the time domain, by Computational Fluid Dynamics (CFD, Computational Structure Dynamics (CSD and Computational Flight Mechanics (CFM coupling. To achieve this objective, a structured, time-accurate flow-solver is coupled with a computational module solving the flight mechanics equations of motion and a structural mechanics code determining the structural deformations. A novel method to determine the trim state of flexible aircraft is also stated. First, the field velocity approach is validated, after the trim state is attained, gust responses for the one-minus-cosine gust profile are analyzed for the longitudinal motion of a slender-wing aircraft configuration with and without the consideration of structural deformation.

  9. The Behavior of Indonesian Stock Market: Structural Breaks and Nonlinearity

    Directory of Open Access Journals (Sweden)

    Rahmat Heru Setianto


    Full Text Available This study empirically examines the behaviour of Indonesian stock market under the efficient market hypothesis framework by emphasizing on the random walk behaviour and nonlinearity over the period of April 1983 - December 2010. In the first step, the standard linear unit root test, namely the augmented Dickey-Fuller (ADF test, Phillip-Perron (PP test and Kwiatkowski-Philllips-Schmidt-Shin (KPSS test identify the random walk behaviour in the indices. In order to take account the possible breaks in the index series Zivot and Adrews (1992 one break and Lumsdaine and Papell (1997 two breaks unit root test are employed to observe whether the presence of breaks in the data series will prevent the stocks from randomly pricing or vice versa. In the third step, we employ Harvey et al. (2008 test to examine the presence of nonlinear behaviour in Indonesian stock indices. The evidence of nonlinear behaviour in the indices, motivate us to use nonlinear unit root test procedure recently developed by Kapetanios et al. (2003 and Kruse (2010. In general, the results from standard linear unit root test, Zivot and Adrews (ZA test and Lumsdaine and Papell (LP test provide evidence that Jakarta Composite Index characterized by a unit root. In addition, structural breaks identified by ZA and LP test are corresponded to the events of financial market liberalization and financial crisis. The nonlinear unit root test procedure fail to rejects the null hypothesis of unit root for all indices, suggesting that Jakarta Composite Index characterized by random walk process supporting the theory of efficient market hypothesis.

  10. Structure/property relationships in non-linear optical materials

    Energy Technology Data Exchange (ETDEWEB)

    Cole, J.M. [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France)]|[Durham Univ. (United Kingdom); Howard, J.A.K. [Durham Univ. (United Kingdom); McIntyre, G.J. [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France)


    The application of neutrons to the study of structure/property relationships in organic non-linear optical materials (NLOs) is described. In particular, charge-transfer effects and intermolecular interactions are investigated. Charge-transfer effects are studied by charge-density analysis and an example of one such investigation is given. The study of intermolecular interactions concentrates on the effects of hydrogen-bonding and an example is given of two structurally similar molecules with very disparate NLO properties, as a result of different types of hydrogen-bonding. (author). 3 refs.

  11. Nonlinear optical response of some Graphene oxide and Graphene fluoride derivatives (United States)

    Liaros, Nikolaos; Orfanos, Ioannis; Papadakis, Ioannis; Couris, Stelios


    The nonlinear optical properties of two graphene derivatives, graphene oxide and graphene fluoride, are investigated by means of the Z-scan technique employing 35 ps and 4 ns, visible (532 nm) laser excitation. Both derivatives were found to exhibit significant third-order nonlinear optical response at both excitation regimes, with the nonlinear absorption being relatively stronger and concealing the presence of nonlinear refraction under ns excitation, while ps excitation reveals the presence of both nonlinear absorption and refraction. Both nonlinear properties are of great interest for several photonics, opto-fluidics, opto-electronics and nanotechnology applications.

  12. Understanding nonlinear responses of the climate system to orbital forcing (United States)

    Rial, J. A.; Anaclerio, C. A.


    We have recently introduced the working hypothesis that frequency modulation (FM) of the orbital eccentricity forcing may be one important source of the nonlinearities observed in δ 18O time series from deep-sea sediment cores (J.H. Rial (1999a) Pacemaking the lce Ages by frequency modulation of Earth's orbital eccentricity. Science 285, 564-568). In this paper we shall discuss further evidence of frequency modulation found in data from the Vostok ice core. Analyses of the 430,000-year long, orbitally untuned, time series of CO 2, deuterium, aerosol and methane, suggest frequency modulation of the 41 kyr (0.0244 kyr -1) obliquity forcing by the 413 kyr-eccentricity signal and its harmonics. Conventional and higher-order spectral analyses show that two distinct spectral peaks at ˜29 kyr (0.034 kyr -1) and ˜69 kyr (0.014 kyr -1) and other, smaller peaks surrounding the 41 kyr obliquity peak are harmonically (nonlinearly) related and likely to be FM-generated sidebands of the obliquity signal. All peaks can be closely matched by the spectrum of an appropriately built theoretical FM signal. A preliminary model, based on the classic logistic growth delay differential equation, reproduces the longer period FM effect and the familiar multiply peaked spectra of the eccentricity band. Since the FM effect appears to be a common feature in climate response, finding out its cause may help understand climate dynamics and global climate change.

  13. Dielectric Response of Glass-Forming Liquids in the Nonlinear Regime (United States)

    Samanta, Subarna

    Broadband dielectric spectroscopy is a powerful technique for understanding the dynamics in supercooled liquids. It generates information about the timescale of the orientational motions of molecular dipoles within the liquid. However, dynamics of liquids measured in the non-linear response regime has recently become an area of significant interest, because additional information can be obtained compared with linear response measurements. The first part of this thesis describes nonlinear dielectric relaxation experiments performed on various molecular glass forming-liquids, with an emphasis on the response at high frequencies (excess wing). A significant nonlinear dielectric effect (NDE) was found to persist in these modes, and the magnitude of this NDE traces the temperature dependence of the activation energy. A time resolved measurement technique monitoring the dielectric loss revealed that for the steady state NDE to develop it would take a very large number of high amplitude alternating current (ac) field cycles. High frequency modes were found to be 'slaved' to the average structural relaxation time, contrary to the standard picture of heterogeneity. Nonlinear measurements were also performed on the Johari-Goldstein beta-relaxation process. High ac fields were found to modify the amplitudes of these secondary modes. The nonlinear features of this secondary process are reminiscent of those found for the excess wing regime, suggesting that these two contributions to dynamics have common origins. The second part of this thesis describes the nonlinear effects observed from the application of high direct current (dc) bias fields superposed with a small amplitude sinusoidal ac field. For several molecular glass formers, the application of a dc field was found to slow down the system via reduction in configurational entropy (Adam-Gibbs relation). Time resolved measurements indicated that the rise of the non-linear effect is slower than its decay, as observed in the

  14. Nonlinear dynamic behaviors of a floating structure in focused waves (United States)

    Cao, Fei-feng; Zhao, Xi-zeng


    Floating structures are commonly seen in coastal and offshore engineering. They are often subjected to extreme waves and, therefore, their nonlinear dynamic behaviors are of great concern. In this paper, an in-house CFD code is developed to investigate the accurate prediction of nonlinear dynamic behaviors of a two-dimensional (2-D) box-shaped floating structure in focused waves. Computations are performed by an enhanced Constrained Interpolation Profile (CIP)-based Cartesian grid model, in which a more accurate VOF (Volume of Fluid) method, the THINC/SW scheme (THINC: tangent of hyperbola for interface capturing; SW: Slope Weighting), is used for interface capturing. A focusing wave theory is used for the focused wave generation. The wave component of constant steepness is chosen. Comparisons between predictions and physical measurements show good agreement including body motions and free surface profiles. Although the overall agreement is good, some discrepancies are observed for impact pressure on the superstructure due to water on deck. The effect of grid resolution on the results is checked. With a fine grid, no obvious improvement is seen in the global body motions and impact pressures due to water on deck. It is concluded that highly nonlinear phenomena, such as distorted free surface, large-amplitude body motions, and violent impact flow, have been predicted successfully.

  15. Structural Health Monitoring under Nonlinear Environmental or Operational Influences

    Directory of Open Access Journals (Sweden)

    Jyrki Kullaa


    Full Text Available Vibration-based structural health monitoring is based on detecting changes in the dynamic characteristics of the structure. It is well known that environmental or operational variations can also have an influence on the vibration properties. If these effects are not taken into account, they can result in false indications of damage. If the environmental or operational variations cause nonlinear effects, they can be compensated using a Gaussian mixture model (GMM without the measurement of the underlying variables. The number of Gaussian components can also be estimated. For the local linear components, minimum mean square error (MMSE estimation is applied to eliminate the environmental or operational influences. Damage is detected from the residuals after applying principal component analysis (PCA. Control charts are used for novelty detection. The proposed approach is validated using simulated data and the identified lowest natural frequencies of the Z24 Bridge under temperature variation. Nonlinear models are most effective if the data dimensionality is low. On the other hand, linear models often outperform nonlinear models for high-dimensional data.

  16. Optical and Nonlinear Optical Response of Light Sensor Thin Films

    Directory of Open Access Journals (Sweden)

    S. Z. Weisz


    Full Text Available For potential ultrafast optical sensor application, both VO2 thin films andnanocomposite crystal-Si enriched SiO2 thin films grown on fused quartz substrates weresuccessfully prepared using pulsed laser deposition (PLD and RF co-sputteringtechniques. In photoluminescence (PL measurement c-Si/SiO2 film containsnanoparticles of crystal Si exhibits strong red emission with the band maximum rangingfrom 580 to 750 nm. With ultrashort pulsed laser excitation all films show extremelyintense and ultrafast nonlinear optical (NLO response. The recorded holography fromall these thin films in a degenerate-four-wave-mixing configuration shows extremelylarge third-order response. For VO2 thin films, an optically induced semiconductor-tometalphase transition (PT immediately occurred upon laser excitation. it accompanied.It turns out that the fast excited state dynamics was responsible to the induced PT. For c-Si/SiO2 film, its NLO response comes from the contribution of charge carriers created bylaser excitation in conduction band of the c-Si nanoparticles. It was verified byintroducing Eu3+ which is often used as a probe sensing the environment variations. Itturns out that the entire excited state dynamical process associated with the creation,movement and trapping of the charge carriers has a characteristic 500 ps duration.

  17. Structure and asymptotic theory for nonlinear models with GARCH errors

    Directory of Open Access Journals (Sweden)

    Felix Chan


    Full Text Available Nonlinear time series models, especially those with regime-switching and/or conditionally heteroskedastic errors, have become increasingly popular in the economics and finance literature. However, much of the research has concentrated on the empirical applications of various models, with little theoretical or statistical analysis associated with the structure of the processes or the associated asymptotic theory. In this paper, we derive sufficient conditions for strict stationarity and ergodicity of three different specifications of the first-order smooth transition autoregressions with heteroskedastic errors. This is essential, among other reasons, to establish the conditions under which the traditional LM linearity tests based on Taylor expansions are valid. We also provide sufficient conditions for consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator for a general nonlinear conditional mean model with first-order GARCH errors.

  18. Nonlinear Helicons ---an analytical solution elucidating multi-scale structure

    CERN Document Server

    Abdelhamid, Hamdi M


    The helicon waves exhibit varying characters depending on plasma parameters, geometry, and wave numbers. Here we elucidate an intrinsic multi-scale property embodied by the combination of dispersive effect and nonlinearity. The extended magnetohydrodynamics model (exMHD) is capable of describing wide range of parameter space. By using the underlying Hamiltonian structure of exMHD, we construct an exact nonlinear solution which turns out to be a combination of two distinct modes, the helicon and Trivelpiece-Gould (TG) waves. In the regime of relatively low frequency or high density, however, the combination is made of the TG mode and an ion cyclotron wave (slow wave). The energy partition between these modes is determined by the helicities carried by the wave fields.

  19. Nonlinear Stochastic Analysis of Subharmonic Response of a Shallow Cable

    DEFF Research Database (Denmark)

    Zhou, Q.; Stærdahl, Jesper Winther; Nielsen, Søren R.K.


    The paper deals with the subharmonic response of a shallow cable due to time variations of the chord length of the equilibrium suspension, caused by time varying support point motions. Initially, the capability of a simple nonlinear two-degree-of-freedom model for the prediction of chaotic...... time-consuming for the finite difference model, most of the results are next based on the reduced model. Under harmonical varying support point motions the stable subharmonic motion consists of a harmonically varying component in the equilibrium plane and a large subharmonic out-of-plane component......, producing a trajectory at the mid-point of shape as an infinity sign. However, when the harmonical variation of the chordwise elongation is replaced by a narrow-banded Gaussian excitation with the same standard deviation and a centre frequency equal to the circular frequency of the harmonic excitation...

  20. Confidence bounds for nonlinear dose-response relationships

    DEFF Research Database (Denmark)

    Baayen, C; Hougaard, P


    . It is well known that Wald confidence intervals are based on linear approximations and are often unsatisfactory in nonlinear models. Apart from incorrect coverage rates, they can be unreasonable in the sense that the lower confidence limit of the difference to placebo can be negative, even when an overall...... test shows a significant positive effect. Bootstrap confidence intervals solve many of the problems of the Wald confidence intervals but are computationally intensive and prone to undercoverage for small sample sizes. In this work, we propose a profile likelihood approach to compute confidence...... intervals for the dose-response curve. These confidence bounds have better coverage than Wald intervals and are more precise and generally faster than bootstrap methods. Moreover, if monotonicity is assumed, the profile likelihood approach takes this automatically into account. The approach is illustrated...

  1. Crystal growth in fluid flow: Nonlinear response effects (United States)

    Peng, H. L.; Herlach, D. M.; Voigtmann, Th.


    We investigate crystal-growth kinetics in the presence of strong shear flow in the liquid, using molecular-dynamics simulations of a binary-alloy model. Close to the equilibrium melting point, shear flow always suppresses the growth of the crystal-liquid interface. For lower temperatures, we find that the growth velocity of the crystal depends nonmonotonically on the shear rate. Slow enough flow enhances the crystal growth, due to an increased particle mobility in the liquid. Stronger flow causes a growth regime that is nearly temperature-independent, in striking contrast to what one expects from the thermodynamic and equilibrium kinetic properties of the system, which both depend strongly on temperature. We rationalize these effects of flow on crystal growth as resulting from the nonlinear response of the fluid to strong shearing forces.

  2. Volterra methods for constructing structural dynamic observables for nonlinear systems: An extended calculation

    Energy Technology Data Exchange (ETDEWEB)

    Manson, G; Worden, K, E-mail:, E-mail: [Dynamics Research Group, Department of Mechanical Engineering, University of Sheffield, Mappin St, Sheffield S1 3JD (United Kingdom)


    Although a great deal of work has been carried out on structural dynamic systems under random excitation, there has been a comparatively small amount of this work concentrating on the calculation of the quantities commonly measured in structural dynamic tests. Among the existing work, the Volterra series, a means of predicting nonlinear system response for weakly nonlinear systems, has allowed the computation of various measurable quantities of interest for structural dynamics, including: auto- and cross-spectra, FRFs, coherences and higher-order spectra. These calculations are quite intensive and are typically only possible using computer algebra. A previous calculation by the authors for the coherence for a Duffing oscillator yielded results which showed some qualitatitive disagreement with numerical simulation; the object of the current paper is simply to extend the calculation in order to see if better agreement can be achieved.

  3. Analysis on nonlinear wind-induced dynamic response of membrane roofs with aerodynamic effects

    Institute of Scientific and Technical Information of China (English)

    LI Qing-xiang; SUN Bing-nan


    Based on the characteristics of membrane structures and the air influence factors, this paper presen-ted a method to simulate the air aerodynamic force effects including the added air mass, the acoustic radiation damping and the pneumatic stiffness. The infinite air was modeled using the acoustic fluid element of commer-cial FE software and the finite element membrane roof models were coupled with fluid models. A comparison be-tween the results obtained by IrE computation and those obtained by the vibration experiment for a cable-mem-brane verified the validity of the method. Furthermore, applying the method to a flat membrane roof structure and using its wind tunnel test results, the analysis of nonlinear wind-induced dynamic responses for such geo-metrically nonlinear roofs, including the roof-air coupled model was performed. The result shows that the air has large influence on vibrating membrane roofs according to results of comparing the nodal time-history displace-ments, accelerations and stress of the two different cases. Meantime, numerical studies show that the method developed can successfully solve the nonlinear wind-induced dynamic response of the membrane roof with aero-dynamic effects.


    Institute of Scientific and Technical Information of China (English)

    LI Yong; ZHANG Zhi-min


    The graded multiweb structure of heterogeneous anisotropic materials, which makes full use of the continuous, gradual and changing physical mechanical performance of material properties, has a widespread application in aeroplane aerofoil structure and automobile lightweight structure. On the basis of laminate buckling theory,the equivalent rigidity method is adopted to establish the corresponding constitutive relation and the non-linear buckling governing equation for the graded multiweb structure. In finding the solution, the critical load of buckling under different complicated boundary conditions together with combined loads were obtained and testification of the experimental analysis shows that the calculation results can satisfy the requirements of engineering design in a satisfactory way. Results obtained from the research say that: graded materials can reduce the concentrated stress on the interface in an effective way and weaken the effect of initial defect in materials and thereby improve the strength and toughness of materials.

  5. Dimensionality of InGaAs nonlinear optical response

    Energy Technology Data Exchange (ETDEWEB)

    Bolton, S.R. [Univ. of California, Berkeley, CA (United States). Dept. of Physics]|[Lawrence Berkeley National Lab., CA (United States). Materials Sciences Div.


    In this thesis the ultrafast optical properties of a series of InGaAs samples ranging from the two to the three dimensional limit are discussed. An optical system producing 150 fs continuum centered at 1.5 microns was built. Using this system, ultrafast pump-probe and four wave mixing experiments were performed. Carrier thermalization measurements reveal that screening of the Coulomb interaction is relatively unaffected by confinement, while Pauli blocking nonlinearities at the band edge are approximately twice as strong in two dimensions as in three. Carrier cooling via phonon emission is influenced by confinement due both to the change in electron distribution function and the reduction in electron phonon coupling. Purely coherent band edge effects, as measured by the AC Stark effect and four wave mixing, are found to be dominated by the changes in excitonic structure which take place with confinement.

  6. Nonlinear laser pulse response in a crystalline lens. (United States)

    Sharma, R P; Gupta, Pradeep Kumar; Singh, Ram Kishor; Strickland, D


    The propagation characteristics of a spatial Gaussian laser pulse have been studied inside a gradient-index structured crystalline lens with constant-density plasma generated by the laser-tissue interaction. The propagation of the laser pulse is affected by the nonlinearities introduced by the generated plasma inside the crystalline lens. Owing to the movement of plasma species from a higher- to a lower-temperature region, an increase in the refractive index occurs that causes the focusing of the laser pulse. In this study, extended paraxial approximation has been applied to take into account the evolution of the radial profile of the Gaussian laser pulse. To examine the propagation characteristics, variation of the beam width parameter has been observed as a function of the laser power and initial beam radius. The cavitation bubble formation, which plays an important role in the restoration of the elasticity of the crystalline lens, has been investigated.

  7. A method for detection and characterisation of structural non-linearities using the Hilbert transform and neural networks (United States)

    Ondra, V.; Sever, I. A.; Schwingshackl, C. W.


    This paper presents a method for detection and characterisation of structural non-linearities from a single frequency response function using the Hilbert transform in the frequency domain and artificial neural networks. A frequency response function is described based on its Hilbert transform using several common and newly introduced scalar parameters, termed non-linearity indexes, to create training data of the artificial neural network. This network is subsequently used to detect the existence of non-linearity and classify its type. The theoretical background of the method is given and its usage is demonstrated on different numerical test cases created by single degree of freedom non-linear systems and a lumped parameter multi degree of freedom system with a geometric non-linearity. The method is also applied to several experimentally measured frequency response functions obtained from a cantilever beam with a clearance non-linearity and an under-platform damper experimental rig with a complex friction contact interface. It is shown that the method is a fast and noise-robust means of detecting and characterising non-linear behaviour from a single frequency response function.

  8. Large nonlocal nonlinear optical response of castor oil (United States)

    Souza, Rogério F.; Alencar, Márcio A. R. C.; Meneghetti, Mario R.; Hickmann, Jandir M.


    The nonlocal nonlinearity of castor oil was investigated using the Z-scan technique in the CW regime at 514 nm and in femtosecond regime at 810 nm. Large negative nonlinear refractive indexes of thermal origin, thermo-optical coefficients and degree of nonlocality were obtained for both laser excitation wavelengths. The results indicate that the electronic part of the nonlinear refractive index and nonlinear absorption were negligible. Our results suggest that castor oil is promising candidate as a nonlinear medium for several nonlocal optical applications, such as in spatial soliton propagation, as well as a dispersant agent in the measurement of absorptive properties of nanoparticles.

  9. The mildly nonlinear imprint of structure on the CMB

    CERN Document Server

    Gebbie, T


    I outline some nonperturbative relativistic effects that arise from gravitational corrections to the Boltzmann equations. These may be important for the study of CMB temperature anisotropies, particularly their interpretation. These terms are not included in the canonical treatment as they arise from the exact equations. Here a weakly nonlinear investigation of these effects is defined and investigated with an emphasis on a Rees-Sciama sourced effect -- the imprint of structure evolution on the CMB. It is shown that gravitational nonlinearity in the weakly nonlinear extension of almost-FLRW temperature anisotropies leads to cancellation on small-scales when threading in the Newtonian frame. In the general frame this cancellation does not occur. In the context of a flat almost-FLRW CDM model I provide a heuristic argument for a nonperturbative small scale correction, due to the Rees-Sciama effect, of not more than $\\Delta T/T \\sim 10^{-6}-10^{-5}$ near $\\ell \\sim 100 - 300$. The effect of mild gravitational no...

  10. Analytical and numerical studies on the nonlinear dynamic response of orthotropic membranes under impact load (United States)

    Liu, Changjiang; Zheng, Zhoulian; Yang, Xiaoyan


    Orthotropic membrane components and structures are widely used in building structures, instruments and meters, electronic engineering, space and aeronautics, etc., because of their light weights. However, the same lightweight combined with low stiffness make membranes prone to vibration under dynamic loads, and in some cases the vibration may lead to structural failure. Herein, the undamped nonlinear vibration response of pretension rectangular orthotropic membrane structures subjected to impact loading is studied by analytical and numerical methods. The analytical solution is obtained by solving the governing equations by the Bubnov-Galerkin method and the Lindstedt-Poincaré perturbation method. Numerical analysis has also been carried out based on the same theoretical model. The analytical and numerical results have been compared and analyzed, and the influence of various model parameters on membrane vibration discussed. The results obtained herein provide some theoretical basis for the vibration control and dynamic design of orthotropic membrane components and structures.

  11. Nonlinear Allometric Equation for Crop Response to Soil Salinity

    Directory of Open Access Journals (Sweden)

    E. Misle


    Full Text Available Crop response to soil salinity has been extensively studied, from empirical works to modelling approach, being described by different equations, first as a piecewise linear model. The equation employed can differ with actual response, causing miscalculation in practical situations, particularly at the higher extremes of the curve. The aim of this work is to propose a new equation, which allows determining the full response to salinity of plant species and to provide a verification using different experimental data sets. A new nonlinear equation is exposed supported by the allometric approach, in which the allometric exponent is salinity-dependent and decreases with the increase in relative salinity. A conversion procedure of parameters of the threshold-slope model is presented; also, a simple procedure for estimating the maximum salinity (zero-yield point when data sets are incomplete is exposed. The equation was tested in a wide range of experimental situations, using data sets from published works, as well as new measurements on seed germination. The statistical indicators of quality (R2, absolute sum of squares and standard deviation of residuals showed that the equation accurately fits the tested empirical results. The new equation for determining crop response to soil salinity is able to follow the response curve of any crop with remarkable accuracy and flexibility. Remarkable characteristics are: a maximum at minimum salinity, a maximum salinity point can be found (zero-yield depending on the data sets, and a meaningful inflection point, as well as the two points at which the slope of the curve equals unity, can be found.

  12. Nonlinear Aerodynamics-Structure Time Simulation for HALE Aircraft Design/Analysis Project (United States)

    National Aeronautics and Space Administration — Time simulation of a nonlinear aerodynamics model (NA) developed at Virginia Tech coupled with a nonlinear structure model (NS) is proposed as a design/analysis...

  13. Power-transfer effects in monomode optical nonlinear waveguiding structures. (United States)

    Jakubczyk, Z; Jerominek, H; Patela, S; Tremblay, R; Delisle, C


    We describe power-transfer effects, over a certain threshold, among constituents of planar waveguiding structures consisting of an optical linear layer deposited onto a nonlinear substrate (CdS(x)Se(1-x)-doped glass). Proper selection of the thickness of the linear waveguiding film and the refractive index of the linear cladding allows one to obtain optical transistor action and to construct all-optical AND, OR, NOT, and XOR logic gates. The effects appear for the TE(0) guided mode.

  14. Structural Optimization for Reliability Using Nonlinear Goal Programming (United States)

    El-Sayed, Mohamed E.


    This report details the development of a reliability based multi-objective design tool for solving structural optimization problems. Based on two different optimization techniques, namely sequential unconstrained minimization and nonlinear goal programming, the developed design method has the capability to take into account the effects of variability on the proposed design through a user specified reliability design criterion. In its sequential unconstrained minimization mode, the developed design tool uses a composite objective function, in conjunction with weight ordered design objectives, in order to take into account conflicting and multiple design criteria. Multiple design criteria of interest including structural weight, load induced stress and deflection, and mechanical reliability. The nonlinear goal programming mode, on the other hand, provides for a design method that eliminates the difficulty of having to define an objective function and constraints, while at the same time has the capability of handling rank ordered design objectives or goals. For simulation purposes the design of a pressure vessel cover plate was undertaken as a test bed for the newly developed design tool. The formulation of this structural optimization problem into sequential unconstrained minimization and goal programming form is presented. The resulting optimization problem was solved using: (i) the linear extended interior penalty function method algorithm; and (ii) Powell's conjugate directions method. Both single and multi-objective numerical test cases are included demonstrating the design tool's capabilities as it applies to this design problem.

  15. An analytical study on performance of a diagrid structure using nonlinear static pushover analysis

    Directory of Open Access Journals (Sweden)

    Kiran Kamath


    Full Text Available In this study, an attempt has been made to study the performance characteristics of diagrid structures using nonlinear static pushover analysis. The models studied are circular in plan with aspect ratio H/B (where H is total height and B is the base width of structure varying from 2.67 to 4.26. The three different angles of external brace considered are 59°, 71° and 78° (Kim et al., 2010. The width of the base is kept constant at 12 m and height of the structure is varied accordingly. The nonlinear behaviour of the elements is modelled using plastic hinges based on moment–curvature relationship as described in FEMA 356 guidelines. Seismic response of structure in terms of base shear and roof displacement corresponding to performance point were evaluated using nonlinear static analysis and the results are compared. For 71° brace angle model base shear at performance shows an increase in all the aspect ratio considered in the study. The performance of the structure is influenced by brace angle and aspect ratio.

  16. On the nonlinear steady-state response of rigid rotors supported by air foil bearings-Theory and experiments (United States)

    Larsen, Jon S.; Santos, Ilmar F.


    The demand for oil-free turbo compressors is increasing. Current trends are divided between active magnetic bearings and air foil bearings (AFB), the latter being important due to mechanical simplicity. AFB supported rotors are sensitive to unbalance due to low damping and nonlinear characteristics, hence accurate prediction of their response is important. This paper gives theoretical and experimental contributions by implementing and validating a new method to simulate the nonlinear steady-state response of a rotor supported by three pads segmented AFBs. The fluid film pressures, foil deflections and rotor movements are simultaneously solved, considering foil stiffness and damping coefficients estimated using a structural model, previously described and validated against experiments.

  17. Simulations of the Ocean Response to a Hurricane: Nonlinear Processes

    KAUST Repository

    Zedler, Sarah E.


    Superinertial internal waves generated by a tropical cyclone can propagate vertically and laterally away from their local generation site and break, contributing to turbulent vertical mixing in the deep ocean and maintenance of the stratification of the main thermocline. In this paper, the results of a modeling study are reported to investigate the mechanism by which superinertial fluctuations are generated in the deep ocean. The general properties of the superinertial wave wake were also characterized as a function of storm speed and central latitude. The Massachusetts Institute of Technology (MIT) Ocean General Circulation Model (OGCM) was used to simulate the open ocean response to realistic westward-tracking hurricane-type surface wind stress and heat and net freshwater buoyancy forcing for regions representative of midlatitudes in the Atlantic, the Caribbean, and low latitudes in the eastern Pacific. The model had high horizontal [Δ(x, y) = 1/6°] and vertical (Δz = 5 m in top 100 m) resolution and employed a parameterization for vertical mixing induced by shear instability. In the horizontal momentum equation, the relative size of the nonlinear advection terms, which had a dominant frequency near twice the inertial, was large only in the upper 200 m of water. Below 200 m, the linear momentum equations obeyed a linear balance to 2%. Fluctuations at nearly twice the inertial frequency (2f) were prevalent throughout the depth of the water column, indicating that these nonlinear advection terms in the upper 200 m forced a linear mode below at nearly twice the inertial frequency via vorticity conservation. Maximum variance at 2f in horizontal velocity occurred on the south side of the track. This was in response to vertical advection of northward momentum, which in the north momentum equation is an oscillatory positive definite term that constituted a net force to the south at a frequency near 2f. The ratio of this term to the Coriolis force was larger on the

  18. Tailoring the nonlinear response of MEMS resonators using shape optimization

    DEFF Research Database (Denmark)

    Li, Lily L.; Polunin, Pavel M.; Dou, Suguang


    We demonstrate systematic control of mechanical nonlinearities in micro-electromechanical (MEMS) resonators using shape optimization methods. This approach generates beams with non-uniform profiles, which have nonlinearities and frequencies that differ from uniform beams. A set of bridge-type mic......We demonstrate systematic control of mechanical nonlinearities in micro-electromechanical (MEMS) resonators using shape optimization methods. This approach generates beams with non-uniform profiles, which have nonlinearities and frequencies that differ from uniform beams. A set of bridge...

  19. Cooperative enhancement of the nonlinear optical response in conjugated energetic materials: A TD-DFT study. (United States)

    Sifain, Andrew E; Tadesse, Loza F; Bjorgaard, Josiah A; Chavez, David E; Prezhdo, Oleg V; Scharff, R Jason; Tretiak, Sergei


    Conjugated energetic molecules (CEMs) are a class of explosives with high nitrogen content that posses both enhanced safety and energetic performance properties and are ideal for direct optical initiation. As isolated molecules, they absorb within the range of conventional lasers. Crystalline CEMs are used in practice, however, and their properties can differ due to intermolecular interaction. Herein, time-dependent density functional theory was used to investigate one-photon absorption (OPA) and two-photon absorption (TPA) of monomers and dimers obtained from experimentally determined crystal structures of CEMs. OPA scales linearly with the number of chromophore units, while TPA scales nonlinearly, where a more than 3-fold enhancement in peak intensity, per chromophore unit, is calculated. Cooperative enhancement depends on electronic delocalization spanning both chromophore units. An increase in sensitivity to nonlinear laser initiation makes these materials suitable for practical use. This is the first study predicting a cooperative enhancement of the nonlinear optical response in energetic materials composed of relatively small molecules. The proposed model quantum chemistry is validated by comparison to crystal structure geometries and the optical absorption of these materials dissolved in solution.

  20. Thioborates: potential nonlinear optical materials with rich structural chemistry. (United States)

    Lian, Yu-Kun; Wu, Li-Ming; Chen, Ling


    Nonlinear optical (NLO) crystal materials with good performance are urgently needed. Various compounds have been explored to date. Metal chalcogenides and borates are common sources of potential NLO materials with desirable properties, particularly in the IR and UV regions, respectively. However, these two types of crystals have their specific drawbacks. Thioborates, as an emerging system, have unique advantages by combining the merits of borates and sulfides, i.e., the high laser damage thresholds and rich structural diversity of borates with large optical nonlinearity and the favorable transparency range of sulfides. However, only a limited number of thioborates are known. This paper summarizes the known thioborates according to structural motifs that range from zero-dimension to three-dimension, most of which are formed by sharing corners of the basic building units (BS3)(3-) and (BS4)(5-). Although nearly one-third of the known thioborates are noncentrosymmetric, most of their properties, especially their NLO behaviors, are unexplored. Further attempts and additional investigations are required with respect to design syntheses, property improvements and micro-mechanism studies.

  1. Current-mode analog nonlinear function synthesizer structures

    CERN Document Server

    Popa, Cosmin Radu


    This book is dedicated to the analysis and design of analog CMOS nonlinear function synthesizer structures, based on original superior-order approximation functions. A variety of analog function synthesizer structures are discussed, based on accurate approximation functions.  Readers will be enabled to implement numerous circuit functions with applications in analog signal processing, including exponential, Gaussian or hyperbolic functions. Generalizing the methods for obtaining these particular functions, the author analyzes superior-order approximation functions, which represent the core for developing CMOS analog nonlinear function synthesizers.   ·         Describes novel methods for generating a multitude of circuit functions, based on superior-order improved accuracy approximation functions; ·         Presents techniques for analog function synthesizers that can be applied easily to a wide variety of analog signal processing circuits; ·         Enables the design of analog s...

  2. Role of nonlinear localized structures and turbulence in magnetized plasma (United States)

    Pathak, Neha; Yadav, Nitin; Uma, R.; Sharma, R. P.


    In the present study, we have analyzed the field localization of kinetic Alfvén wave (KAW) due to the presence of background density perturbation, which are assumed to be originated by the three dimensionally propagating low frequency KAW. These localized structures play an important role for energy transportation at smaller scales in the dispersion range of magnetic power spectrum. For the present model, governing dynamic equations of high frequency pump KAW and low frequency KAW has been derived by considering ponderomotive nonlinearity. Further, these coupled equations have been numerically solved to analyze the resulting localized structures of pump KAW and magnetic power spectrum in the magnetopause regime. Numerically calculated spectrum exhibits inertial range having spectral index of -3/2 followed by steeper scaling; this steepening in the turbulent spectrum is a signature of energy transportation from larger to smaller scales. In this way, the proposed mechanism, which is based on nonlinear wave-wave interaction, may be useful for understanding the particle acceleration and turbulence in magnetopause.

  3. Studying Climate Response to Forcing by the Nonlinear Dynamical Mode Decomposition (United States)

    Mukhin, Dmitry; Gavrilov, Andrey; Loskutov, Evgeny; Feigin, Alexander


    An analysis of global climate response to external forcing, both anthropogenic (mainly, CO2 and aerosol) and natural (solar and volcanic), is needed for adequate predictions of global climate change. Being complex dynamical system, the climate reacts to external perturbations exciting feedbacks (both positive and negative) making the response non-trivial and poorly predictable. Thus an extraction of internal modes of climate system, investigation of their interaction with external forcings and further modeling and forecast of their dynamics, are all the problems providing the success of climate modeling. In the report the new method for principal mode extraction from climate data is presented. The method is based on the Nonlinear Dynamical Mode (NDM) expansion [1,2], but takes into account a number of external forcings applied to the system. Each NDM is represented by hidden time series governing the observed variability, which, together with external forcing time series, are mapped onto data space. While forcing time series are considered to be known, the hidden unknown signals underlying the internal climate dynamics are extracted from observed data by the suggested method. In particular, it gives us an opportunity to study the evolution of principal system's mode structure in changing external conditions and separate the internal climate variability from trends forced by external perturbations. Furthermore, the modes so obtained can be extrapolated beyond the observational time series, and long-term prognosis of modes' structure including characteristics of interconnections and responses to external perturbations, can be carried out. In this work the method is used for reconstructing and studying the principal modes of climate variability on inter-annual and decadal time scales accounting the external forcings such as anthropogenic emissions, variations of the solar activity and volcanic activity. The structure of the obtained modes as well as their response to

  4. Phase disruption as a new design paradigm for optimizing the nonlinear-optical response

    CERN Document Server

    Lytel, Rick; Kuzyk, Mark G


    The intrinsic optical nonlinearities of quasi-one dimensional structures, including conjugated chain polymers and nanowires, are shown to be dramatically enhanced by the judicious placement of a side group or wire of sufficiently short length to create a large phase disruption in the dominant eigenfunctions along the main path of probability current. Phase disruption is proposed as a new general principle for the design of molecules, nanowires and any quasi-1D quantum system with large intrinsic response and does not require charge donors-acceptors at the ends.

  5. Structural response synthesis

    Energy Technology Data Exchange (ETDEWEB)

    Ozisik, H.; Keltie, R.F.


    The open loop control technique of predicting a conditioned input signal based on a specified output response for a second order system has been analyzed both analytically and numerically to gain a firm understanding of the method. Differences between this method of control and digital closed loop control using pole cancellation were investigated as a follow up to previous experimental work. Application of the technique to diamond turning using a fast tool is also discussed.

  6. Multiscale numerical study on ferroelectric nonlinear response of PZT thin films (Conference Presentation) (United States)

    Wakabayashi, Hiroki; Uetsuji, Yasutomo; Tsuchiya, Kazuyoshi


    PZT thin films have excellent performance in deformation precision and response speed, so it is used widely for actuators and sensors of Micro Electro Mechanical System (MEMS). Although PZT thin films outputs large piezoelectricity at morphotropic phase bounfary (MPB), it shows a complicated hysteresis behavior caused by domain switching and structural phase transition between tetragonal and rhombohedral. In general, PZT thin films have some characteristic crystal morphologies. Additionally mechanical strains occur by lattice mismatch with substrate. Therefore it is important for fabrication and performance improvement of PZT thin films to understand the relation between macroscopic hysteresis response and microstructural changes. In this study, a multiscale nonlinear finite element simulation was proposed for PZT thin films at morphotropic phase boundary (MPB) on the substrate. The homogenization theory was employed for scale-bridging between macrostructure and microstructure. Figure 1 shows the proposed multiscale nonlinear simulation [1-3] based on the homogenization theory. Macrostructure is a homogeneous structure to catch the whole behaviors of actuators and sensors. And microstructure is a periodic inhomogeneous structure consisting of domains and grains. Macrostructure and microstructure are connected perfectly by homogenization theory and are analyzed by finite element method. We utilized an incremental form of fundamental constitutive law in consideration with physical property change caused by domain switching and structural phase transition. The developed multiscale finite element method was applied to PZT thin films with lattice mismatch strain on the substrate, and the relation between the macroscopic hysteresis response and microscopic domain switching and structural phase transition were investigated. Especially, we discuss about the effect of crystal morphologies and lattice mismatch strain on hysteresis response.

  7. Coupled large earthquakes in the Baikal rift system: Response to bifurcations in nonlinear resonance hysteresis

    Directory of Open Access Journals (Sweden)

    Anatoly V. Klyuchevskii


    Full Text Available The current lithospheric geodynamics and tectonophysics in the Baikal rift are discussed in terms of a nonlinear oscillator with dissipation. The nonlinear oscillator model is applicable to the area because stress change shows up as quasi-periodic inharmonic oscillations at rifting attractor structures (RAS. The model is consistent with the space-time patterns of regional seismicity in which coupled large earthquakes, proximal in time but distant in space, may be a response to bifurcations in nonlinear resonance hysteresis in a system of three oscillators corresponding to the rifting attractors. The space-time distribution of coupled MLH > 5.5 events has been stable for the period of instrumental seismicity, with the largest events occurring in pairs, one shortly after another, on two ends of the rift system and with couples of smaller events in the central part of the rift. The event couples appear as peaks of earthquake ‘migration’ rate with an approximately decadal periodicity. Thus the energy accumulated at RAS is released in coupled large events by the mechanism of nonlinear oscillators with dissipation. The new knowledge, with special focus on space-time rifting attractors and bifurcations in a system of nonlinear resonance hysteresis, may be of theoretical and practical value for earthquake prediction issues. Extrapolation of the results into the nearest future indicates the probability of such a bifurcation in the region, i.e., there is growing risk of a pending M ≈ 7 coupled event to happen within a few years.

  8. Nonlinear thermoelectric efficiency of superlattice-structured nanowires (United States)

    Karbaschi, Hossein; Lovén, John; Courteaut, Klara; Wacker, Andreas; Leijnse, Martin


    We theoretically investigate nonlinear ballistic thermoelectric transport in a superlattice-structured nanowire. By a special choice of nonuniform widths of the superlattice barriers—analogous to antireflection coating in optical systems—it is possible to achieve a transmission which comes close to a square profile as a function of energy. We calculate the low-temperature output power and power-conversion efficiency of a thermoelectric generator based on such a structure and show that the efficiency remains high also when operating at a significant power. To provide guidelines for experiments, we study how the results depend on the nanowire radius, the number of barriers, and on random imperfections in barrier width and separation. Our results indicate that high efficiencies can indeed be achieved with today's capabilities in epitaxial nanowire growth.

  9. Order reduction and efficient implementation of nonlinear nonlocal cochlear response models. (United States)

    Filo, Maurice; Karameh, Fadi; Awad, Mariette


    The cochlea is an indispensable preliminary processing stage in auditory perception that employs mechanical frequency-tuning and electrical transduction of incoming sound waves. Cochlear mechanical responses are shown to exhibit active nonlinear spatiotemporal response dynamics (e.g., otoacoustic emission). To model such phenomena, it is often necessary to incorporate cochlear fluid-membrane interactions. This results in both excessively high-order model formulations and computationally intensive solutions that limit their practical use in simulating the model and analyzing its response even for simple single-tone inputs. In order to address these limitations, the current work employs a control-theoretic framework to reformulate a nonlinear two-dimensional cochlear model into discrete state space models that are of considerably lower order (factor of 8) and are computationally much simpler (factor of 25). It is shown that the reformulated models enjoy sparse matrix structures which permit efficient numerical manipulations. Furthermore, the spatially discretized models are linearized and simplified using balanced transformation techniques to result in lower-order (nonlinear) realizations derived from the dominant Hankel singular values of the system dynamics. Accuracy and efficiency of the reduced-order reformulations are demonstrated under the response to two fixed tones, sweeping tones and, more generally, a brief speech signal. The corresponding responses are compared to those produced by the original model in both frequency and spatiotemporal domains. Although carried out on a specific instance of cochlear models, the introduced framework of control-theoretic model reduction could be applied to a wide class of models that address the micro- and macro-mechanical properties of the cochlea.

  10. Nonlinear response of superconductors to alternating fields and currents

    Energy Technology Data Exchange (ETDEWEB)

    McDonald, Jason [Iowa State Univ., Ames, IA (United States)


    This report discusses the following topics on superconductivity: nonlinearities in hard superconductors such as surface impedance of a type II superconductimg half space and harmonic generation and intermodulation due to alternating transport currents; and nonlinearities in superconducting weak links such as harmonic generation by a long Josephson Junction in a superconducting slab.

  11. Synthesis, X-Ray crystal structure, photophysical characterization and nonlinear optical properties of the unique manganese complex with picolinate and 1,10 phenantroline: toward the designing of new high NLO response crystal (United States)

    Tamer, Ömer; Avcı, Davut; Atalay, Yusuf


    The first manganese complex of picolinic acid (also known as 2-pyridinecarboxylic acid) and 1,10 phenantroline has been synthesized, and its structure has been fully characterized by means of X-Ray diffraction method as well as FT-IR, Raman and UV-vis spectroscopies. In order to provide a deep understanding about the relation among the nonlinear optical properties, structural, spectroscopic and electronic behaviors, density functional theory (DFT) calculations have been performed by using hybrid B3LYP level. The intensive interactions between the bonding orbitals of donor O/N atoms and antibonding orbitals of Mn(II) lone pairs confirm the X-Ray diffraction results. Each of the conditions such as small energy gap between HOMO and LUMO, high energy second order perturbation interaction, elongation of conjugated π system and high spin Mn(II) ion induce the first static hyperpolarizability (β) parameter of investigated complex. The β parameter for [Mn(pic)2(phen)]·H2O complex has been found to be approximately 22 times higher than p-nitroaniline.

  12. Nonlinear Simulation of Plasma Response to the NSTX Error Field (United States)

    Breslau, J. A.; Park, J. K.; Boozer, A. H.; Park, W.


    In order to better understand the effects of the time-varying error field in NSTX on rotation braking, which impedes RWM stabilization, we model the plasma response to an applied low-n external field perturbation using the resistive MHD model in the M3D code. As an initial benchmark, we apply an m=2, n=1 perturbation to the flux at the boundary of a non-rotating model equilibrium and compare the resulting steady-state island sizes with those predicted by the ideal linear code IPEC. For sufficiently small perturbations, the codes agree; for larger perturbations, the nonlinear correction yields an upper limit on the island width beyond which stochasticity sets in. We also present results of scaling studies showing the effects of finite resistivity on island size in NSTX, and of time-dependent studies of the interaction between these islands and plasma rotation. The M3D-C1 code is also being evaluated as a tool for this analysis; first results will be shown. J.E. Menard, et al., Nucl. Fus. 47, S645 (2007). W. Park, et al., Phys. Plasmas 6, 1796 (1999). J.K. Park, et al., Phys. Plasmas 14, 052110 (2007). S.C. Jardin, et al., J. Comp. Phys. 226, 2146 (2007).

  13. Microscopic investigations of the terahertz and the extreme nonlinear optical response of semiconductors

    Energy Technology Data Exchange (ETDEWEB)

    Golde, Daniel


    In the major part of this Thesis, we discuss the linear THz response of semiconductor nanostructures based on a microscopic theory. Here, two different problems are investigated: intersubband transitions in optically excited quantum wells and the THz plasma response of two-dimensional systems. In the latter case, we analyze the response of correlated electron and electron-hole plasmas. Extracting the plasma frequency from the linear response, we find significant deviations from the commonly accepted two-dimensional plasma frequency. Besides analyzing the pure plasma response, we also consider an intermediate regime where the response of the electron-hole plasma consists of a mixture of plasma contributions and excitonic transitions. A quantitative experiment-theory comparison provides novel insights into the behavior of the system at the transition from one regime to the other. The discussion of the intersubband transitions mainly focuses on the coherent superposition of the responses from true THz transitions and the ponderomotively accelerated carriers. We present a simple method to directly identify ponderomotive effects in the linear THz response. Apart from that, the excitonic contributions to intersubband transitions are investigated. The last part of the present Thesis deals with a completely different regime. Here, the extreme nonlinear optical response of low-dimensional semiconductor structures is discussed. Formally, extreme nonlinear optics describes the regime of light-matter interaction where the exciting field is strong enough such that the Rabi frequency is comparable to or larger than the characteristic transition frequency of the investigated system. Here, the Rabi frequency is given by the product of the electrical field strength and the dipole-matrix element of the respective transition. Theoretical investigations have predicted a large number of novel nonlinear effects arising for such strong excitations. Some of them have been observed in

  14. Third-order nonlinear optical response of push-pull azobenzene polymers (United States)

    Papagiannouli, I.; Iliopoulos, K.; Gindre, D.; Sahraoui, B.; Krupka, O.; Smokal, V.; Kolendo, A.; Couris, S.


    The nonlinear optical response of a series of azo-containing side-chain polymers is investigated using Z-scan technique, employing 35 ps and 4 ns laser pulses, at 532 nm. The systems were found to exhibit strong nonlinear optical response, dominated by nonlinear refraction. In all cases, the nonlinear absorption and refraction have been determined and are compared with those of disperse red 1 considered as reference. The corresponding third-order susceptibilities χ(3) were determined to be as large as 10-7 and 10-5 esu under ps and ns laser excitation, respectively. Finally, the results are discussed and compared with other reported data.

  15. Analysis of interlaminar stress and nonlinear dynamic response for composite laminated plates with interfacial damage (United States)

    Zhu, F. H.; Fu, Y. M.


    By considering the effect of interfacial damage and using the variation principle, three-dimensional nonlinear dynamic governing equations of the laminated plates with interfacial damage are derived based on the general six-degrees-of-freedom plate theory towards the accurate stress analysis. The solutions of interlaminar stress and nonlinear dynamic response for a simply supported laminated plate with interfacial damage are obtained by using the finite difference method, and the results are validated by comparison with the solution of nonlinear finite element method. In numerical calculations, the effects of interfacial damage on the stress in the interface and the nonlinear dynamic response of laminated plates are discussed.

  16. Enhanced nonlinear optical response of one-dimensional metal-dielectric photonic crystals. (United States)

    Lepeshkin, Nick N; Schweinsberg, Aaron; Piredda, Giovanni; Bennink, Ryan S; Boyd, Robert W


    We describe a new type of artificial nonlinear optical material composed of a one-dimensional metal-dielectric photonic crystal. Because of the resonant nature of multiple Bragg reflections, the transmission within the transmission band can be quite large, even though the transmission through the same total thickness of bulk metal would be very small. This procedure allows light to penetrate into the highly nonlinear metallic layers, leading to a large nonlinear optical response. We present experimental results for a Cu/SiO(2) crystal which displays a strongly enhanced nonlinear optical response (up to 12X) in transmission.

  17. An Enhanced Asymptotic Expansion for the Stability of Nonlinear Elastic Structures

    DEFF Research Database (Denmark)

    Christensen, Claus Dencker; Byskov, Esben


    A new, enhanced asymptotic expansion applicable to stability of structures made of nonlinear elastic materials is established. The method utilizes “hyperbolic” terms instead of the conventional polynomial terms, covers full kinematic nonlinearity and is applied to nonlinear elastic Euler columns ...

  18. Nonlinear finite element model updating for damage identification of civil structures using batch Bayesian estimation (United States)

    Ebrahimian, Hamed; Astroza, Rodrigo; Conte, Joel P.; de Callafon, Raymond A.


    This paper presents a framework for structural health monitoring (SHM) and damage identification of civil structures. This framework integrates advanced mechanics-based nonlinear finite element (FE) modeling and analysis techniques with a batch Bayesian estimation approach to estimate time-invariant model parameters used in the FE model of the structure of interest. The framework uses input excitation and dynamic response of the structure and updates a nonlinear FE model of the structure to minimize the discrepancies between predicted and measured response time histories. The updated FE model can then be interrogated to detect, localize, classify, and quantify the state of damage and predict the remaining useful life of the structure. As opposed to recursive estimation methods, in the batch Bayesian estimation approach, the entire time history of the input excitation and output response of the structure are used as a batch of data to estimate the FE model parameters through a number of iterations. In the case of non-informative prior, the batch Bayesian method leads to an extended maximum likelihood (ML) estimation method to estimate jointly time-invariant model parameters and the measurement noise amplitude. The extended ML estimation problem is solved efficiently using a gradient-based interior-point optimization algorithm. Gradient-based optimization algorithms require the FE response sensitivities with respect to the model parameters to be identified. The FE response sensitivities are computed accurately and efficiently using the direct differentiation method (DDM). The estimation uncertainties are evaluated based on the Cramer-Rao lower bound (CRLB) theorem by computing the exact Fisher Information matrix using the FE response sensitivities with respect to the model parameters. The accuracy of the proposed uncertainty quantification approach is verified using a sampling approach based on the unscented transformation. Two validation studies, based on realistic

  19. Harmonic response of a class of finite extensibility nonlinear oscillators (United States)

    Febbo, M.


    Finite extensibility oscillators are widely used to simulate those systems that cannot be extended to infinity. For example, they are used when modelling the bonds between molecules in a polymer or DNA molecule or when simulating filaments of non-Newtonian liquids. In this paper, the dynamic behavior of a harmonically driven finite extensibility oscillator is presented and studied. To this end, the harmonic balance method is applied to determine the amplitude-frequency and amplitude-phase equations. The distinguishable feature in this case is the bending of the amplitude-frequency curve to the frequency axis, making it asymptotically approach the limit of maximum elongation of the oscillator, which physically represents the impossibility of the system reaching this limit. Also, the stability condition that defines stable and unstable steady-state solutions is derived. The study of the effect of the system parameters on the response reveals that a decreasing value of the damping coefficient or an increasing value of the excitation amplitude leads to the appearance of a multi-valued response and to the existence of a jump phenomenon. In this sense, the critical amplitude of the excitation, which means here a certain value of external excitation that results in the occurrence of jump phenomena, is also derived. Numerical experiments to observe the effects of system parameters on the frequency-amplitude response are performed and compared with analytical calculations. At a low value of the damping coefficient or at a high value of excitation amplitude, the agreement is poor for low frequencies but good for high frequencies. It is demonstrated that the disagreement is caused by the neglect of higher-order harmonics in the analytical formulation. These higher-order harmonics, which appear as distinguishable peaks at certain values in the frequency response curves, are possible to calculate considering not the linearized frequency of the oscillator but its actual

  20. Stress Response of Offshore Structures by Equivalent Polynomial Expansion Techniques

    DEFF Research Database (Denmark)

    Sigurdsson, Gudfinnur; Nielsen, Søren R.K.

    This paper concerns an investigation of the effects of nonlinearity of drag loading on offshore structures excited by 2D wave fields, where the nonlinear term in the Morison equation is replaced by an equivalent cubic expansion. The equivalent cubic expansion coefficients for the equivalent drag...... model are obtained using the least mean square procedure. Numerical results are given. The displacement response and stress response processes obtained using the above loading model are compared with simulation results and those obtained from equivalent linearization of the drag term....

  1. Finsler geometry of nonlinear elastic solids with internal structure (United States)

    Clayton, J. D.


    Concepts from Finsler differential geometry are applied towards a theory of deformable continua with internal structure. The general theory accounts for finite deformation, nonlinear elasticity, and various kinds of structural features in a solid body. The general kinematic structure of the theory includes macroscopic and microscopic displacement fields-i.e., a multiscale representation-whereby the latter are represented mathematically by the director vector of pseudo-Finsler space, not necessarily of unit magnitude. A physically appropriate fundamental (metric) tensor is introduced, leading to affine and nonlinear connections. A deformation gradient tensor is defined via differentiation of the macroscopic motion field, and another metric indicative of strain in the body is a function of this gradient. A total energy functional of strain, referential microscopic coordinates, and horizontal covariant derivatives of the latter is introduced. Variational methods are applied to derive Euler-Lagrange equations and Neumann boundary conditions. The theory is shown to encompass existing continuum physics models such as micromorphic, micropolar, strain gradient, phase field, and conventional nonlinear elasticity models, and it can reduce to such models when certain assumptions on geometry, kinematics, and energy functionals are imposed. The theory is applied to analyze two physical problems in crystalline solids: shear localization/fracture in a two-dimensional body and cavitation in a spherical body. In these examples, a conformal or Weyl-type transformation of the fundamental tensor enables a description of dilatation associated, respectively, with cleavage surface roughness and nucleation of voids or vacancies. For the shear localization problem, the Finsler theory is able to accurately reproduce the surface energy of Griffith's fracture mechanics, and it predicts dilatation-induced toughening as observed in experiments on brittle crystals. For the cavitation problem

  2. Stochastic filtering for damage identification through nonlinear structural finite element model updating (United States)

    Astroza, Rodrigo; Ebrahimian, Hamed; Conte, Joel P.


    This paper describes a novel framework that combines advanced mechanics-based nonlinear (hysteretic) finite element (FE) models and stochastic filtering techniques to estimate unknown time-invariant parameters of nonlinear inelastic material models used in the FE model. Using input-output data recorded during earthquake events, the proposed framework updates the nonlinear FE model of the structure. The updated FE model can be directly used for damage identification and further used for damage prognosis. To update the unknown time-invariant parameters of the FE model, two alternative stochastic filtering methods are used: the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). A three-dimensional, 5-story, 2-by-1 bay reinforced concrete (RC) frame is used to verify the proposed framework. The RC frame is modeled using fiber-section displacement-based beam-column elements with distributed plasticity and is subjected to the ground motion recorded at the Sylmar station during the 1994 Northridge earthquake. The results indicate that the proposed framework accurately estimate the unknown material parameters of the nonlinear FE model. The UKF outperforms the EKF when the relative root-mean-square error of the recorded responses are compared. In addition, the results suggest that the convergence of the estimate of modeling parameters is smoother and faster when the UKF is utilized.

  3. Component mode synthesis and large deflection vibration of complex structures. Volume 3: Multiple-mode nonlinear free and forced vibrations of beams using finite element method (United States)

    Mei, Chuh; Shen, Mo-How


    Multiple-mode nonlinear forced vibration of a beam was analyzed by the finite element method. Inplane (longitudinal) displacement and inertia (IDI) are considered in the formulation. By combining the finite element method and nonlinear theory, more realistic models of structural response are obtained more easily and faster.

  4. Nonlinear interface optical switch structure for dual mode switching revisited (United States)

    Bussjager, Rebecca J.; Osman, Joseph M.; Chaiken, Joseph


    There is a need for devices which will allow integration of photonic/optical computing subsystems into electronic computing architectures. This presentation reviews the nonlinear interface optical switch (NIOS) concept and then describes a new effect, the erasable optical memory (EOM) effect. We evaluate an extension of the NIOS device to allow simultaneous optical/electronic, i.e. dual mode, switching of light utilizing the EOM effect. Specific devices involve the fabrication of thin film tungsten (VI) oxide (WO3) and tungsten (V) oxide (W2O5) on the hypotenuse of glass (BK-7), fused silica (SiO2) and zinc selenide (ZnSe) right angle prisms. Chemical reactions and temporal response tests were performed and are discussed.

  5. Evaluation of the ductility demand in partial strength steel structures in seismic areas using non-linear static analysis


    Nogueiro, Pedro; Bento, Rita; Silva, Luís Simões da


    The performance of a structural system can be evaluated resorting to non-linear static analysis, also commonly referred to as Pushover Analysis, because of the nature of application of lateral loads while defining the capacity of the structure. This analysis involves the estimation of the structural strength and deformation demands and the comparison with the available capacities at desired performance levels. This paper aims at evaluating the seismic response of three steel struc...

  6. Fault Diagnosis of Nonlinear Systems Using Structured Augmented State Models

    Institute of Scientific and Technical Information of China (English)

    Jochen Aβfalg; Frank Allg(o)wer


    This paper presents an internal model approach for modeling and diagnostic functionality design for nonlinear systems operating subject to single- and multiple-faults. We therefore provide the framework of structured augmented state models. Fault characteristics are considered to be generated by dynamical exosystems that are switched via equality constraints to overcome the augmented state observability limiting the number of diagnosable faults. Based on the proposed model, the fault diagnosis problem is specified as an optimal hybrid augmented state estimation problem. Sub-optimal solutions are motivated and exemplified for the fault diagnosis of the well-known three-tank benchmark. As the considered class of fault diagnosis problems is large, the suggested approach is not only of theoretical interest but also of high practical relevance.

  7. Nonlinear Electrodynamics Analysis Of The Fine Structure Constant (United States)

    Mbelek, Jean Paul


    It has been claimed that during the late time history of our universe, the fine structure constant, α, has been increasing [1],[2]. However, other teams has claimed a discordant result [3],[4]. Also, the current precision of laboratory tests is not sufficient to either comfort or reject any of these astronomical observations. Here we suggest that a nonlinear electrodynamics (NLED) interaction of photons with the weak local background magnetic fields of a gas cloud absorber can reconcile the null result of refs.[3] and [4] with the negative variation found by refs. [2] and [1] and also to find a bridge with the positive variation found later by Levshakov et al.. [5]-[7]. Moreover, NLED photon propagation in a vacuum permeated by a background magnetic field is actually in full agreement with constraints from Oklo natural reactor data.

  8. Modeling of nonlinear responses for reciprocal transducers involving polarization switching

    DEFF Research Database (Denmark)

    Willatzen, Morten; Wang, Linxiang


    Nonlinearities and hysteresis effects in a reciprocal PZT transducer are examined by use of a dynamical mathematical model on the basis of phase-transition theory. In particular, we consider the perovskite piezoelectric ceramic in which the polarization process in the material can be modeled....... We present numerical results for the reciprocal-transducer system and identify the influence of nonlinearities on the system dynamics at high and low frequency as well as electrical impedance effects due to tuning by a series inductance. It is found that nonlinear effects are not important at high...... by Landau theory for the first-order phase transformation, in which each polarization state is associated with a minimum of the Landau free-energy function. Nonlinear constitutive laws are obtained by using thermodynamical equilibrium conditions, and hysteretic behavior of the material can be modeled...

  9. Structure-induced nonlinear viscoelasticity of non-woven fibrous matrices. (United States)

    Rizvi, Mohd Suhail; Pal, Anupam; Das, Sovan Lal


    Fibrous materials are widely utilized as tissue engineering scaffolds for tissue regeneration and other bioengineering applications. The structural as well as mechanical characteristics of the fibrous matrices under static and dynamic mechanical loading conditions influence the response of the cells. In this paper, we study the mechanical response of the non-woven fibrous matrices under oscillatory loading conditions and its dependence on the structural properties of fibrous matrix. We demonstrate that under oscillatory shear and elongation, the fibrous matrices demonstrate nonlinear viscoelasticity at all strain amplitudes. This is contrary to the behavior of other soft polymeric materials for which nonlinearity in the viscoelastic response vanishes for small strains. These observations suggest that despite their prevalence, the measures of linear viscoelasticity (e.g., storage and loss moduli) are inadequate for the general description of the viscoelastic nature of the fibrous materials. It was, however, found that linear viscoelastic nature of fibrous matrices for small amplitudes is restored when a pre-stretch is applied to the fibrous matrix along with oscillatory strains. Further, we also explored the influence of the structural properties of the fibrous matrices (fiber orientation, alignment and curvature) on their viscoelastic nature.

  10. Mapping nonlinear receptive field structure in primate retina at single cone resolution. (United States)

    Freeman, Jeremy; Field, Greg D; Li, Peter H; Greschner, Martin; Gunning, Deborah E; Mathieson, Keith; Sher, Alexander; Litke, Alan M; Paninski, Liam; Simoncelli, Eero P; Chichilnisky, E J


    The function of a neural circuit is shaped by the computations performed by its interneurons, which in many cases are not easily accessible to experimental investigation. Here, we elucidate the transformation of visual signals flowing from the input to the output of the primate retina, using a combination of large-scale multi-electrode recordings from an identified ganglion cell type, visual stimulation targeted at individual cone photoreceptors, and a hierarchical computational model. The results reveal nonlinear subunits in the circuity of OFF midget ganglion cells, which subserve high-resolution vision. The model explains light responses to a variety of stimuli more accurately than a linear model, including stimuli targeted to cones within and across subunits. The recovered model components are consistent with known anatomical organization of midget bipolar interneurons. These results reveal the spatial structure of linear and nonlinear encoding, at the resolution of single cells and at the scale of complete circuits.

  11. Efficient Model Order Reduction for the Dynamics of Nonlinear Multilayer Sheet Structures with Trial Vector Derivatives

    Directory of Open Access Journals (Sweden)

    Wolfgang Witteveen


    Full Text Available The mechanical response of multilayer sheet structures, such as leaf springs or car bodies, is largely determined by the nonlinear contact and friction forces between the sheets involved. Conventional computational approaches based on classical reduction techniques or the direct finite element approach have an inefficient balance between computational time and accuracy. In the present contribution, the method of trial vector derivatives is applied and extended in order to obtain a-priori trial vectors for the model reduction which are suitable for determining the nonlinearities in the joints of the reduced system. Findings show that the result quality in terms of displacements and contact forces is comparable to the direct finite element method but the computational effort is extremely low due to the model order reduction. Two numerical studies are presented to underline the method’s accuracy and efficiency. In conclusion, this approach is discussed with respect to the existing body of literature.

  12. Vibration Control of Structures using Vibro-Impact Nonlinear Energy Sinks

    Directory of Open Access Journals (Sweden)

    M. Ahmadi


    Full Text Available Using Vibro-Impact Nonlinear Energy Sinks (VI NESs is one of the novel strategies to control structural vibrations and mitigate their seismic response. In this system, a mass is tuned on the structure floor, so that it has a specific distance from an inelastic constraint connected to the floor mass. In case of structure stimulation, the displaced VI NES mass collides with the  inelastic constraint and upon impacts, energy is dissipated. In the present work, VI NES is studied when its parameters, including clearance and stiffness ratio, are simultaneously optimized. Harmony search as a recent meta-heuristic algorithm is efficiently specialized and utilized for the aforementioned continuous optimization problem. The optimized attached VI NES is thus shown to be capable of interacting with the primary structure over a wide range of frequencies. The resulting controlled response is then investigated, in a variety of low and medium rise steel moment frames, via nonlinear dynamic time history analyses. Capability of the VI NES to dissipate siesmic input energy of earthquakes and their capabilitiy in reducing response of srtructures effectively, through vibro-impacts between the energy sink’s mass and the floor mass, is discussed by extracting several performance indices and the corresponding Fourier spectra. Results of the numerical simulations done on some structural model examples reveal that the optimized VI NES has caused successive redistribution of energy from low-frequency high-amplitude vibration modes to high-frequency low-amplitude modes, bringing about the desired attenuation of the structural responses.

  13. A Space-Time Finite Element Model for Design and Control Optimization of Nonlinear Dynamic Response

    Directory of Open Access Journals (Sweden)

    P.P. Moita


    Full Text Available A design and control sensitivity analysis and multicriteria optimization formulation is derived for flexible mechanical systems. This formulation is implemented in an optimum design code and it is applied to the nonlinear dynamic response. By extending the spatial domain to the space-time domain and treating the design variables as control variables that do not change with time, the design space is included in the control space. Thus, one can unify in one single formulation the problems of optimum design and optimal control. Structural dimensions as well as lumped damping and stiffness parameters plus control driven forces, are considered as decision variables. The dynamic response and its sensitivity with respect to the design and control variables are discretized via space-time finite elements, and are integrated at-once, as it is traditionally used for static response. The adjoint system approach is used to determine the design sensitivities. Design optimization numerical examples are performed. Nonlinear programming and optimality criteria may be used for the optimization process. A normalized weighted bound formulation is used to handle multicriteria problems.

  14. Distributed Dynamic Condition Response Structures

    DEFF Research Database (Denmark)

    Hildebrandt, Thomas; Mukkamala, Raghava Rao

    We present distributed dynamic condition response structures as a declarative process model inspired by the workflow language employed by our industrial partner and conservatively generalizing labelled event structures. The model adds to event structures the possibility to 1) finitely specify...... repeated, possibly infinite behavior, 2) finitely specify fine-grained acceptance conditions for (possibly infinite) runs based on the notion of responses and 3) distribute events via roles. We give a graphical notation inspired by related work by van der Aalst et al and formalize the execution semantics...

  15. Effective Response of Nonlinear Composite under External AC and DC Electric Field

    Institute of Scientific and Technical Information of China (English)

    LIU Ye; LIANG Fang-Chu; SHEN Hong-Liang


    A perturbation method is used to study effective response of nonlinear Kerr composites, which are subject to the constitutive relation of electric displacement and electric field, Dα = εαE + xα|E|2E. Under the external AC and DC electric field Eapp = Eα(1 + sinwt), the effective nonlinear responses and local potentials are induced by the cubic nonlinearity of Kerr materials at all harmonics. As an example in three dimensions, we have investigated this kind of nonlinear composites with spherical inclusions embedded in a host. At all harmonic frequencies, the potentials in inclusion and host regions are derived. Furthermore, the formulae of the effective linear and nonlinear responses are given in the dilute limit.

  16. PCI-SS: MISO dynamic nonlinear protein secondary structure prediction

    Directory of Open Access Journals (Sweden)

    Aboul-Magd Mohammed O


    Full Text Available Abstract Background Since the function of a protein is largely dictated by its three dimensional configuration, determining a protein's structure is of fundamental importance to biology. Here we report on a novel approach to determining the one dimensional secondary structure of proteins (distinguishing α-helices, β-strands, and non-regular structures from primary sequence data which makes use of Parallel Cascade Identification (PCI, a powerful technique from the field of nonlinear system identification. Results Using PSI-BLAST divergent evolutionary profiles as input data, dynamic nonlinear systems are built through a black-box approach to model the process of protein folding. Genetic algorithms (GAs are applied in order to optimize the architectural parameters of the PCI models. The three-state prediction problem is broken down into a combination of three binary sub-problems and protein structure classifiers are built using 2 layers of PCI classifiers. Careful construction of the optimization, training, and test datasets ensures that no homology exists between any training and testing data. A detailed comparison between PCI and 9 contemporary methods is provided over a set of 125 new protein chains guaranteed to be dissimilar to all training data. Unlike other secondary structure prediction methods, here a web service is developed to provide both human- and machine-readable interfaces to PCI-based protein secondary structure prediction. This server, called PCI-SS, is available at In addition to a dynamic PHP-generated web interface for humans, a Simple Object Access Protocol (SOAP interface is added to permit invocation of the PCI-SS service remotely. This machine-readable interface facilitates incorporation of PCI-SS into multi-faceted systems biology analysis pipelines requiring protein secondary structure information, and greatly simplifies high-throughput analyses. XML is used to represent the input

  17. Nonlinear response to a click in a time-domain model of the mammalian ear. (United States)

    Meaud, Julien; Lemons, Charlsie


    In this paper, a state-space implementation of a previously developed frequency-domain model of the cochlea is coupled to a lumped parameter model of the middle ear. After validation of the time-domain model by comparison of its steady-state response to results obtained with a frequency-domain formulation, the nonlinear response of the cochlea to clicks is investigated. As observed experimentally, a compressive nonlinearity progressively develops within the first few cycles of the response of the basilar membrane (BM). Furthermore, a time-frequency analysis shows that the instantaneous frequency of the BM response to a click progressively approaches the characteristic frequency. This phenomenon, called glide, is predicted at all stimulus intensities, as in experiments. In typical experiments with sensitive animals, the click response is characterized by a long ringing and the response envelope includes several lobes. In order to achieve similar results, inhomogeneities are introduced in the cochlear model. Simulations demonstrate the strong link between characteristics of the frequency response, such as dispersion and frequency-dependent nonlinearity, and characteristics of the time-domain response, such as the glide and a time-dependent nonlinearity. The progressive buildup of cochlear nonlinearity in response to a click is shown to be a consequence of the glide and of frequency-dependent nonlinearity.

  18. Linear and nonlinear optical response of one-dimensional semiconductors: finite-size and Franz–Keldysh effects (United States)

    Bonabi, Farzad; Pedersen, Thomas G.


    The dipole moment formalism for the optical response of finite electronic structures breaks down in infinite ones, for which a momentum-based method is better suited. Focusing on simple chain structures, we compare the linear and nonlinear optical response of finite and infinite one-dimensional semiconductors. This comparison is then extended to cases including strong electro-static fields breaking translational invariance. For large electro-static fields, highly non-perturbative Franz–Keldysh (FK) features are observed in both linear and nonlinear spectra. It is demonstrated that dipole and momentum formalisms agree in the limit of large structures provided the intraband momentum contributions are carefully treated. This convergence is established even in the presence of non-perturbative electro-static fields.

  19. Z-scan for thin media with more than one nonlocal nonlinear response. (United States)

    Irivas, B A Martinez; Carrasco, M L Arroyo; Otero, M M Mendez; García, R Ramos; Castillo, M D Iturbe


    A model to characterize the response of a thin media that can exhibit more than one nonlocal nonlinear response when it is illuminated with a Gaussian beam in a z-scan experiment is proposed. The model considers that these nonlocal contributions can be treated as independent contributions in the refractive or absorptive nonlinear response. Numerical results for two nonlocal nonlinear contributions with different magnitudes between them are presented. Experimental results obtained from a hydrogenated amorphous silicon sample are used to corroborate this model.


    Institute of Scientific and Technical Information of China (English)

    GAO Shi-qiao(高世桥); JIN Lei(金磊); H.J.Niemann; LIU Hai-peng(刘海鹏)


    An iteration method of statistic linearization (IMSL) is presented. By this method, an equivalent linear term was formed in geometric relation and then an equivalent stiffness matrix for nonlinear term in vibration equation was established. Using the method to solve the statistic linear vibration equations, the effect of geometric nonlinearity on the random response of rotational shell is obtained.

  1. Measurements of dynamical response of non-linear systems. How hard can it be?

    DEFF Research Database (Denmark)

    Darula, Radoslav


    Measurements of a dynamical response of linear system are widely used in praxis, they are standardized and well known. On the other hand, for the non-linear systems the principle of superposition can’t be applied and also the non-linear systems can excite the harmonics or undergo jump phenomena...

  2. Modeling the toxicity of aromatic compounds to tetrahymena pyriformis: the response surface methodology with nonlinear methods. (United States)

    Ren, Shijin


    Response surface models based on multiple linear regression had previously been developed for the toxicity of aromatic chemicals to Tetrahymena pyriformis. However, a nonlinear relationship between toxicity and one of the molecular descriptors in the response surface model was observed. In this study, response surface models were established using six nonlinear modeling methods to handle the nonlinearity exhibited in the aromatic chemicals data set. All models were validated using the method of cross-validation, and prediction accuracy was tested on an external data set. Results showed that response surface models based on locally weighted regression scatter plot smoothing (LOESS), multivariate adaptive regression splines (MARS), neural networks (NN), and projection pursuit regression (PPR) provided satisfactory power of model fitting and prediction and had similar applicabilities. The response surface models based on nonlinear methods were difficult to interpret and conservative in discriminating toxicity mechanisms.

  3. Nonlinear dielectric properties of planar structures based on ferroelectric betaine phosphite films (United States)

    Balashova, E. V.; Krichevtsov, B. B.; Svinarev, F. B.; Yurko, E. I.


    Ferroelectric films of partly deuterated betaine phosphite are grown on NdGaO3(001) substrates with an interdigitated system of electrodes on their surfaces by evaporation at room temperature. These films have a high capacitance in the ferroelectric phase transition range. The dielectric nonlinearity of the grown structures is studied in small-signal and strong-signal response modes and in the intermediate region between these two modes by measuring the capacitance in a dc bias field, dielectric hysteresis loops, and the Fourier spectra of an output signal in the Sawyer-Tower circuit. In the phase transition range, the capacitance control ratio at a bias voltage U bias = 40 V is K ≅ 7. The dielectric nonlinearity of the structures in the paraelectric phase is described by the Landau theory of second-order phase transitions. The additional contribution to the nonlinearity in the ferroelectric phase is related to the motion of domain walls and manifests itself when the input signal amplitude is higher than U st ˜ 0.7-1.0 V. The relaxation times of domain walls are determined from an analysis of the frequency dependences of the dielectric hysteresis.

  4. Nonlinear Response of High Arch Dams to Nonuniform Seismic Excitation Considering Joint Effects

    Directory of Open Access Journals (Sweden)

    Masoomeh Akbari


    Full Text Available Nonuniform excitation due to spatially varying ground motions on nonlinear responses of concrete arch dams is investigated. A high arch dam was selected as numerical example, reservoir was modelled as incompressible material, foundation was assumed as mass-less medium, and all contraction and peripheral joints were modelled considering the ability of opening/closing. This study used Monte-Carlo simulation approach for generating spatially nonuniform ground motion. In this approach, random seismic characteristics due to incoherence and wave passage effects were investigated and finally their effects on structural response were compared with uniform excitation at design base level earthquake. Based on the results, nonuniform input leads to some differences than uniform input. Moreover using nonuniform excitation increase, stresses on dam body.

  5. Non-Linear Vibrations, Stability, and Dynamics of Structures and Mechanisms (United States)


    particle of matter can occupy only one position in space. On the basis of this law, it is not difficult to show that a rigid body can assume only one...Em+n) is desired, with m > 0, then all terms of O(em +n) must be retained in the expanded equations. With this in mind , we address some other...concerning the 3 nonlinear non-planar response of inextensional beams and of beam-like structures. These include modal interactins both in the

  6. Finite element analysis of steady and transiently moving/rolling nonlinear viscoelastic structure. I - Theory (United States)

    Padovan, Joe


    In a three-part series of papers, a generalized finite element analysis scheme is developed to handle the steady and transient response of moving/rolling nonlinear viscoelastic structure. This paper considers the development of the moving/rolling element strategy, including the effects of large deformation kinematics and viscoelasticity modeled by fractional integrodifferential operators. To improve the solution strategy, a special hierarchical constraint procedure is developed for the case of steady rolling/translating, as well as a transient scheme involving the use of a Grunwaldian representation of the fractional operator.

  7. Structural and nonlinear optical studies of a salt with an octupolar chromophore: Guanidinium cyclopropanecarboxylate (United States)

    Pereira Silva, Pedro S.; Pereira Gonçalves, M. A.; Ramos Silva, Manuela; Paixão, José A.


    A new organic compound, guanidinium cyclopropanecarboxylate, has been synthesized and characterized by single crystal X-ray diffraction, infrared spectroscopy and nonlinear optical measurements. The infrared spectrum was calculated with density functional theory (DFT). The second-order NLO response was evaluated with the Kurtz and Perry powder method. From the molecular structure, the molecular hyperpolarizability tensor was determined with Hartree-Fock and DFT methods. The second-order susceptibility tensor of the crystal was evaluated by the summation of the effective hyperpolarizability tensors calculated for the asymmetric unit surrounded by ESP-derived charges.

  8. Organic nanoclusters for nonlinear optics: from model systems to cooperative nanoassemblies with enhanced NLO responses (United States)

    Terenziani, Francesca; Parthasarathy, Venkatakrishnan; Ghosh, Sampa; Pandey, Ravindra; Das, Puspendu K.; Blanchard-Desce, Mireille


    While structure-properties relationships are quite actively and successfully investigated at the molecular level of engineering of optical nonlinear responses, supramolecular structure-property relationships are an appealing field. The realization that interchromophoric interactions between strongly polar/polarizable NLO chromophores can significantly affect the NLO response of each chromophoric unit as well as promote associations has opened new dimensions for molecular design. Several elegant routes have been implemented to hinder or counterbalance dipole-dipole interactions between dipolar NLO chromophores for the elaboration of second-order materials (for SHG or electro-optical modulation). At opposite, we have implemented a reverse strategy by confining discrete numbers of NLO push-pull chromophores in close proximity within covalent organic nanoclusters with the aim to exploit interchromophoric interactions in order to achieve enhanced NLO responses. As a proof of concept, we present here the investigation of two-series of multichromophoric covalent assemblies built from NLO push-pull chromophores showing that cooperative enhancement can be achieved both for second-order optical responses (first hyperpolarizabilities) or third-order responses (two-photon absorption cross-sections).

  9. Dynamical soil-structure interactions: influence of soil behaviour nonlinearities; Interaction Dynamique Sol-Structure: Influence des Nonlinearites de Comportement du Sol

    Energy Technology Data Exchange (ETDEWEB)

    Gandomzadeh, Ali


    The interaction of the soil with the structure has been largely explored the assumption of material and geometrical linearity of the soil. Nevertheless, for moderate or strong seismic events, the maximum shear strain can easily reach the elastic limit of the soil behavior. Considering soil-structure interaction, the nonlinear effects may change the soil stiffness at the base of the structure and therefore energy dissipation into the soil. Consequently, ignoring the nonlinear characteristics of the dynamic soil-structure interaction (DSSI) this phenomenon could lead to erroneous predictions of structural response. The goal of this work is to implement a fully nonlinear constitutive model for soils into a numerical code in order to investigate the effect of soil nonlinearity on dynamic soil structure interaction. Moreover, different issues are taken into account such as the effect of confining stress on the shear modulus of the soil, initial static condition, contact elements in the soil-structure interface, etc. During this work, a simple absorbing layer method based on a Rayleigh/Caughey damping formulation, which is often already available in existing Finite Element softwares, is also presented. The stability conditions of the wave propagation problems are studied and it is shown that the linear and nonlinear behavior are very different when dealing with numerical dispersion. It is shown that the 10 points per wavelength rule, recommended in the literature for the elastic media is not sufficient for the nonlinear case. The implemented model is first numerically verified by comparing the results with other known numerical codes. Afterward, a parametric study is carried out for different types of structures and various soil profiles to characterize nonlinear effects. Different features of the DSSI are compared to the linear case: modification of the amplitude and frequency content of the waves propagated into the soil, fundamental frequency, energy dissipation in

  10. Equivalent circuit simulation of HPEM-induced transient responses at nonlinear loads

    Directory of Open Access Journals (Sweden)

    M. Kotzev


    Full Text Available In this paper the equivalent circuit modeling of a nonlinearly loaded loop antenna and its transient responses to HPEM field excitations are investigated. For the circuit modeling the general strategy to characterize the nonlinearly loaded antenna by a linear and a nonlinear circuit part is pursued. The linear circuit part can be determined by standard methods of antenna theory and numerical field computation. The modeling of the nonlinear circuit part requires realistic circuit models of the nonlinear loads that are given by Schottky diodes. Combining both parts, appropriate circuit models are obtained and analyzed by means of a standard SPICE circuit simulator. It is the main result that in this way full-wave simulation results can be reproduced. Furthermore it is clearly seen that the equivalent circuit modeling offers considerable advantages with respect to computation speed and also leads to improved physical insights regarding the coupling between HPEM field excitation and nonlinearly loaded loop antenna.


    Directory of Open Access Journals (Sweden)

    Turgay ÇOŞGUN


    Full Text Available The progress made on the analysis of the structures by using non-linear theory and the significant findings on both theorical and empirical works, enable better understanding of the behaviours of structures under external loads. Determination of the failure load and designing the structures accordingly requires developments of analysis methods, which take both the non-linear behaviour of structural elements and the non-linear effects of geometric changes into consideration. Therefore, in this study, a FORTRAN code, which analyses structures and calculates the failure loads by considering the non-linear behaviour of materials under increasing loads (due to the non-linear relationship of stress-strain and moment-curvature and second-order theory of structural systems is developed.

  12. Some Problems in Nonlinear Dynamic Instability and Bifurcation Theory for Engineering Structures

    Institute of Scientific and Technical Information of China (English)

    彭妙娟; 程玉民


    In civil engineering, the nonlinear dynamic instability of structures occurs at a bifurcation point or a limit point. The instability at a bifurcation point can be analyzed with the theory of nonlinear dynamics, and that at a limit point can be discussed with the theory of elastoplasticity. In this paper, the nonlinear dynamic instability of structures was treated with mathematical and mechanical theories. The research methods for the problems of structural nonlinear dynamic stability were discussed first, and then the criterion of stability or instability of structures, the method to obtain the bifurcation point and the limit point, and the formulae of the directions of the branch solutions at a bifurcation point were elucidated. These methods can be applied to the problems of nonlinear dynamic instability of structures such as reticulated shells, space grid structures, and so on.

  13. Nonlinear Optical Response of Conjugated Polymer to Electric Field

    Institute of Scientific and Technical Information of China (English)

    ZHOU Yu-fang; ZHUANG De-xin; CUI Bin


    The organic π-conjugated polymers are of major interest materials for the use in electro-optical and nonlinear optical devices. In this work, for a selected polyacetylene chain, the optical absorption spectra in UV/Vis regime as well as the linear polarizabilitiy and nonlinear hyperpolarizability are calculated by using quantum chemical ab initio and semiempirical methods. The relationship of its optical property to electric field is obtained. Some physical mechanism of electric field effect on molecular optical property is discussed by means of electron distribution and intramolecular charge transfer.

  14. Cardiovascular Response Identification Based on Nonlinear Support Vector Regression (United States)

    Wang, Lu; Su, Steven W.; Chan, Gregory S. H.; Celler, Branko G.; Cheng, Teddy M.; Savkin, Andrey V.

    This study experimentally investigates the relationships between central cardiovascular variables and oxygen uptake based on nonlinear analysis and modeling. Ten healthy subjects were studied using cycle-ergometry exercise tests with constant workloads ranging from 25 Watt to 125 Watt. Breath by breath gas exchange, heart rate, cardiac output, stroke volume and blood pressure were measured at each stage. The modeling results proved that the nonlinear modeling method (Support Vector Regression) outperforms traditional regression method (reducing Estimation Error between 59% and 80%, reducing Testing Error between 53% and 72%) and is the ideal approach in the modeling of physiological data, especially with small training data set.

  15. Composite structures for the enhancement of nonlinear optical materials. (United States)

    Neeves, A E; Birnboim, M H


    Calculations of the nonlinear optical behavior are developed for model composites consisting of nanospheres with a metallic core and a nonlinear shell suspended in a nonlinear medium. The concept for the enhancement of optical phase conjugation from all these nonlinear regions is that the optical field can be concentrated both inside and in the neighborhood of the metallic core, aided by surface-mediated plasmon resonance. Calculations for gold cores and aluminum cores indicate that phase-conjugate reflectivity enhancements of 10(8) may be possible.

  16. Nonlinear dynamical model and response of avian cranial kinesis. (United States)

    Meekangvan, Preeda; A Barhorst, Alan; Burton, Thomas D; Chatterjee, Sankar; Schovanec, Lawrence


    All modern birds have kinetic skulls in which the upper bill can move relative to the braincase, but the biomechanics and motion dynamics of cranial kinesis in birds are poorly understood. In this paper, we model the dynamics of avian cranial kinesis, such as prokinesis and proximal rhynchokinesis in which the upper jaw pivots around the nasal-frontal (N-F) hinge. The purpose of this paper is to present to the biological community an approach that demonstrates the application of sophisticated predictive mathematical modeling tools to avian kinesis. The generality of the method, however, is applicable to the advanced study of the biomechanics of other skeletal systems. The paper begins with a review of the relevant biological literature as well as the essential morphology of avian kinesis, especially the mechanical coupling of the upper and lower jaw by the postorbital ligament. A planar model of the described bird jaw morphology is then developed that maintains the closed kinematic topology of the avian jaw mechanism. We then develop the full nonlinear equations of motion with the assumption that the M. protractor pterygoideus and M. depressor mandibulae act on the quadrate as a pure torque, and the nasal frontal hinge is elastic with damping. The mechanism is shown to be a single degree of freedom device due to the holonomic constraints present in the quadrate-jugal bar-upper jaw-braincase-quadrate kinematic chain as well as the quadrate-lower jaw-postorbital ligament-braincase-quadrate kinematic chain. The full equations are verified via simulation and animation using the parameters of a Grey Heron (Ardea cinerea). Next we develop a simplified analytical model of the equations by power series expansion. We demonstrate that this model reproduces the dynamics of the full model to a high degree of fidelity. We proceed to use the harmonic balance technique to develop the frequency response characteristics of the jaw mechanism. It is shown that this avian cranial

  17. Tuning the nonlinear response of (6,5)-enriched single-wall carbon nanotubes dispersions (United States)

    Aréstegui, O. S.; Silva, E. C. O.; Baggio, A. L.; Gontijo, R. N.; Hickmann, J. M.; Fantini, C.; Alencar, M. A. R. C.; Fonseca, E. J. S.


    Ultrafast nonlinear optical properties of (6,5)-enriched single-wall carbon nanotubes (SWCNTs) dispersions are investigated using the thermally managed Z-scan technique. As the (6,5) SWCNTs presented a strong resonance in the range of 895-1048 nm, the nonlinear refractive index (n2) and the absorption coefficients (β) measurements were performed tuning the laser exactly around absorption peak of the (6,5) SWCNTs. It is observed that the nonlinear response is very sensitive to the wavelength and the spectral behavior of n2 is strongly correlated to the tubes one-photon absorption band, presenting also a peak when the laser photon energy is near the tube resonance energy. This result suggests that a suitable selection of nanotubes types may provide optimized nonlinear optical responses in distinct regions of the electromagnetic spectrum. Analysis of the figures of merit indicated that this material is promising for ultrafast nonlinear optical applications under near infrared excitation.

  18. Nonlinear response of metallic acGNR to an elliptically-polarized terahertz excitation field

    CERN Document Server

    Wang, Yichao


    We present a theoretical description of the nonlinear response induced by an elliptically-polarized terahertz beam normally-incident on intrinsic and extrinsic metallic armchair graphene nanorib- bons. Our results show that using a straightforward experimental setup, it should be possible to observe novel polarization-dependent nonlinearities at low excitation field strengths of the or- der of 10 4 V/m. At low temperatures the Kerr nonlinearities in extrinsic nanoribbons persist to significantly higher excitation frequencies than they do for linear polarizations, and at room tem- peratures, the third-harmonic nonlinearities are enhanced by 2-3 orders of magnitude. Finally, the Fermi-level and temperature dependence of the nonlinear response is characterized.

  19. Nonlinear Structural Analysis Methodology and Dynamics Scaling of Inflatable Parabolic Reflector Antenna Concepts (United States)

    Sreekantamurthy, Tham; Gaspar, James L.; Mann, Troy; Behun, Vaughn; Pearson, James C., Jr.; Scarborough, Stephen


    Ultra-light weight and ultra-thin membrane inflatable antenna concepts are fast evolving to become the state-of-the-art antenna concepts for deep-space applications. NASA Langley Research Center has been involved in the structural dynamics research on antenna structures. One of the goals of the research is to develop structural analysis methodology for prediction of the static and dynamic response characteristics of the inflatable antenna concepts. This research is focused on the computational studies to use nonlinear large deformation finite element analysis to characterize the ultra-thin membrane responses of the antennas. Recently, structural analyses have been performed on a few parabolic reflector antennas of varying size and shape, which are referred in the paper as 0.3 meters subscale, 2 meters half-scale, and 4 meters full-scale antenna. The various aspects studied included nonlinear analysis methodology and solution techniques, ways to speed convergence in iterative methods, the sensitivities of responses with respect to structural loads, such as inflation pressure, gravity, and pretension loads in the ground and in-space conditions, and the ultra-thin membrane wrinkling characteristics. Several such intrinsic aspects studied have provided valuable insight into evaluation of structural characteristics of such antennas. While analyzing these structural characteristics, a quick study was also made to assess the applicability of dynamics scaling of the half-scale antenna. This paper presents the details of the nonlinear structural analysis results, and discusses the insight gained from the studies on the various intrinsic aspects of the analysis methodology. The predicted reflector surface characteristics of the three inflatable ultra-thin membrane parabolic reflector antenna concepts are presented as easily observable displacement fringe patterns with associated maximum values, and normal mode shapes and associated frequencies. Wrinkling patterns are

  20. Asymmetric bistable reflection and polarization switching in a magnetic nonlinear multilayer structure

    DEFF Research Database (Denmark)

    Tuz, Vladimir R.; Novitsky, Denis V.; Prosvirnin, Sergey L.


    Optical properties of one-dimensional photonic structures consisting of Kerr-type nonlinear and magnetic layers under the action of an external static magnetic field in the Faraday geometry are investigated. The structure is a periodic arrangement of alternating nonlinear and magnetic layers (a one...

  1. A Novel Rational Design Method for Laminated Composite Structures Exhibiting Complex Geometrically Nonlinear Buckling Behaviour

    DEFF Research Database (Denmark)

    Lindgaard, Esben; Lund, Erik


    This paper presents a novel FEM-based approach for fiber angle optimal design of laminated composite structures exhibiting complicated nonlinear buckling behavior, thus enabling design of lighter and more cost-effective structures. The approach accounts for the geometrically nonlinear behavior...

  2. Maximum Likelihood Analysis of Nonlinear Structural Equation Models with Dichotomous Variables (United States)

    Song, Xin-Yuan; Lee, Sik-Yum


    In this article, a maximum likelihood approach is developed to analyze structural equation models with dichotomous variables that are common in behavioral, psychological and social research. To assess nonlinear causal effects among the latent variables, the structural equation in the model is defined by a nonlinear function. The basic idea of the…

  3. Estimating Nonlinear Structural Models: EMM and the Kenny-Judd Model (United States)

    Lyhagen, Johan


    The estimation of nonlinear structural models is not trivial. One reason for this is that a closed form solution of the likelihood may not be feasible or does not exist. We propose to estimate nonlinear structural models using the efficient method of moments, as generating data according to the models is often very easy. A simulation study of the…

  4. A system identification analysis of neural adaptation dynamics and nonlinear responses in the local reflex control of locust hind limbs. (United States)

    Dewhirst, Oliver P; Angarita-Jaimes, Natalia; Simpson, David M; Allen, Robert; Newland, Philip L


    Nonlinear type system identification models coupled with white noise stimulation provide an experimentally convenient and quick way to investigate the often complex and nonlinear interactions between the mechanical and neural elements of reflex limb control systems. Previous steady state analysis has allowed the neurons in such systems to be categorised by their sensitivity to position, velocity or acceleration (dynamics) and has improved our understanding of network function. These neurons, however, are known to adapt their output amplitude or spike firing rate during repetitive stimulation and this transient response may be more important than the steady state response for reflex control. In the current study previously used system identification methods are developed and applied to investigate both steady state and transient dynamic and nonlinear changes in the neural circuit responsible for controlling reflex movements of the locust hind limbs. Through the use of a parsimonious model structure and Monte Carlo simulations we conclude that key system dynamics remain relatively unchanged during repetitive stimulation while output amplitude adaptation is occurring. Whilst some evidence of a significant change was found in parts of the systems nonlinear response, the effect was small and probably of little physiological relevance. Analysis using biologically more realistic stimulation reinforces this conclusion.

  5. On the effects of nonlinearities in room impulse response measurements with exponential sweeps

    DEFF Research Database (Denmark)

    Ciric, Dejan; Markovic, Milos; Mijic, Miomir


    In room impulse response measurements, there are some common disturbances that affect the measured results. These disturbances include nonlinearity, noise and time variance. In this paper, the effects of nonlinearities in the measurements with exponential sweep-sine signals are analyzed from...... different perspectives. The analysis combines theoretical approach, simulations and measurements. The focus is on distortion artifacts in the causal part of the impulse response and their effects on room acoustical parameters. The results show that the sweep-sine method is vulnerable to a certain extent...... to nonlinearities from a theoretical standpoint, but the consequences of this vulnerability are reduced in the responses measured in practice. However, due to irretrievable contamination of the impulse responses, the nonlinearities (especially strong ones) should be avoided....

  6. Non-Gaussian approach for parametric random vibration of non-linear structures (United States)

    Ibrahim, R. A.; Soundararajan, A.


    The dynamic response of a nonlinear, single degree of freedom structural system subjected to a physically white noise parametric excitation is investigated. The Ito stochastic calculus is employed to derive a general differential equation for the moments of the response coordinates. The differential equations of moments of any order are found to be coupled with higher order moments. A non-Gaussian closure scheme is developed to truncate the moment equations up to fourth order. The statistical of the stationary response are computed numerically and compared with analytical solutions predicted by a Gaussian closure scheme and the stochastic averaging method. It is found that the computed results exhibit the jump phenomenon which is typical of the characteristics of deterministic nonlinear systems. In addition, the numerical algorithm leads to multiple solutions all of which give positive mean squares. However, two of these solutions are found to violate the properties of high order moments. One solution preserves the moments properties and demonstrates that the system achieves a stationary response.

  7. A Novel Method for Prediction of Nonlinear Aeroelastic Responses (United States)


    Brian A. Freno Graduate Student, Texas A&M University Publications Journal articles: 1. Gargoloff, J. I. and Cizmas, P. G. A., “Mesh Generation and...papers: 1. Cizmas, P. G. A., Freno , B. A., Brenner, T. A., Worley, G. D., “A High-Fidelity Nonlinear Aeroelastic Model for Aircraft with Large Wing

  8. Nonlinear Control Structure of Grid Connected Modular Multilevel Converters

    DEFF Research Database (Denmark)

    Hajizadeh, Amin; Norum, Lars; Ahadpour Shal, Alireza


    in the prediction step in order to preserve the stochastic characteristics of a nonlinear system. In order to design adaptive robust control strategy and nonlinear observer, mathematical model of MMC using rotating d-q theory has been used. Digital time-domain simulation studies are carried out in the Matlab/Simulink...

  9. Nonlinear Control Structure of Grid Connected Modular Multilevel Converters

    DEFF Research Database (Denmark)

    Hajizadeh, Amin; Norum, Lars; Ahadpour Shal, Alireza


    in the prediction step in order to preserve the stochastic characteristics of a nonlinear system. In order to design adaptive robust control strategy and nonlinear observer, mathematical model of MMC using rotating d-q theory has been used. Digital time-domain simulation studies are carried out in the Matlab...

  10. Numerical Simulation of Seabed Response and Liquefaction due to Non-linear Waves

    Institute of Scientific and Technical Information of China (English)

    ZHANG Jin-feng; ZHANG Qing-he; HAN Tao; QIN Chong-ren


    Based on Biot's consolidation theory, a two-dimensional model for computation of the seabed response to waves is presented with the finite element method. Numerical results for different wave conditions are obtained, and the effects of wave non-linearity on the wave-induced seabed response are examined. Moreover, the wave-induced momentary liquefaction in uniform and inhomogeneous seabeds is investigated. It is shown that the wave non-linearity affects the distribution of the wave-induced pore pressure and effective stresses, while the influence of wave non-linearity on the seabed liquefaction potential is not so significant.

  11. Synthesis, characterization and non-linear optical response of organophilic carbon dots

    KAUST Repository

    Bourlinos, Athanasios B.


    For the first time ever we report the nonlinear optical (NLO) properties of carbon dots (C-dots). The C-dots for these experiments were synthesized by mild pyrolysis of lauryl gallate. The resulting C-dots bear lauryl chains and, hence, are highly dispersible in polar organic solvents, like chloroform. Dispersions in CHCl3 show significant NLO response. Specifically, the C-dots show negative nonlinear absorption coefficient and negative nonlinear refraction. Using suspensions with different concentrations these parameters are quantified and compared to those of fullerene a well-known carbon molecule with proven NLO response. © 2013 Elsevier Ltd. All rights reserved.

  12. Nonlinear evolution of large-scale structure in the universe

    Energy Technology Data Exchange (ETDEWEB)

    Frenk, C.S.; White, S.D.M.; Davis, M.


    Using N-body simulations we study the nonlinear development of primordial density perturbation in an Einstein--de Sitter universe. We compare the evolution of an initial distribution without small-scale density fluctuations to evolution from a random Poisson distribution. These initial conditions mimic the assumptions of the adiabatic and isothermal theories of galaxy formation. The large-scale structures which form in the two cases are markedly dissimilar. In particular, the correlation function xi(r) and the visual appearance of our adiabatic (or ''pancake'') models match better the observed distribution of galaxies. This distribution is characterized by large-scale filamentary structure. Because the pancake models do not evolve in a self-similar fashion, the slope of xi(r) steepens with time; as a result there is a unique epoch at which these models fit the galaxy observations. We find the ratio of cutoff length to correlation length at this time to be lambda/sub min//r/sub 0/ = 5.1; its expected value in a neutrino dominated universe is 4(..cap omega..h)/sup -1/ (H/sub 0/ = 100h km s/sup -1/ Mpc/sup -1/). At early epochs these models predict a negligible amplitude for xi(r) and could explain the lack of measurable clustering in the Ly..cap alpha.. absorption lines of high-redshift quasars. However, large-scale structure in our models collapses after z = 2. If this collapse precedes galaxy formation as in the usual pancake theory, galaxies formed uncomfortably recently. The extent of this problem may depend on the cosmological model used; the present series of experiments should be extended in the future to include models with ..cap omega..<1.

  13. Deflection determination of concrete structures considering nonlinearity based on long-gauge strain sensors (United States)

    Hong, Wan; Lv, Kui; Li, Bing; Jiang, Yuchen; Hu, Xiamin; Qu, Qizhong


    Deflection determination of concrete structures using distributed long-gauge strain sensors is investigated in this paper. Firstly, the relationship between deflection and distributed long-gauge strain of concrete beams is presented, and the method is independent of external load and takes account of structural nonlinearity. The deflection distribution along the span of a beam-like structure can be predicted from strain response for the whole process of loading (elastic stage, concrete cracking stage and steel yielding stage). Secondly, experiment of a reinforced concrete beam has been conducted to verify the accuracy of the method. Experimental results show that the relative error between the estimated and actual deflection can be controlled within about 5% while the error can reach up to about 70% if structural nonlinearity is not considered. Finally, the influence of error of material parameters and sensor gauge length on deflection estimation has been analyzed. The error of concrete compression strength has a limited influence on deflection prediction while the contribution of tensile concrete should be considered before concrete cracking. The error of area of tensile bars will affect the deflection accuracy after concrete cracking.

  14. All-metal electride molecules CuAg@Ca7M (M = Be, Mg, and Ca) with multi-excess electrons and all-metal polyanions: molecular structures and bonding modes as well as large infrared nonlinear optical responses. (United States)

    He, Hui-Min; Li, Ying; Sun, Wei-Ming; Wang, Jia-Jun; Wu, Di; Zhong, Rong-Lin; Zhou, Zhong-Jun; Li, Zhi-Ru


    All-metal electride molecules, CuAg@Ca7M (M = Be, Mg and Ca), have been designed and researched in theory for the first time. In these molecules, a pull-push electron relay occurs. Unusually, the all-metal polyanions of fourfold negatively charged [Cu-Ag-Be/Mg](4-) and [Cu-Ag](4-) with 4 extra electrons gained from Ca atoms push the remaining valence electrons of the Ca atoms forming the multi-excess electrons (Ne = 10/12). Therefore, these molecules can be described as salt-like [(Ca(2+))7(CuAgM)(4-)] + 10e(-) (M = Be and Mg) and [(Ca(2+))8(CuAg)(4-)] + 12e(-). In these salt-like molecules, there are extraordinary covalent bonding modes, which include 2c-2e/3c-2e σ-bonding in the polyanions and the Ca(2+) cations sharing the diffuse multi-excess electrons. For an intriguing nonlinear optical (NLO) response, these all-metal electride molecules display large electronic first hyperpolarizabilities (β0), thus a new class of NLO molecules, all-metal electride NLO molecules, emerge. Moreover, it is also found that manipulating the atomic number and position of M is a new strategy to enhance β0. As a result, CuAg@Ca7Mg(1) exhibits a considerable β0 (1.43 × 10(4) au), which is 16 times the β0 sum of two isolated CuAg and Ca7Mg(1) subunits, and this deeply reveals the fundamental origin of the considerable β0, namely, the multi-excess electrons generated by the subunit interaction. These all-metal electride molecules have the infrared (IR) transparent region of 1.3-6 μm, and hence are new IR NLO molecules. In addition the electronic contribution, β0, the large effects of vibrations on the static first hyperpolarizabilities of these all-metal electride molecules are also estimated. Thus, this study opens the new research field of all-metal electride IR NLO molecules.

  15. Nonlinear density fluctuation field theory for large scale structure

    Institute of Scientific and Technical Information of China (English)

    Yang Zhang; Hai-Xing Miao


    We develop an effective field theory of density fluctuations for a Newtonian self-gravitating N-body system in quasi-equilibrium and apply it to a homogeneous uni-verse with small density fluctuations. Keeping the density fluctuations up to second or-der, we obtain the nonlinear field equation of 2-pt correlation ξ(r), which contains 3-pt correlation and formal ultra-violet divergences. By the Groth-Peebles hierarchical ansatz and mass renormalization, the equation becomes closed with two new terms beyond the Gaussian approximation, and their coefficients are taken as parameters. The analytic solu-tion is obtained in terms of the hypergeometric functions, which is checked numerically.With one single set of two fixed parameters, the correlation ξ(r) and the corresponding power spectrum P(k) simultaneously match the results from all the major surveys, such as APM, SDSS, 2dfGRS, and REFLEX. The model gives a unifying understanding of several seemingly unrelated features of large scale structure from a field-theoretical per-spective. The theory is worth extending to study the evolution effects in an expanding universe.

  16. Structure-preserving integrators in nonlinear structural dynamics and flexible multibody dynamics

    CERN Document Server


    This book focuses on structure-preserving numerical methods for flexible multibody dynamics, including nonlinear elastodynamics and geometrically exact models for beams and shells. It also deals with the newly emerging class of variational integrators as well as Lie-group integrators. It discusses two alternative approaches to the discretization in space of nonlinear beams and shells. Firstly, geometrically exact formulations, which are typically used in the finite element community and, secondly, the absolute nodal coordinate formulation, which is popular in the multibody dynamics community. Concerning the discretization in time, the energy-momentum method and its energy-decaying variants are discussed. It also addresses a number of issues that have arisen in the wake of the structure-preserving discretization in space. Among them are the parameterization of finite rotations, the incorporation of algebraic constraints and the computer implementation of the various numerical methods. The practical application...

  17. Nonlinear optical response of a two-dimensional atomic crystal. (United States)

    Merano, Michele


    The theory of Bloembergen and Pershan for the light waves at the boundary of nonlinear media is extended to a nonlinear two-dimensional (2D) atomic crystal, i.e., a single planar atomic lattice, placed between linear bulk media. The crystal is treated as a zero-thickness interface, a real 2D system. Harmonic waves emanate from it. Generalization of the laws of reflection and refraction give the direction and the intensity of the harmonic waves. As a particular case that contains all the essential physical features, second-order harmonic generation is considered. The theory, due to its simplicity that stems from the special character of a single planar atomic lattice, is able to elucidate and explain the rich experimental details of harmonic generation from a 2D atomic crystal.

  18. Terahertz-Driven Nonlinear Spin Response of Antiferromagnetic Nickel Oxide (United States)

    Baierl, S.; Mentink, J. H.; Hohenleutner, M.; Braun, L.; Do, T.-M.; Lange, C.; Sell, A.; Fiebig, M.; Woltersdorf, G.; Kampfrath, T.; Huber, R.


    Terahertz magnetic fields with amplitudes of up to 0.4 Tesla drive magnon resonances in nickel oxide while the induced dynamics is recorded by femtosecond magneto-optical probing. We observe distinct spin-mediated optical nonlinearities, including oscillations at the second harmonic of the 1 THz magnon mode. The latter originate from coherent dynamics of the longitudinal component of the antiferromagnetic order parameter, which are probed by magneto-optical effects of second order in the spin deflection. These observations allow us to dynamically disentangle electronic from lattice-related contributions to magnetic linear birefringence and dichroism—information so far only accessible by ultrafast THz spin control. The nonlinearities discussed here foreshadow physics that will become essential in future subcycle spin switching.

  19. The emergence of a coherent structure for coherent structures: localized states in nonlinear systems


    Dawes, Jonathan


    Coherent structures emerge from the dynamics of many kinds of dissipative, externally driven, nonlinear systems, and continue to provoke new questions that challenge our physical and mathematical understanding. In one specific sub-class of such problems, where a pattern-forming, or `Turing', instability occurs, rapid progress has been made recently in our understanding of the formation of localized states: patches of regular pattern surrounded by the unpatterned homogeneous background state. ...

  20. Frequency Response of Synthetic Vocal Fold Models with Linear and Nonlinear Material Properties (United States)

    Shaw, Stephanie M.; Thomson, Scott L.; Dromey, Christopher; Smith, Simeon


    Purpose The purpose of this study was to create synthetic vocal fold models with nonlinear stress-strain properties and to investigate the effect of linear versus nonlinear material properties on fundamental frequency during anterior-posterior stretching. Method Three materially linear and three materially nonlinear models were created and stretched up to 10 mm in 1 mm increments. Phonation onset pressure (Pon) and fundamental frequency (F0) at Pon were recorded for each length. Measurements were repeated as the models were relaxed in 1 mm increments back to their resting lengths, and tensile tests were conducted to determine the stress-strain responses of linear versus nonlinear models. Results Nonlinear models demonstrated a more substantial frequency response than did linear models and a more predictable pattern of F0 increase with respect to increasing length (although range was inconsistent across models). Pon generally increased with increasing vocal fold length for nonlinear models, whereas for linear models, Pon decreased with increasing length. Conclusions Nonlinear synthetic models appear to more accurately represent the human vocal folds than linear models, especially with respect to F0 response. PMID:22271874

  1. Nonlinear Kalman Filtering in Affine Term Structure Models

    DEFF Research Database (Denmark)

    Christoffersen, Peter; Dorion, Christian; Jacobs, Kris;


    The extended Kalman filter, which linearizes the relationship between security prices and state variables, is widely used in fixed-income applications. We investigate whether the unscented Kalman filter should be used to capture nonlinearities and compare the performance of the Kalman filter...... with that of the particle filter. We analyze the cross section of swap rates, which are mildly nonlinear in the states, and cap prices, which are highly nonlinear. When caps are used to filter the states, the unscented Kalman filter significantly outperforms its extended counterpart. The unscented Kalman filter also...

  2. Structural Identification of Nonlinear Static System on Basis of Analysis Sector Sets

    Directory of Open Access Journals (Sweden)

    Nikolay Karabutov


    Full Text Available Methods of structural identification of static systems with a vector input and several nonlinearities in the conditions of uncertainty are considered. We consider inputs irregular. The concept of structural space is introduced. In this space special structures (virtual portraits are analyzed. The Holder condition is applied to construction of sector set, to which belongs a virtual portrait of system of identification. Criteria of decision-making on a class of nonlinear functions on the basis of the analysis of proximity of sector sets are described. Procedures of an estimation of structural parameters of two classes of nonlinearities are stated: power and a hysteresis.

  3. Optimization Formulations for the Maximum Nonlinear Buckling Load of Composite Structures

    DEFF Research Database (Denmark)

    Lindgaard, Esben; Lund, Erik


    , benchmarked on a number of numerical examples of laminated composite structures for the maximization of the buckling load considering fiber angle design variables. The optimization formulations are based on either linear or geometrically nonlinear analysis and formulated as mathematical programming problems...... solved using gradient based techniques. The developed local criterion is formulated such it captures nonlinear effects upon loading and proves useful for both analysis purposes and as a criterion for use in nonlinear buckling optimization. © 2010 Springer-Verlag....

  4. Measurement of nonlinear elastic response in rock by the resonant bar method

    Energy Technology Data Exchange (ETDEWEB)

    Johnson, P.A. [Los Alamos National Lab., NM (United States); Rasolofosaon, P.; Zinszner, B. [Institut Francais du Petrole (IFP), 92 - Rueil-Malmaison (France)


    In this work we are studying the behavior of the fundamental (Young`s) mode resonant peak as a function of drive amplitude in rock samples. Our goal from these studies is to obtain nonlinear moduli for many rock types, and to study the nonlinear moduli as a function of water saturation and other changes in physical properties. Measurements were made on seven different room dry rock samples. For one sample measurements were taken at 16 saturation levels between 1 and 98%. All samples display a ``softening`` nonlinearity, that is, the resonant frequency shifts downward with increasing drive amplitude. In extreme cases, the resonant frequency changes by as much as 25% over a strain interval of 10{sup {minus}7} to {approximately}4 {times} 10{sup {minus}5}. Measurements indicate that the nonlinear response is extremely sensitive to saturation. Estimates of a combined cubic and quartic nonlinear parameter {Gamma} range from approximately {minus}300 to {minus}10{sup 9} for the rock samples.

  5. Numerical investigation of amplitude-dependent dynamic response in acoustic metamaterials with nonlinear oscillators. (United States)

    Manimala, James M; Sun, C T


    The amplitude-dependent dynamic response in acoustic metamaterials having nonlinear local oscillator microstructures is studied using numerical simulations on representative discrete mass-spring models. Both cubically nonlinear hardening and softening local oscillator cases are considered. Single frequency, bi-frequency, and wave packet excitations at low and high amplitude levels were used to interrogate the models. The propagation and attenuation characteristics of harmonic waves in a tunable frequency range is found to correspond to the amplitude and nonlinearity-dependent shifts in the local resonance bandgap for such nonlinear acoustic metamaterials. A predominant shift in the propagated wave spectrum towards lower frequencies is observed. Moreover, the feasibility of amplitude and frequency-dependent selective filtering of composite signals consisting of individual frequency components which fall within propagating or attenuating regimes is demonstrated. Further enrichment of these wave manipulation mechanisms in acoustic metamaterials using different combinations of nonlinear microstructures presents device implications for acoustic filters and waveguides.

  6. Review of Response and Damage of Linear and Nonlinear Systems under Multiaxial Vibration

    Directory of Open Access Journals (Sweden)

    Ed Habtour


    Full Text Available A review of past and recent developments in multiaxial excitation of linear and nonlinear structures is presented. The objective is to review some of the basic approaches used in the analytical and experimental methods for kinematic and dynamic analysis of flexible mechanical systems, and to identify future directions in this research area. In addition, comparison between uniaxial and multiaxial excitations and their impact on a structure’s life-cycles is provided. The importance of understanding failure mechanisms in complex structures has led to the development of a vast range of theoretical, numerical, and experimental techniques to address complex dynamical effects. Therefore, it is imperative to identify the failure mechanisms of structures through experimental and virtual failure assessment based on correctly identified dynamic loads. For that reason, techniques for mapping the dynamic loads to fatigue were provided. Future research areas in structural dynamics due to multiaxial excitation are identified as (i effect of dynamic couplings, (ii modal interaction, (iii modal identification and experimental methods for flexible structures, and (iv computational models for large deformation in response to multiaxial excitation.

  7. Nonlinear Dynamic Behavior of a Flexible Structure to Combined External Acoustic and Parametric Excitation

    Directory of Open Access Journals (Sweden)

    Paulo S. Varoto


    Full Text Available Flexible structures are frequently subjected to multiple inputs when in the field environment. The accurate determination of the system dynamic response to multiple inputs depends on how much information is available from the excitation sources that act on the system under study. Detailed information include, but are not restricted to appropriate characterization of the excitation sources in terms of their variation in time and in space for the case of distributed loads. Another important aspect related to the excitation sources is how inputs of different nature contribute to the measured dynamic response. A particular and important driving mechanism that can occur in practical situations is the parametric resonance. Another important input that occurs frequently in practice is related to acoustic pressure distributions that is a distributed type of loading. In this paper, detailed theoretical and experimental investigations on the dynamic response of a flexible cantilever beam carrying a tip mass to simultaneously applied external acoustic and parametric excitation signals have been performed. A mathematical model for transverse nonlinear vibration is obtained by employing Lagrange’s equations where important nonlinear effects such as the beam’s curvature and quadratic viscous damping are accounted for in the equation of motion. The beam is driven by two excitation sources, a sinusoidal motion applied to the beam’s fixed end and parallel to its longitudinal axis and a distributed sinusoidal acoustic load applied orthogonally to the beam’s longitudinal axis. The major goal here is to investigate theoretically as well as experimentally the dynamic behavior of the beam-lumped mass system under the action of these two excitation sources. Results from an extensive experimental work show how these two excitation sources interacts for various testing conditions. These experimental results are validated through numerically simulated results

  8. Modelling the nonlinear response of fibre-reinforced bending fluidic actuators (United States)

    Cacucciolo, Vito; Renda, Federico; Poccia, Ernesto; Laschi, Cecilia; Cianchetti, Matteo


    Soft actuators are receiving increasing attention from the engineering community, not only in research but even for industrial applications. Among soft actuators, fibre-reinforced bending fluidic actuators (BFAs) became very popular thanks to features such as robustness and easy design and fabrication. However, an accurate modelling of these smart structures, taking into account all the nonlinearities involved, is a challenging task. In this effort, we propose an analytical mechanical model to capture the quasi-static response of fibre-reinforced BFAs. The model is fully 3D and for the first time includes the effect of the pressure on the lateral surface of the chamber as well as the non-constant torque produced by the pressure at the tip. The presented model can be used for design and control, while providing information about the mechanics of these complex actuators.

  9. Analysis of Dynamic Model of a Structure with Nonlinear Damped Behavior

    Directory of Open Access Journals (Sweden)

    G. Domairry


    Full Text Available In this work, it has been attempted to analytically treat the nonlinear behavior of structures. Since analysing nonlinear problems is of great difficulty, different numerical methods and software are advised to treat such problems. Despite the increasing expenses of building structures to maintain their linear behavior, nonlinearity has been inevitable, and therefore, nonlinear analysis has beenof great importance to the scientists in the field. As structures confront lateral forces and intense earthquakes especially near fault regions, a part of the structure remains linear, but some part of itbehaves nonlinearly for example dampers, columns and beams. This is simulated by a damped in nonlinear oscillator. In this paper, the nonlinear equation of oscillator with damping which has nonlinear behavior is representative of the dynamic behavior of a structure has been solved analytically. In the end, the obtained results are compared with numerical ones and shown in graphs and in tables;analytical solutions are in good agreement with those of the numerical method.

  10. Indications of nonlinear structures in brain electrical activity (United States)

    Gautama, Temujin; Mandic, Danilo P.; van Hulle, Marc M.


    The dynamical properties of electroencephalogram (EEG) segments have recently been analyzed by Andrzejak and co-workers for different recording regions and for different brain states, using the nonlinear prediction error and an estimate of the correlation dimension. In this paper, we further investigate the nonlinear properties of the EEG signals using two established nonlinear analysis methods, and introduce a “delay vector variance” (DVV) method for better characterizing a time series. The proposed DVV method is shown to enable a comprehensive characterization of the time series, allowing for a much improved classification of signal modes. This way, the analysis of Andrzejak and co-workers can be extended toward classification of different brain states. The obtained results comply with those described by Andrzejak et al., and provide complementary indications of nonlinearity in the signals.

  11. Extending modal testing technology for model validation of engineering structures with sparse nonlinearities: A first case study (United States)

    delli Carri, Arnaldo; Weekes, B.; Di Maio, Dario; Ewins, D. J.


    Modal testing is widely used today as a means of validating theoretical (Finite Element) models for the dynamic analysis of engineering structures, prior to these models being used for optimisation of product design. Current model validation methodology is confined to linear models and is primarily concerned with (i) correcting inaccurate model parameters and (ii) ensuring that sufficient elements are included for these cases, using measured data. Basic experience is that this works quite well, largely because the weaknesses in the models are relatively sparse and, as a result, are usually identifiable and correctable. The current state-of-the-art in linear model validation has contributed to an awareness that residual errors in FE models are increasingly the consequence of some unrepresented nonlinearity in the structure. In these cases, additional, higher order parameters are required to improve the model so that it can represent the nonlinear behaviour. This is opposed to the current practice of simply refining the mesh. Again, these nonlinear features are generally localised, and are often associated with joints. We seek to provide a procedure for extending existing modal testing to enable these nonlinear elements to be addressed using current nonlinear identification methods directed at detection, characterisation, location and then quantification - in order to enhance the elements in an FE model as necessary to describe nonlinear dynamic behaviour. Emphasis is placed on the outcome of these extended methods to relate specifically to the physical behaviour of the relevant components of the structure, rather than to the nonlinear response characteristics that are the result of their presence.

  12. Nonlinear dynamic response and active control of fiber metal laminated plates with piezoelectric actuators and sensors in unsteady temperature field (United States)

    Shao, Xuefei; Fu, Yiming; Chen, Yang


    Based on the higher order shear deformation theory and the geometric nonlinear theory, the nonlinear motion equations, to which the effects of the positive and negative piezoelectric and the thermal are introduced by piezoelectric fiber metal laminated (FML) plates in an unsteady temperature, are established by Hamilton’s variational principle. Then, the control algorithm of negative-velocity feedback is applied to realize the vibration control of the piezoelectric FML plates. During the solving process, firstly, the formal functions of the displacements that fulfilled the boundary conditions are proposed. Then, heat conduction equations and nonlinear differential equations are dealt with using the differential quadrature (DQ) and Galerkin methods, respectively. On the basis of the previous processing, the time domain is dispersed by the Newmark-β method. Finally, the whole problem can be investigated by the iterative method. In the numerical examples, the influence of the applied voltage, the temperature loading and geometric parameters on the nonlinear dynamic response of the piezoelectric FML plates is analyzed. Meanwhile, the effect of feedback control gain and the position of the piezoelectric layer, the initial deflection and the external temperature on the active control effect of the piezoelectric layers has been studied. The model development and the research results can serve as a basis for nonlinear vibration analysis of the FML structures.

  13. The Effect of Temperature Dependent Material Nonlinearities on the Response of Piezoelectric Composite Plates (United States)

    Lee, Ho-Jun; Saravanos, Dimitris A.


    Previously developed analytical formulations for piezoelectric composite plates are extended to account for the nonlinear effects of temperature on material properties. The temperature dependence of the composite and piezoelectric properties are represented at the material level through the thermopiezoelectric constitutive equations. In addition to capturing thermal effects from temperature dependent material properties, this formulation also accounts for thermal effects arising from: (1) coefficient of thermal expansion mismatch between the various composite and piezoelectric plies and (2) pyroelectric effects on the piezoelectric material. The constitutive equations are incorporated into a layerwise laminate theory to provide a unified representation of the coupled mechanical, electrical, and thermal behavior of smart structures. Corresponding finite element equations are derived and implemented for a bilinear plate element with the inherent capability to model both the active and sensory response of piezoelectric composite laminates. Numerical studies are conducted on a simply supported composite plate with attached piezoceramic patches under thermal gradients to investigate the nonlinear effects of material property temperature dependence on the displacements, sensory voltages, active voltages required to minimize thermal deflections, and the resultant stress states.

  14. Enhanced optical and nonlinear optical responses in a polyelectrolyte templated Langmuir-Blodgett film. (United States)

    Rajesh, K; Balaswamy, B; Yamamoto, K; Yamaki, H; Kawamata, J; Radhakrishnan, T P


    Optical and nonlinear optical properties like fluorescence and second harmonic generation (SHG) of molecular materials can be strongly influenced by the mode of assembly of the molecules. The Langmuir-Blodgett (LB) technique is an elegant route to the controlled assembly of molecules in ultrathin films, and complexation of ionic amphiphiles in the Langmuir film by polyions introduced in the aqueous subphase provides a simple and efficient access to further control, stabilization, and optimization. The monolayer LB film of the hemicyanine-based amphiphile, N-n-octadecyl-4-[2-(4-(N,N-ethyloctadecylamino)phenyl)ethenyl]pyridinium possessing a "tail-head-tail" structure, shows fluorescence as well as SHG response. The concomitant enhancement of both of these linear and nonlinear optical attributes is achieved through templating with the polyanion of carboxymethylcellulose. Brewster angle and atomic force microscopy reveal the influence of polyelectrolyte templating on the morphology of the Langmuir and LB films. Polarized absorption and fluorescence spectroscopy provide insight into the impact of complexation with the polyelectrolyte on the orientation and deaggregation of the hemicyanine headgroup leading to fluorescence and SHG enhancement in the LB film.

  15. Structural analysis of composite wind turbine blades nonlinear mechanics and finite element models with material damping

    CERN Document Server

    Chortis, Dimitris I


    This book concerns the development of novel finite elements for the structural analysis of composite beams and blades. The introduction of material damping is also an important aspect of composite structures and it is presented here in terms of their static and dynamic behavior. The book thoroughly presents a new shear beam finite element, which entails new blade section mechanics, capable of predicting structural blade coupling due to composite coupling and/or internal section geometry. Theoretical background is further expanded towards the inclusion of nonlinear structural blade models and damping mechanics for composite structures. The models effectively include geometrically nonlinear terms due to large displacements and rotations, improve the modeling accuracy of very large flexible blades, and enable the modeling of rotational stiffening and buckling, as well as, nonlinear structural coupling. Validation simulations on specimen level study the geometric nonlinearities effect on the modal frequencies and...


    Institute of Scientific and Technical Information of China (English)

    罗达玲; 杨健明; 等


    Either sublinear or supralinear responses of dosimeters to γ-ray can be described by a response function derived from statistical Poisson distribution.The characteristic parameters of the function determine linearity,sublinearity and supralinearlty in their responses.The experimental data of gamma dose-responses of alanine ESR dosimeters film dosimeters.LiF(Mg,Cu,P) and LiF(Mg,Ti) thermoluminescence dosimeters are used to test the response function.

  17. Analysis of interlaminar stress and nonlinear dynamic response for composite laminated plates with interfacial damage

    Institute of Scientific and Technical Information of China (English)

    F. H. Zhu; Y. M. Fu


    By considering the effect of interfacial damage and using the variation principle, three-dimensional nonli-near dynamic governing equations of the laminated plates with interfacial damage are derived based on the general six-degrees-of-freedom plate theory towards the accurate stress analysis. The solutions of interlaminar stress and nonlinear dynamic response for a simply supported laminated plate with interfacial damage are obtained by using the finite dif-ference method, and the results are validated by compari-son with the solution of nonlinear finite element method. In numerical calculations, the effects of interfacial damage on the stress in the interface and the nonlinear dynamic response of laminated plates are discussed.

  18. Experimental Detection and Quantification of Structural Nonlinearity Using Homogeneity and Hilbert Transform Methods

    DEFF Research Database (Denmark)

    Kragh, Knud Abildgaard; Thomsen, Jon Juel; Tcherniak, Dmitri


    exists. The present study suggests a framework for the detection of structural nonlinearities. Two methods for detection are compared, the homogeneity method and a Hilbert transform based method. Based on these two methods, a nonlinearity index is suggested. Through simulations and laboratory experiments...

  19. Nonlinear Super Integrable Couplings of Super Dirac Hierarchy and Its Super Hamiltonian Structures

    Institute of Scientific and Technical Information of China (English)



    We construct nonlinear super integrable couplings of the super integrable Dirac hierarchy based on an enlarged matrix Lie superalgebra. Then its super Hamiltonian structure is furnished by super trace identity. As its reduction, we gain the nonlinear integrable couplings of the classical integrable Dirac hierarchy.

  20. Optimization of hardening/softening behavior of plane frame structures using nonlinear normal modes

    DEFF Research Database (Denmark)

    Dou, Suguang; Jensen, Jakob Søndergaard


    /softening behavior of nonlinear mechanical systems. The iterative optimization procedure consists of calculation of nonlinear normal modes, solving an adjoint equation system for sensitivity analysis and an update of design variables using a mathematical programming tool. We demonstrate the method with examples......Devices that exploit essential nonlinear behavior such as hardening/softening and inter-modal coupling effects are increasingly used in engineering and fundamental studies. Based on nonlinear normal modes, we present a gradient-based structural optimization method for tailoring the hardening...

  1. Cylindrical PVF2 film based fiber optic phase modulator - Phase shift nonlinearity and frequency response (United States)

    Sudarshanam, V. S.; Claus, Richard O.


    A new cylindrical coil configuration for polyvinylidene flouride (PVF2) film based fiber optic phase modulator is studied for the frequency response and nonlinearity of phase shift at the resonance frequency. This configuration, hitherto unapproached for PVF2 film modulators, offers resonance at well defined, controllable and higher frequencies than possible for the flat-strip configuration. Two versions of this configuration are presented that differ strongly in both the resonance frequency and the phase shift nonlinearity coefficient.

  2. Nonlinear Site Response Due to Large Ground Acceleration: Observation and Computer Simulation (United States)

    Noguchi, S.; Furumura, T.; Sasatani, T.


    We studied nonlinear site response due to large ground acceleration during the 2003 off-Miyagi Earthquake (Mw7.0) in Japan by means of horizontal-to-vertical spectral ratio analysis of S-wave motion. The results were then confirmed by finite-difference method (FDM) simulation of nonlinear seismic wave propagation. A nonlinear site response is often observed at soft sediment sites, and even at hard bedrock sites which are covered by thin soil layers. Nonlinear site response can be induced by strong ground motion whose peak ground acceleration (PGA) exceeds about 100 cm/s/s, and seriously affects the amplification of high frequency ground motion and PGA. Noguchi and Sasatani (2008) developed an efficient technique for quantitative evaluation of nonlinear site response using the horizontal-to-vertical spectral ratio of S-wave (S-H/V) derived from strong ground motion records, based on Wen et al. (2006). We applied this technique to perform a detailed analysis of the properties of nonlinear site response based on a large amount of data recorded at 132 K-NET and KiK-net strong motion stations in Northern Japan during the off-Miyagi Earthquake. We succeeded in demonstrating a relationship between ground motion level, nonlinear site response and surface soil characteristics. For example, the seismic data recorded at KiK-net IWTH26 showed obvious characteristics of nonlinear site response when the PGA exceeded 100 cm/s/s. As the ground motion level increased, the dominant peak of S-H/V shifted to lower frequency, the high frequency level of S-H/V dropped, and PGA amplification decreased. On the other hand, the records at MYGH03 seemed not to be affected by nonlinear site response even for high ground motion levels in which PGA exceeds 800 cm/s/s. The characteristics of such nonlinear site amplification can be modeled by evaluating Murnaghan constants (e.g. McCall, 1994), which are the third-order elastic constants. In order to explain the observed characteristics of

  3. Nonlinear electromagnetic responses of active membrane protein complexes in live cells and organelles (United States)

    Nawarathna, Dharmakirthi

    The response of biological cells to an applied oscillating electric field contains both linear and nonlinear components (eg. induced harmonics). Such noninvasive measurements can be used to study active processes taking place inside the cells. The measurement of induced harmonics is the tool used for the study described here. A highly sensitive superconducting quantum interference device (SQUID) is used to detect the response at low frequencies, which greatly reduces electrode polarization effects. At high frequencies, a four- probe method is used. At low frequencies, harmonic generation by budding yeast cells in response to a sinusoidal electric field is reported, which is seen to be minimal when the field amplitude is less than a threshold value. Surprisingly, sodium metavanadate, an inhibitor of P-type ATPases and glucose, a substrate of P-type ATPase responsible for nonlinear response in yeast, reduces the threshold field amplitude, increasing harmonic generation at low amplitudes while reducing it at large amplitudes. We have thus proposed a model that explicitly introduces a threshold field, similar to those observed in density waves, where fields above threshold drive charge transport through an energy landscape with multiple wells, and in Coulomb blockade tunnel junctions, recently exploited to define the current standard. At high frequencies, the induced harmonics exhibit pronounced features that depend on the specific organism. Budding yeast (S. cerevisiae ) cells produce numerous harmonics. When the second or third harmonic amplitude is plotted vs. applied frequency, we observe two peaks, around 3 kHz and 12 kHz, which are suppressed by the respiratory inhibitor potassium cyanide. We then measured the response to oscillatory electric fields of intact bovine heart mitochondria, a reproducible second harmonic (at ˜3-4 kHz applied frequency) was detected. Further, with coupled mouse mitochondria, an ADP sensitive peak (˜ 12-15 kHz applied frequency) was

  4. Nonlinear system identification in structural dynamics: 10 more years of progress (United States)

    Noël, J. P.; Kerschen, G.


    Nonlinear system identification is a vast research field, today attracting a great deal of attention in the structural dynamics community. Ten years ago, an MSSP paper reviewing the progress achieved until then [1] concluded that the identification of simple continuous structures with localised nonlinearities was within reach. The past decade witnessed a shift in emphasis, accommodating the growing industrial need for a first generation of tools capable of addressing complex nonlinearities in larger-scale structures. The objective of the present paper is to survey the key developments which arose in the field since 2006, and to illustrate state-of-the-art techniques using a real-world satellite structure. Finally, a broader perspective to nonlinear system identification is provided by discussing the central role played by experimental models in the design cycle of engineering structures.

  5. Nonlinearity of dose-response functions for carcinogenicity.


    Hoel, D G; Portier, C J


    Carcinogenesis data for 315 chemicals were obtained from the National Cancer Institute-National Toxicology Program (NCI-NTP) bioassay programs and were analyzed to examine the shape of carcinogenesis dose-response curves. Tumor site data were more often consistent with a quadratic response than with a linear response, suggesting that the routine use of linear dose-response models will often overestimate risk. Information from in vivo short-term mutagenicity and genotoxicity assays was also ob...

  6. Computational Modelling Strategies for Nonlinear Response Prediction of Corroded Circular RC Bridge Piers

    Directory of Open Access Journals (Sweden)

    Mohammad M. Kashani


    Full Text Available A numerical model is presented that enables simulation of the nonlinear flexural response of corroded reinforced concrete (RC components. The model employs a force-based nonlinear fibre beam-column element. A new phenomenological uniaxial material model for corroded reinforcing steel is used. This model accounts for the impact of corrosion on buckling strength, postbuckling behaviour, and low-cycle fatigue degradation of vertical reinforcement under cyclic loading. The basic material model is validated through comparison of simulated and observed responses for uncorroded RC columns. The model is used to explore the impact of corrosion on the inelastic response of corroded RC columns.

  7. Analytical and Experimental Random Vibration of Nonlinear Aeroelastic Structures. (United States)


    full) are belon- ging to the first normal mode which obviously pre- 0 0.3 oC og s .a ,i e domiwates the response. It is also seen that asmas the...543. New Mexico Ewins. D 1 (1969). The effects of dentuning upon the forced vibrations of Bliven. D 0. and Soong. T T (1969) On frequencies of elastic...1986) Interactive multiobjective fuzzy optim- thesis. Univ of New Mexico . zation design of ship grillage structure Proa of the 1st ant conference on

  8. On the Nonlinear Structural Analysis of Wind Turbine Blades using Reduced Degree-of-Freedom Models

    DEFF Research Database (Denmark)

    Holm-Jørgensen, Kristian; Larsen, Jesper Winther; Nielsen, Søren R.K.


    , modelling geometrical and inertial nonlinear couplings in the fundamental flap and edge direction. The purpose of this article is to examine the applicability of such a reduced-degree-of-freedom model in predicting the nonlinear response and stability of a blade by comparison to a full model based...... on a nonlinear co-rotating FE formulation. By use of the reduced-degree-of-freedom model it is shown that under strong resonance excitation of the fundamental flap or edge modes, significant energy is transferred to higher modes due to parametric or nonlinear coupling terms, which influence the response...... representing the case of infinitely many included modes, is shown to predict stable and ordered response for all considered parameters. Further, the analysis shows that the reduced-degree-of-freedom model of relatively low order overestimates the response near resonance peaks, which is a consequence...

  9. Nonlinear oscillatory rheology and structure of wormlike micellar solutions and colloidal suspensions (United States)

    Gurnon, Amanda Kate

    this constitutive model are tested by comparison with experiments on model WLM solutions. Further comparisons to the nonlinear oscillatory shear responses measured from colloidal suspensions establishes this analysis as a promising, quantitative method for understanding the underlying mechanisms responsible for the nonlinear dynamic response of complex fluids. A new experimental technique is developed to measure the microstructure of complex fluids during steady and transient shear flow using small-angle neutron scattering (SANS). The Flow-SANS experimental method is now available to the broader user communities at the NIST Center for Neutron Research, Gaithersburg, MD and the Institut Laue-Langevin, Grenoble, France. Using this new method, a model shear banding WLM solution is interrogated under steady and oscillatory shear. For the first time, the flow-SANS methods identify new metastable states for shear banding WLM solutions, thus establishing the method as capable of probing new states not accessible using traditional steady or linear oscillatory shear methods. The flow-induced three-dimensional microstructure of a colloidal suspension under steady and dynamic oscillatory shear is also measured using these rheo- and flow-SANS methods. A new structure state is identified in the shear thickening regime that proves critical for defining the "hydrocluster" microstructure state of the suspension that is responsible for shear thickening. For both the suspensions and the WLM solutions, stress-SANS rules with the measured microstructures define the individual stress components arising separately from conservative and hydrodynamic forces and these are compared with the macroscopic rheology. Analysis of these results defines the crucial length- and time-scales of the transient microstructure response. The novel dynamic microstructural measurements presented in this dissertation provide new insights into the complexities of shear thickening and shear banding flow phenomena

  10. Ultrafast third-order nonlinear optical response of pyrene derivatives (United States)

    Shi, Yufang; Li, Zhongguo; Fang, Yu; Sun, Jinyu; Zhao, Minggen; Song, Yinglin


    Two mono-substituted pyrene derivatives with delocalized electron system 1-(pyren-1-yl)-3-(4-Methyl thiophene-2-yl) acrylic ketone (13#) and 1-(pyren-1-yl)-3-(4-bromo thiophene-2-yl) acrylic ketone (15#) were successfully synthesized. The resultant compounds were characterized by nuclear magnetic resonance (NMR), infrared spectroscopy (IR), high resolution mass spectrum (HR-MS), and UV-vis spectra. The third-order nonlinear optical properties of the compounds were investigated using Z-scan technique with femtosecond laser pulses at 500 nm and 700 nm, respectively. Both of the compounds showed a decrease in transmittance about the focus, which are typical of two-photon absorption. It was found that the two-photon absorption behavior of the pyrene derivatives were modified by substituents on thiophene ring. These results indicate that both compounds can be promising candidates for future optoelectronic and bio-imaging applications.


    Institute of Scientific and Technical Information of China (English)

    XingJ.T; PriceW.G; ChenY.G


    A numerical method for simulating nonlinear fluid-rigid structure interaction problems is developed. The structure is assumed to undergo large rigid body motions and the fluid flow is governed by nonlinear, viscous or non-viscous, field equations with nonlinear boundary conditions applied to the free surface and fluid-solid interaction interfaces. An Arbitrary-Lagrangian-Eulerian (ALE) mesh system is used to construct the numerical model. A multi-block numerical scheme of study is adopted allowing for the relative motion between moving overset grids, which are independent of one another. This provides a convenient method to overcome the difficulties in matching fluid meshes with large solid motions. Nonlinear numerical equations describing nonlinear fluid-solid interaction dynamics are derived through a numerical discretization scheme of study. A coupling iteration process is used to solve these numerical equations. Numerical examples are presented to demonstrate applications of the model developed.

  12. Metamodel for nonlinear dynamic response analysis of damaged laminated composites

    Directory of Open Access Journals (Sweden)

    Mahmoudi S.


    Full Text Available Damage affects negatively the safety of the structure and can lead to failure. Thus, it is recommended to use structural health monitoring techniques in order to detect, localize and quantify damage. The main aim of the current work is the development of a numerical metamodel to investigate the dynamic behavior of damaged composite structures. Hence, a metamodelling for damage prediction and dynamic behavior analysis of laminate composite structures is proposed, wherein the stress state in the structure is used as indicative parameters and artificial neural networks as a learning tool.

  13. Excitonic effects in the nonlinear optical response of a Si(111) surface

    Energy Technology Data Exchange (ETDEWEB)

    Stamova, Maria; Rebentrost, Frank [Max-Planck-Institut fuer Quantenoptik, 85748 Garching (Germany)


    We discuss methods to calculate the linear and nonlinear optical spectra for cyclic cluster models of an ideal Si(111) surface. The cluster approach offers the possibility to implement the excitonic effects due to the Coulomb interaction between electron and hole in a relatively straight-forward way. In order to appproximate a situation resembling a surface we use clusters with several hundreds of Si atoms. The electronic structure is obtained from a tight-binding parametrization of the hamiltonian. A time-dependent density operator formalism is used to calculate the response functions S({tau}) and S({tau}{sub 1},{tau}{sub 2}) for the optical polarization, which also directly describe the response to ultrashort pulses. Their Fourier transforms are the frequency-dependent optical susceptibilities {chi}{sup (1)}(-{omega};{omega}) and {chi}{sup (2)} (-{omega}{sub 1}-{omega}{sub 2};{omega}{sub 1},{omega}{sub 2}) for second-harmonic ({omega}{sub 1} ={omega}{sub 2}) or sum-frequency generation from surfaces. The excitonic Coulomb interaction is treated in the time-dependent Hartree-Fock approximation, leading to large sets of differential equations that are integrated explicitly. The results on the linear susceptibility are in accord with earlier findings on the excitonic origin of the relative intensities of the E{sub 1} and E{sub 2} peaks near 3.4 and 4.3 eV. We present new results on excitonic effects in the nonlinear spectra and investigate in particular the surface-related peaks near 2{Dirac_h}{omega}= 1.3-1.5 and 2.4 eV that govern the strong enhancement observed in SHG of clean silicon surfaces. (Abstract Copyright [2010], Wiley Periodicals, Inc.)

  14. Generalized Dromion Structures of New (2 + 1)-Dimensional Nonlinear EvolutionEquation

    Institute of Scientific and Technical Information of China (English)

    ZHANG Jie-Fang


    We derive the generalized dromions of the new (2 + 1)-dimensional nonlinear evolution equation by the arbitrary function presented in the bilinearized linear equations. The rich soliton and dromion structures for this system are released.

  15. Nonlinear variable structure excitation and steam valving controllers for power system stability

    Institute of Scientific and Technical Information of China (English)

    Ben WANG; Zongyuan MAO


    A set of novel nonlinear variable structure excitation and steam-valving controllers are proposed in this paper.On the basis of the classical dynamic equations of a generator,excitation control and steam valving control are si-multaneously considered.Design of these controllers combines the differential geometry theory with the variable structure controlling theory.The mathematical model in the form of "an affine nonlinear system" is set up for the control design of a large-scale power plant.The dynamic performance of the nonlinear variable structure controllers proposed for a single ma-chine connected to an infinite bus power system is simulated.Simulation results show that the nonlinear variable structure excitation and steam-valving controllers give satisfactory dynamic performance and good robustness.

  16. Longtime dynamics of the quasi-linear wave equations with structural damping and supercritical nonlinearities (United States)

    Yang, Zhijian; Liu, Zhiming


    The paper investigates the well-posedness and the longtime dynamics of the quasilinear wave equations with structural damping and supercritical nonlinearities: {{u}tt}- Δ u+{{≤ft(- Δ \\right)}α}{{u}t}-\

  17. Bifurcation of Positive Equilibria in Nonlinear Structured Population Models with Varying Mortality Rates

    CERN Document Server

    Walker, Christoph


    A parameter-dependent model involving nonlinear diffusion for an age-structured population is studied. The parameter measures the intensity of the mortality. A bifurcation approach is used to establish existence of positive equilibrium solutions.

  18. Long term structural dynamics of mechanical systems with local nonlinearities

    NARCIS (Netherlands)

    Fey, R.H.B.; Campen, D.H. van; Kraker, A. de


    This paper deals with the long term behavior of periodically excited mechanical systems consisting of linear components and local nonlinearities. The number of degrees of freedom of the linear components is reduced by applying a component mode synthesis technique. Lyapunov exponents are used to iden

  19. Note About Hamiltonian Structure of Non-Linear Massive Gravity

    CERN Document Server

    Kluson, J


    We perform the Hamiltonian analysis of non-linear massive gravity action studied recently in arXiv:1106.3344 [hep-th]. We show that the Hamiltonian constraint is the second class constraint. As a result the theory possesses an odd number of the second class constraints and hence all non physical degrees of freedom cannot be eliminated.

  20. Structure and Asymptotic theory for Nonlinear Models with GARCH Errors

    NARCIS (Netherlands)

    F. Chan (Felix); M.J. McAleer (Michael); M.C. Medeiros (Marcelo)


    textabstractNonlinear time series models, especially those with regime-switching and conditionally heteroskedastic errors, have become increasingly popular in the economics and finance literature. However, much of the research has concentrated on the empirical applications of various models, with li


    Institute of Scientific and Technical Information of China (English)

    TANG You-gang; GU Jia-yang; ZUO Jian-li; MIN Jian-qin


    The vortex-induced nonlinear vibration of casing pipes in the deep water was studied considering the loads of current and combined wave-current. The vortex-induced vibration equation of a casing pipe was set up considering the beam mode and Morison's nonlinear fluid loads as well as the vortex-excited loads. The approach of calculating vortex-excited nonlinear vibration by Galerkin's method was proposed. The natural vibration frequencies and modes were obtained, and the response including primary resonance induced by current and the composite resonance under combined wave-current for the 170 m long casing pipe in the 160 m depth of water were investigated. The results show that the dynamics response of casing pipe obviously increases, and the complicated response behaviors of casing pipe are described under combined wave-current.

  2. Regular nonlinear response of the driven Duffing oscillator to chaotic time series

    Institute of Scientific and Technical Information of China (English)

    YuanYe; Li Yue; Danilo P. Mandic; Yang Bao-Jun


    Nonlinear response of the driven Duffing oscillator to periodic or quasi-periodic signals has been well studied. In this paper, we investigate the nonlinear response of the driven Duffing oscillator to non-periodic, more specifically, chaotic time series. Through numerical simulations, we find that the driven Duffing oscillator can also show regular nonlinear response to the chaotic time series with different degree of chaos as generated by the same chaotic series generating model, and there exists a relationship between the state of the driven Duffing oscillator and the chaoticity of the input signal of the driven Duffing oscillator. One real-world and two artificial chaotic time series are used to verify the new feature of Duffing oscillator. A potential application of the new feature of Duffing oscillator is also indicated.

  3. RBFNN Model for Predicting Nonlinear Response of Uniformly Loaded Paddle Cantilever

    Directory of Open Access Journals (Sweden)

    Abdullah H. Abdullah


    Full Text Available The Radial basis Function neural network (RBFNN model has been developed for the prediction of nonlinear response for paddle Cantilever with built-in edges and different sizes, thickness and uniform loads. Learning data was performed by using a nonlinear finite element program, incremental stages of the nonlinear finite element analysis were generated by using 25 schemes of built paddle Cantilevers with different thickness and uniform distributed loads. The neural network model has 5 input nodes representing the uniform distributed load and paddle size, length, width and thickness, eight nodes at hidden layer and one output node representing the max. deflection response (1500×1 represent the deflection response of load. Regression analysis between finite element results and values predicted by the neural network model shows the least error.

  4. High-order finite difference solution for 3D nonlinear wave-structure interaction

    DEFF Research Database (Denmark)

    Ducrozet, Guillaume; Bingham, Harry B.; Engsig-Karup, Allan Peter;


    This contribution presents our recent progress on developing an efficient fully-nonlinear potential flow model for simulating 3D wave-wave and wave-structure interaction over arbitrary depths (i.e. in coastal and offshore environment). The model is based on a high-order finite difference scheme...... OceanWave3D presented in [1, 2]. A nonlinear decomposition of the solution into incident and scattered fields is used to increase the efficiency of the wave-structure interaction problem resolution. Application of the method to the diffraction of nonlinear waves around a fixed, bottom mounted circular...

  5. On the nonlinear trapping nature of undamped, coherent structures in collisionless plasmas and its impact on stability (United States)

    Schamel, Hans; Mandal, Debraj; Sharma, Devendra


    An outstanding notion for collisionless plasmas is the essential nonlinear character of their coherent structures, which in the stationary, weak amplitude limit are described by a continuum of cnoidal electron and ion hole modes governed by a multiparametric nonlinear dispersion relation. The well-known discrete structure of undamped linear plasma modes is seamlessly embedded in this nonlinear continuum as the microscopic texture of plasma begins to reveal itself in the high temperature collisionless plasma limit. This transforms the linear-threshold-based operating mechanism of plasma turbulence into a fundamental nonlinear, multifaceted one. Based on a comprehensive three-level description of increasing profundity, a proof of this novel dictum is presented, which makes use of the joint properties of such structures, their coherency and stationarity, and uses in succession a fluid, linear Vlasov and a full Vlasov description. It unifies discrete and continuum limits by resolving the inevitable resonant region and shows that coherent electrostatic equilibria are generally controlled by kinetic particle trapping and are hence fundamentally nonlinear. By forging a link between damped and growing wave solutions, these modes render plasma stability complex and difficult to evaluate due to the entangled pattern of the stability boundary in function and parameter space, respectively. A direct consequence is the existence of negative energy modes of arbitrarily small amplitudes in the subcritical region of the two-stream instability as well as the failure of linear Landau (Vlasov, van Kampen) theory, whenever resonant particles are involved, in addressing the onset of instability in a current-carrying plasma. Responsible for this subtle phase space behavior is hence the thresholdless omnipresence of the trapping nonlinearity originating from coherency. A high resolution, exact-mass-ratio, multispecies, and collisionless plasma simulation is employed to illustrate

  6. Study of Nonlinear Seismic Response and TMD Primary Control of the Cable-Stayed Bridge Section of the Third Macao-Taipa Bridge

    Institute of Scientific and Technical Information of China (English)

    Long Xiaohong; Li Li


    The practical design of the cable-stayed bridge of the 3rd Macao-Taipa bridge is investigated by the finite element analysis program ANSYS, and 3-D elements BEAM188 and BEAM4 are adopted to create a dynamic calculation model. In order to analyze the material nonlinear seismic response of the cable-stayed bridge, the nonlinear behaviors of the ductile plastic hinges of the bridge towers are taken into account by employing the nonlinear rotational spring element COMBIN40. To simulate a major earthquake, three earthquake records were chosen using a wave-choosing program and input into the bridge structure along longitudinal and transversal directions. Comparisons of the linear and nonlinear seismic responses of the cable-stayed bridge are performed. In addition, a study of TMD primary control is carried out using element MASS21 and element COMBIN14, and it is indicated that the effects of mitigation monitoring are evident.

  7. Understanding and Ameliorating Non-Linear Phase and Amplitude Responses in AMCW Lidar

    Directory of Open Access Journals (Sweden)

    John P. Godbaz


    Full Text Available Amplitude modulated continuous wave (AMCW lidar systems commonly suffer from non-linear phase and amplitude responses due to a number of known factors such as aliasing and multipath inteference. In order to produce useful range and intensity information it is necessary to remove these perturbations from the measurements. We review the known causes of non-linearity, namely aliasing, temporal variation in correlation waveform shape and mixed pixels/multipath inteference. We also introduce other sources of non-linearity, including crosstalk, modulation waveform envelope decay and non-circularly symmetric noise statistics, that have been ignored in the literature. An experimental study is conducted to evaluate techniques for mitigation of non-linearity, and it is found that harmonic cancellation provides a significant improvement in phase and amplitude linearity.

  8. Comparison of Seismic Responses for Reinforced Concrete Buildings with Mass and Stiffness Irregularities Using Pushover and Nonlinear Time History Analysis (United States)

    Teruna, D. R.


    Pushover analysis or also known as nonlinear static procedures (NSP) have been recognized in recent years for practical evaluation of seismic demands and for structural design by estimating a structural building capacities and deformation demands. By comparing these demands and capacities at the performance level interest, the seismic performance of a building can be evaluated. However, the accuracy of NSP for assessment irregular building is not yet a fully satisfactory solution, since irregularities of a building influence the dynamic responses of the building. The objective of the study presented herein is to understand the nonlinear behaviour of six story RC building with mass irregularities at different floors and stiffness irregularity at first story (soft story) using NSP. For the purpose of comparison on the performance level obtained with NSP, nonlinear time history analysis (THA) were also performed under ground motion excitation with compatible to response spectra design. Finally, formation plastic hinges and their progressive development from elastic level to collapse prevention are presented and discussed.

  9. Interpreting the nonlinear dielectric response of glass-formers in terms of the coupling model

    Energy Technology Data Exchange (ETDEWEB)

    Ngai, K. L. [CNR-IPCF, Largo Bruno Pontecorvo 3, I-56127 Pisa, Italy and Dipartimento di Fisica, Università di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa (Italy)


    Nonlinear dielectric measurements at high electric fields of glass-forming glycerol and propylene carbonate initially were carried out to elucidate the dynamic heterogeneous nature of the structural α-relaxation. Recently, the measurements were extended to sufficiently high frequencies to investigate the nonlinear dielectric response of faster processes including the so-called excess wing (EW), appearing as a second power law at high frequencies in the loss spectra of many glass formers without a resolved secondary relaxation. While a strong increase of dielectric constant and loss is found in the nonlinear dielectric response of the α-relaxation, there is a lack of significant change in the EW. A surprise to the experimentalists finding it, this difference in the nonlinear dielectric properties between the EW and the α-relaxation is explained in the framework of the coupling model by identifying the EW investigated with the nearly constant loss (NCL) of caged molecules, originating from the anharmonicity of the intermolecular potential. The NCL is terminated at longer times (lower frequencies) by the onset of the primitive relaxation, which is followed sequentially by relaxation processes involving increasing number of molecules until the terminal Kohlrausch α-relaxation is reached. These intermediate faster relaxations, combined to form the so-called Johari-Goldstein (JG) β-relaxation, are spatially and dynamically heterogeneous, and hence exhibit nonlinear dielectric effects, as found in glycerol and propylene carbonate, where the JG β-relaxation is not resolved and in D-sorbitol where it is resolved. Like the linear susceptibility, χ{sub 1}(f), the frequency dispersion of the third-order dielectric susceptibility, χ{sub 3}(f), was found to depend primarily on the α-relaxation time, and independent of temperature T and pressure P. I show this property of the frequency dispersions of χ{sub 1}(f) and χ{sub 3}(f) is the characteristic of the many

  10. Role of annealing temperatures on structure polymorphism, linear and nonlinear optical properties of nanostructure lead dioxide thin films (United States)

    Zeyada, H. M.; Makhlouf, M. M.


    The powder of as synthesized lead dioxide (PbO2) has polycrystalline structure β-PbO2 phase of tetragonal crystal system. It becomes nanocrystallites α-PbO2 phase with orthorhombic crystal system upon thermal deposition to form thin films. Annealing temperatures increase nanocrystallites size from 28 to 46 nm. The optical properties of α-PbO2 phase were calculated from absolute values of transmittance and reflectance at nearly normal incidence of light by spectrophotometer measurements. The refractive and extinction indices were determined and showed a response to annealing temperatures. The absorption coefficient of α-PbO2 films is >106 cm-1 in UV region of spectra. Analysis of the absorption coefficient spectra near optical edge showed indirect allowed transition. Annealing temperature decreases the value of indirect energy gap for α-PbO2 films. The dispersion parameters such as single oscillator energy, dispersion energy, dielectric constant at high frequency and lattice dielectric constant were calculated and its variations with annealing temperatures are reported. The nonlinear refractive index (n2), third-order nonlinear susceptibility (χ(3)) and nonlinear absorption coefficient (βc) were determined. It was found that χ(3), n2 and β increase with increasing photon energy and decrease with increasing annealing temperature. The pristine film of α-PbO2 has higher values of nonlinear optical constants than for annealed films; therefore it is suitable for applications in manufacturing nonlinear optical devices.

  11. Finite element analysis of steady and transiently moving/rolling nonlinear viscoelastic structure. Part 1: Theory (United States)

    Padovan, Joe


    In a three part series of papers, a generalized finite element analysis scheme is developed to handle the steady and transient response of moving/rolling nonlinear viscoelastic structure. This paper considers the development of the moving/rolling element strategy, including the effects of large deformation kinematics and viscoelasticity modelled by fractional integro-differential operators. To improve the solution strategy, a special hierarchical constraint procedure is developed for the case of steady rolling/translating as well as a transient scheme involving the use of a Grunwaldian representation of the fractional operator. In the second and third parts of the paper, 3-D extensions are developed along with transient contact strategies enabling the handling of impacts with obstructions. Overall, the various developments are benchmarked via comprehensive 2- and 3-D simulations. These are correlated with experimental data to define modelling capabilities.

  12. Investigation of planar barrier discharges for coherent nonlinear structures (United States)

    Uzun-Kaymak, I. U.


    Nonlinear pattern formations are ubiquitous in nature. One of the analogous configurations in laboratory experiments to such nonlinear systems is the current filament formations observed in glow plasmas. These filaments can generate oscillatory fluctuations in glow, which are also observed in voltage and current measurements. Specifically, semiconductor-gas discharges are known to breed these types of current filaments naturally. The plasma discharge is initiated by applying a DC high voltage to electrodes while they are immersed in nitrogen gas at partial atmospheric pressure. Observed discharge behaves oscillatory in time. Harmonic frequency generation and coherency levels among these modes are investigated. Parametric scans are performed to study the transition to chaotic behavior. Observed results are discussed in detail.

  13. Nonlinear modeling of the cyclic response of RC columns


    De Melo, J; Varum,H.; T. Rossetto; C. Fernandes; A. Costa


    Cyclic load reversals (like those induced by earthquakes) result in accelerated bond degradation, leading to significant bar slippage. The bond-slip mechanism is reported to be one of the most common causes of damage and even collapse of existing RC structures subjected to earthquake loading. RC structures with plain reinforcing bars, designed and built prior to the enforcement of the modern seismic-oriented design philosophies, are particularly sensitive to bond degradation. However, perfect...

  14. Numerical Analysis of the Dynamics of Nonlinear Solids and Structures (United States)


    of the conservation/ dissipation properties in time for the elastoplastic case 64 11.6. Concluding remarks 70 References 71 li...development of stable time-stepping algorithms for nonlinear dynamics. The focus was on inelastic solids, including finite strain elastoplastic and...set of plas- tic/ damage evolution equations (usually of a unilaterally constrained character due to the presence of the so-called yield/ damage

  15. Travelling and standing envelope solitons in discrete non-linear cyclic structures (United States)

    Grolet, Aurelien; Hoffmann, Norbert; Thouverez, Fabrice; Schwingshackl, Christoph


    Envelope solitons are demonstrated to exist in non-linear discrete structures with cyclic symmetry. The analysis is based on the Non-Linear Schrodinger Equation for the weakly non-linear limit, and on numerical simulation of the fully non-linear equations for larger amplitudes. Envelope solitons exist for parameters in which the wave equation is focussing and they have the form of shape-conserving wave packages propagating roughly with group velocity. For the limit of maximum wave number, where the group velocity vanishes, standing wave packages result and can be linked via a bifurcation to the non-localised non-linear normal modes. Numerical applications are carried out on a simple discrete system with cyclic symmetry which can be seen as a reduced model of a bladed disk as found in turbo-machinery.

  16. Statistical characterization of the internal structure of noiselike pulses using a nonlinear optical loop mirror (United States)

    Pottiez, O.; Paez-Aguirre, R.; Cruz, J. L.; Andrés, M. V.; Kuzin, E. A.


    In this work we study statistically the internal structure of noiselike pulses generated by a passively mode-locked fiber laser. For this purpose, we use a technique that allows estimating the distribution of the amplitudes of the sub-pulses in the bunch. The technique takes advantage of the fast response of the optical Kerr effect in a fiber nonlinear optical loop mirror (NOLM). It requires the measurement of the energy transfer characteristic of the pulses through the NOLM, and the numerical resolution of a system of nonlinear algebraic equations. The results yield a strongly asymmetric distribution, with a high-amplitude tail that is compatible with the existence of extreme-intensity sub-pulses in the bunch. Following the recent discovery of pulse-energy rogue waves and spectral rogue waves in the noiselike pulse regime, we propose a new way to look for extreme events in this particular mode of operation of mode-locked fiber lasers, and confirm that rogue wave generation is a key ingredient in the complex dynamics of these unconventional pulses.

  17. A Taylor-Galerkin finite element algorithm for transient nonlinear thermal-structural analysis (United States)

    Thornton, E. A.; Dechaumphai, P.


    A Taylor-Galerkin finite element method for solving large, nonlinear thermal-structural problems is presented. The algorithm is formulated for coupled transient and uncoupled quasistatic thermal-structural problems. Vectorizing strategies ensure computational efficiency. Two applications demonstrate the validity of the approach for analyzing transient and quasistatic thermal-structural problems.

  18. Third-order nonlinear optical response of colloidal gold nanoparticles prepared by sputtering deposition

    Energy Technology Data Exchange (ETDEWEB)

    Castro, Hemerson P. S.; Alencar, Márcio A. R. C.; Hickmann, Jandir M. [Optics and Materials Group–OPTMA, Universidade Federal de Alagoas, CAIXA POSTAL 2051, 57061-970 Maceió (Brazil); Wender, Heberton [Brazilian Synchrotron National Laboratory (LNLS), CNPEM, Rua Giuseppe Máximo Scolfaro 10.000, 13083-970 Campinas (Brazil); Department of Physics, Universidade Federal do Mato Grosso do Sul, 79070-900, Campo Grande (Brazil); Teixeira, Sergio R. [Institute of Physics, Universidade Federal do Rio Grande do Sul, 91501-970, Porto Alegre (Brazil); Dupont, Jairton [Laboratory of Molecular Catalysis, Institute of Chemistry, Universidade Federal do Rio Grande do Sul, 91501-970, Porto Alegre (Brazil)


    The nonlinear optical responses of gold nanoparticles dispersed in castor oil produced by sputtering deposition were investigated, using the thermally managed Z-scan technique. Particles with spherical shape and 2.6 nm of average diameter were obtained and characterized by transmission electron microscopy and small angle X-ray scattering. This colloid was highly stable, without the presence of chemical impurities, neither stabilizers. It was observed that this system presents a large refractive third-order nonlinear response and a negligible nonlinear absorption. Moreover, the evaluation of the all-optical switching figures of merit demonstrated that the colloidal nanoparticles prepared by sputtering deposition have a good potential for the development of ultrafast photonic devices.

  19. On the Boundary between Nonlinear Jump Phenomenon and Linear Response of Hypoid Gear Dynamics

    Directory of Open Access Journals (Sweden)

    Jun Wang


    Full Text Available A nonlinear time-varying (NLTV dynamic model of a hypoid gear pair system with time-dependent mesh point, line-of-action vector, mesh stiffness, mesh damping, and backlash nonlinearity is formulated to analyze the transitional phase between nonlinear jump phenomenon and linear response. It is found that the classical jump discontinuity will occur if the dynamic mesh force exceeds the mean value of tooth mesh force. On the other hand, the propensity for the gear response to jump disappears when the dynamic mesh force is lower than the mean mesh force. Furthermore, the dynamic analysis is able to distinguish the specific tooth impact types from analyzing the behaviors of the dynamic mesh force. The proposed theory is general and also applicable to high-speed spur, helical and spiral bevel gears even though those types of gears are not the primary focus of this paper.

  20. Nonlinear optics response of semiconductor quantum wells under high magnetic fields

    Energy Technology Data Exchange (ETDEWEB)

    Chemla, D.S.


    Recent investigations on the nonlinear optical response of semiconductor quantum wells in a strong perpendicular magnetic field, H, are reviewed. After some introductory material the evolution of the linear optical properties of GaAs QW`s as a function of H is discussed; an examination is made of how the magneto-excitons (MX) extrapolate continuously between quasi-2D QW excitons (X) when H = 0, and pairs of Landau levels (LL) when H {yields} {infinity}. Next, femtosecond time resolved investigations of their nonlinear optical response are presented; the evolution of MX-MX interactions with increasing H is stressed. Finally, how, as the dimensionality is reduced by application of H, the number of scattering channels is limited and relaxation of electron-hole pairs is affected. How nonlinear optical spectroscopy can be exploited to access the relaxation of angular momentum within magneto-excitons is also discussed.

  1. Wind energy conversion. Volume VI. Nonlinear response of wind turbine rotor

    Energy Technology Data Exchange (ETDEWEB)

    Chopra, I.


    The nonlinear equations of motor for a rigid rotor restrained by three flexible springs representing, respectively, the flapping, lagging, and feathering motions are derived using Lagrange's equations, for arbitrary angular rotations. These are reduced to a consistent set of nonlinear equations using nonlinear terms up to third order. The complete analysis is divided into three parts, A, B, and C. Part A consists of forced response of two-degree flapping-lagging rotor under the excitation of pure gravitational field (i.e., no aerodynamic forces). In Part B, the effect of aerodynamic forces on the dynamic response of two-degree flapping-lagging rotor is investigated. In Part C, the effect of third degree of motion, feathering, is considered.

  2. Sonic-boom-induced building structure responses including damage. (United States)

    Clarkson, B. L.; Mayes, W. H.


    Concepts of sonic-boom pressure loading of building structures and the associated responses are reviewed, and results of pertinent theoretical and experimental research programs are summarized. The significance of sonic-boom load time histories, including waveshape effects, are illustrated with the aid of simple structural elements such as beams and plates. Also included are discussions of the significance of such other phenomena as three-dimensional loading effects, air cavity coupling, multimodal responses, and structural nonlinearities. Measured deflection, acceleration, and strain data from laboratory models and full-scale building tests are summarized, and these data are compared, where possible, with predicted values. Damage complaint and claim experience due both to controlled and uncontrolled supersonic flights over communities are summarized with particular reference to residential, commercial, and historic buildings. Sonic-boom-induced building responses are compared with those from other impulsive loadings due to natural and cultural events and from laboratory simulation tests.

  3. FORTRAN programs for calculating nonlinear seismic ground response in two dimensions (United States)

    Joyner, W.B.


    The programs described here were designed for calculating the nonlinear seismic response of a two-dimensional configuration of soil underlain by a semi-infinite elastic medium representing bedrock. There are two programs. One is for plane strain motions, that is, motions in the plane perpendicular to the long axis of the structure, and the other is for antiplane strain motions, that is motions parallel to the axis. The seismic input is provided by specifying what the motion of the rock-soil boundary would be if the soil were absent and the boundary were a free surface. This may be done by supplying a magnetic tape containing the values of particle velocity for every boundary point at every instant of time. Alternatively, a punch card deck may be supplied giving acceleration values at every instant of time. In the plane strain program it is assumed that the acceleration values apply simultaneously to every point on the boundary; in the antiplane strain program it is assumed that the acceleration values characterize a plane shear wave propagating upward in the underlying elastic medium at a specified angle with the vertical. The nonlinear hysteretic behavior of the soil is represented by a three-dimensional rheological model. A boundary condition is used which takes account of finite rigidity in the elastic substratum. The computations are performed by an explicit finite-difference scheme that proceeds step by step in space and time. Computations are done in terms of stress departures from an unspecified initial state. Source listings are provided here along with instructions for preparing the input. A more detailed discussion of the method is presented elsewhere.

  4. Synchronous and non-synchronous responses of systems with multiple identical nonlinear vibration absorbers (United States)

    Issa, Jimmy S.; Shaw, Steven W.


    In this work we investigate the nonlinear dynamic response of systems composed of a primary inertia to which multiple identical vibration absorbers are attached. This problem is motivated by observations of systems of centrifugal pendulum vibration absorbers that are designed to reduce engine order torsional vibrations in rotating systems, but the results are relevant to translational systems as well. In these systems the total absorber mass is split into multiple equal masses for purposes of distribution and/or balance, and it is generally expected that the absorbers will act in unison, corresponding to a synchronous response. In order to capture nonlinear effects of the responses of the absorbers, specifically, their amplitude-dependent frequency, we consider them to possess nonlinear stiffness. The equations of motion for the system are derived and it is shown how one can uncouple the equations for the absorbers from that for the primary inertia, resulting in a system of identical resonators that are globally coupled. These symmetric equations are scaled for weak nonlinear effects, near resonant forcing, and small damping. The method of averaging is applied, from which steady-state responses and their stability are investigated. The response of systems with two, three, and four absorbers are considered in detail, demonstrating a rich variety of bifurcations of the synchronous response, resulting in responses with various levels of symmetry in which sub-groups of absorbers are mutually synchronous. It is also shown that undamped models with more than two absorbers possess a degenerate response, which is made robust by the addition of damping to the model. Design guidelines are proposed based on the nature of the system response, with the aim of minimizing the acceleration of the primary system. It is shown that the desired absorber parameters are selected so that the system achieves a stable synchronous response which does not undergo jumps via saddle

  5. Quantifying the contributions of structure to annulus fibrosus mechanical function using a nonlinear, anisotropic, hyperelastic model. (United States)

    Guerin, Heather Lynch; Elliott, Dawn M


    The annulus fibrosus of the intervertebral disc is comprised of concentric lamella of oriented collagen fibers embedded in a hydrated proteoglycan matrix with smaller amounts of minor collagens, elastin, and small proteoglycans. Its structure and composition enable the disc to withstand complex loads and result in inhomogeneous, anisotropic, and nonlinear mechanical behaviors. The specific contributions of the annulus fibrosus constituent structures to mechanical function remain unclear. Therefore, the objective of this study was to use a structurally motivated, anisotropic, nonlinear strain energy model of annulus fibrosus to determine the relative contributions of its structural components to tissue mechanical behavior. A nonlinear, orthotropic hyperelastic model was developed for the annulus fibrosus. Terms to describe fibers, matrix, and interactions between annulus fibrosus structures (shear and normal to the fiber directions) were explicitly included. The contributions of these structures were analyzed by including or removing terms and determining the effect on the fit to multidimensional experimental data. Correlation between experimental and model-predicted stress, a Bland-Altman analysis of bias and standard deviation of residuals, and the contribution of structural terms to overall tissue stress were calculated. Both shear and normal interaction terms were necessary to accurately model multidimensional behavior. Inclusion of shear interactions more accurately described annulus fibrosus nonlinearity. Fiber stretch and shear interactions dominated contributions to circumferential direction stress, while normal and shear interactions dominated axial stress. The results suggest that interactions between fibers and matrix, perhaps facilitated by crosslinks, elastin, or minor collagens, augment traditional (i.e., fiber-uncrimping) models of nonlinearity.

  6. Observation of large nonlinear responses in a graphene-Bi2Te3 heterostructure at a telecommunication wavelength (United States)

    Wang, Yingwei; Mu, Haoran; Li, Xiaohong; Yuan, Jian; Chen, Jiazhang; Xiao, Si; Bao, Qiaoliang; Gao, Yongli; He, Jun


    We report the large nonlinear response and ultrafast carrier relaxation dynamics of a graphene-Bi2Te3 heterostructure produced by two-step chemical vapour deposition. The nonlinear refractive index reaches n2 = 0.2 × 10-7 cm2/W at the telecommunication wavelength of 1550 nm, which is almost seven orders of magnitude larger than that of the bulk Si material. Additionally, a pump-probe experiment is performed to investigate the ultrafast dynamic process (intraband relaxation time τ1 = 270 ± 20 fs; interband relaxation time τ2 = 3.6 ± 0.2 ps) of the graphene-Bi2Te3 heterostructure. Then, based on the donor-acceptor structure model, we propose a theoretical model to explain the dynamic relaxation process. Our results show that the graphene-Bi2Te3 heterostructure is a promising saturable absorber for ultrafast pulse laser applications at telecommunication wavelengths.

  7. Third-order nonlinear optical response of Ag-CdSe/PVA hybrid nanocomposite

    Energy Technology Data Exchange (ETDEWEB)

    Tripathi, S.K.; Kaur, Ramneek; Kaur, Jaspreet; Sharma, Mamta [Panjab University, Department of Physics, Center of Advanced Study in Physics, Chandigarh (India)


    Hybrid nanocomposites of II-VI semiconductor nanoparticles are gaining great interest in nonlinear optoelectronic devices. Present work includes the characterization of CdSe polymer nanocomposite prepared by chemical in situ technique. From X-ray diffraction, the hexagonal wurtzite structure of nanoparticles has been confirmed with spherical morphology from transmission electron microscopy. Ag-CdSe hybrid polymer nanocomposite has been prepared chemically at different Ag concentrations. The presence of Ag in hybrid nanocomposite has been confirmed with energy-dispersive X-ray spectroscopy. The effect of varying Ag concentration on the linear and nonlinear optical properties of the nanocomposites has been studied. In linear optical parameters, the linear absorption coefficient, refractive index, extinction coefficient and optical conductivity have been calculated. The third-order nonlinear optical properties have been observed with open- and closed-aperture Z-scan technique. The large nonlinear refractive index ∝10{sup -5} cm{sup 2}/W with self-focusing behaviour is due to the combined effect of quantum confinement and thermo-optical effects. The enhanced nonlinearity with increasing Ag content is due to the surface plasmon resonance, which enhances the local electric field near the nanoparticle surface. Thus, Ag-CdSe hybrid polymer nanocomposite has favourable nonlinear optical properties for various optoelectronic applications. (orig.)

  8. Response of Saturated Porous Nonlinear Materials to Dynamic Loadings (United States)


    the following section a bilinear hysteretic skeleton was modeled, followed by calculations on an actual sand from Enewetak Atoll . In this section...the response of saturated sand from Enewetak Atoll . The skeleton properties are taken from laboratory data reported in the second volunie of this study...with an actual saturated sand from Enewetak Atoll . In Section 2, the theoretical background and numerical code, TPDAP, used in this study are described

  9. Formation of super-resolution spot through nonlinear Fabry-Perot cavity structures: theory and simulation. (United States)

    Wei, Jingsong; Wang, Rui; Yan, Hui; Fan, Yongtao


    This study explores how interference manipulation breaks through the diffraction limit and induces super-resolution nano-optical hot spots through the nonlinear Fabry-Perot cavity structure. The theoretical analytical model is established, and the numerical simulation results show that when the thickness of the nonlinear thin film inside the nonlinear Fabry-Perot cavity structure is adjusted to centain value, the constructive interference effect can be formed in the central point of the spot, which causes the nanoscale optical hot spot in the central region to be produced. The simulation results also tell us that the hot spot size is sensitive to nonlinear thin film thickness, and the accuracy is required to be up to nanometer or even subnanometer scale, which is very large challenging for thin film deposition technique, however, slightly changing the incident laser power can compensate for drawbacks of low thickness accuracy of nonlinear thin films. Taking As(2)S(3) as the nonlinear thin film, the central hot spot with a size of 40nm is obtained at suitable nonlinear thin film thickness and incident laser power. The central hot spot size is only about λ/16, which is very useful in super-high density optical recording, nanolithography, and high-resolving optical surface imaging.

  10. Accuracy of three-dimensional seismic ground response analysis in time domain using nonlinear numerical simulations (United States)

    Liang, Fayun; Chen, Haibing; Huang, Maosong


    To provide appropriate uses of nonlinear ground response analysis for engineering practice, a three-dimensional soil column with a distributed mass system and a time domain numerical analysis were implemented on the OpenSees simulation platform. The standard mesh of a three-dimensional soil column was suggested to be satisfied with the specified maximum frequency. The layered soil column was divided into multiple sub-soils with a different viscous damping matrix according to the shear velocities as the soil properties were significantly different. It was necessary to use a combination of other one-dimensional or three-dimensional nonlinear seismic ground analysis programs to confirm the applicability of nonlinear seismic ground motion response analysis procedures in soft soil or for strong earthquakes. The accuracy of the three-dimensional soil column finite element method was verified by dynamic centrifuge model testing under different peak accelerations of the earthquake. As a result, nonlinear seismic ground motion response analysis procedures were improved in this study. The accuracy and efficiency of the three-dimensional seismic ground response analysis can be adapted to the requirements of engineering practice.

  11. Non-Linear Wave Loads and Ship responses by a time-domain Strip Theory

    DEFF Research Database (Denmark)

    Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher


    A non-linear time-domain strip theory for vertical wave loads and ship responses is presented. The theory is generalized from a rigorous linear time-domain strip theory representaton. The hydrodynamic memory effect due to the free surface is approximated by a higher order differential equation...

  12. Scaling of ac susceptibility and the nonlinear response function of high-temperature superconductors

    Institute of Scientific and Technical Information of China (English)

    CHEN; Kaixuan; NING; Zhenhua; XU; Hengyi; QI; Zhi; LU; Guo


    The amplitude-dependent ac susceptibility of high-temperature superconductors is shown to obey some empirical scaling relations. We try to analyze this behavior by extending a dc nonlinear response function of mixed state to the ac cases. The derived equations for critical current and ac susceptibility x(T) agree with the scaling relations of experimental data.

  13. Nonlinear optical response in condensed phases : A microscopic theory using the multipolar Hamiltonian

    NARCIS (Netherlands)

    Knoester, Jasper; Mukamel, Shaul


    A general scheme is presented for calculating the nonlinear optical response in condensed phases that provides a unified picture of excitons, polaritons, retardation, and local-field effects in crystals and in disordered systems. A fully microscopic starting point is taken by considering the evoluti

  14. Nonlinear optical response of C60 in solvents: picosecond transient grating experiments (United States)

    Khudyakov, Dmitriy V.; Rubtsov, Igor V.; Lobach, Anatolii S.; Nadtochenko, Victor A.


    Time-resolved resonant nonlinear optical response of C60 in a chlorobenzene solution was measured for 528 nm excitation and 1055, 528, and 351 nm probing for zzzz and zzyy configurations. The slow part of the signal (8 +/- 2 ps) was attributed to the orientational motion of C60 excited molecules.

  15. Nonlinear Optical Response of Disordered J Aggregates in the Motional Narrowing Limit

    NARCIS (Netherlands)

    Knoester, Jasper


    We discuss the theory of nonlinear optical response of molecular aggregates with frequency disorder. In contrast to the usual modeling, we allow for spatial correlations in the disorder. We show that the joint distribution of all multi-exciton frequencies can be determined analytically to first orde

  16. A generalized hybrid transfinite element computational approach for nonlinear/linear unified thermal/structural analysis (United States)

    Tamma, Kumar K.; Railkar, Sudhir B.


    The present paper describes the development of a new hybrid computational approach for applicability for nonlinear/linear thermal structural analysis. The proposed transfinite element approach is a hybrid scheme as it combines the modeling versatility of contemporary finite elements in conjunction with transform methods and the classical Bubnov-Galerkin schemes. Applicability of the proposed formulations for nonlinear analysis is also developed. Several test cases are presented to include nonlinear/linear unified thermal-stress and thermal-stress wave propagations. Comparative results validate the fundamental capablities of the proposed hybrid transfinite element methodology.

  17. Using nonlinearity and spatiotemporal property modulation to control effective structural properties: dynamic rods

    DEFF Research Database (Denmark)

    Thomsen, Jon Juel; Blekhman, Iliya I.


    , and to call these dynamic materials or spatiotemporal composites. Also, according to theoretical predictions, structural nonlinearity enhances the possibilities of achieving specific effective properties. For example, with an elastic rod having cubical elastic nonlinearities, it seems possible to control......, and exemplified. Then simple approximate analytical expressions are derived for the effective wave speed and natural frequencies for one-dimensional wave propagation in a nonlinear elastic rod, where the spatiotemporal modulation is imposed as a high-frequency standing wave, supposed to be given. Finally the more...

  18. Nonlinear dynamics of phase space zonal structures and energetic particle physics in fusion plasmas

    CERN Document Server

    Zonca, Fulvio; Briguglio, Sergio; Fogaccia, Giuliana; Vlad, Gregorio; Wang, Xin


    A general theoretical framework for investigating nonlinear dynamics of phase space zonal structures is presented in this work. It is then, more specifically, applied to the limit where the nonlinear evolution time scale is smaller or comparable to the wave-particle trapping period. In this limit, both theoretical and numerical simulation studies show that non-adiabatic frequency chirping and phase locking could lead to secular resonant particle transport on meso- or macro-scales. The interplay between mode structures and resonant particles then provides the crucial ingredient to properly understand and analyze the nonlinear dynamics of Alfv\\'en wave instabilities excited by non-perturbative energetic particles in burning fusion plasmas. Analogies with autoresonance in nonlinear dynamics and with superradiance in free electron lasers are also briefly discussed.

  19. Stabilization of nonlinear systems with parametric uncertainty using variable structure techniques

    Energy Technology Data Exchange (ETDEWEB)

    Schoenwald, D.A. [Oak Ridge National Lab., TN (United States); Oezguener, Ue. [Ohio State Univ., Columbus, OH (United States). Dept. of Electrical Engineering


    The authors present a result on the robust stabilization of a class of nonlinear systems exhibiting parametric uncertainty. They consider feedback linearizable nonlinear systems with a vector of unknown constant parameters perturbed about a known value. A Taylor series of the system about the nominal parameter vector coupled with a feedback linearizing control law yields a linear system plus nonlinear perturbations. Via a structure matching condition, a variable structure control law is shown to exponentially stabilize the full system. The novelty of the result is that the linearizing coordinates are completely known since they are defined about the nominal parameter vector, and fewer restrictions are imposed on the nonlinear perturbations than elsewhere in the literature.

  20. Geometric Structure-Preserving Discretization Schemes for Nonlinear Elasticity (United States)


    conditions. 15.  SUBJECT TERMS geometric theory for nonlinear elasticity, discrete exterior calculus 16.  SECURITY CLASSIFICATION OF: 17.  LIMITATION...associated Laplacian. We use the general theory for approximation of Hilbert complexes and the finite element exterior calculus and introduce some stable mixed...Ωk(B)→ Ωk+1(B) be the standard exterior derivative given by (dβ)I0⋯Ik = k ∑ i=0 (−1)iβI0⋯Îi⋯Ik, Ii , where the hat over an index implies the

  1. Thermal rectification in non-linear structures with bulk losses (United States)

    Schmidt, Martin; Kottos, Tsampikos


    A mechanism for thermal rectification based on the interplay between non-uniform bulk losses with nonlinearity is presented. We theoretically analyze the phenomenon using an anharmonic array of coupled oscillators coupled to the left and right with two Langevin reservoirs. A third probe thermostat (with temperature TB) is placed in an asymmetric position in the bulk of the lattice thus breaking the translational symmetry and leading to rectification of heat flow. We note that for TB = 0 this Langevin term is equivalent to a simple friction. We find that an increase of the friction strength can increase both the asymmetry and heat flux. Visiting Student from Germany

  2. Microscopic structures from reduction of continuum nonlinear problems

    CERN Document Server

    Lovison, Alberto


    We present an application of the Amann-Zehnder exact finite reduction to a class of nonlinear perturbations of elliptic elasto-static problems. We propose the existence of minmax solutions by applying Ljusternik-Schnirelmann theory to a finite dimensional variational formulation of the problem, based on a suitable spectral cut-off. As a by-product, with a choice of fit variables, we establish a variational equivalence between the above spectral finite description and a discrete mechanical model. By doing so, we decrypt the abstract information encoded in the AZ reduction and give rise to a concrete and finite description of the continuous problem.

  3. Continuous Dynamic Simulation of Nonlinear Aerodynamics/Nonlinear Structure Interaction (NANSI) for Morphing Vehicles (United States)


    comprised linear structural dynamics (e.g. [7.2]), vibro-acoustics, aeroelasticity (e.g. [7.1]), rotordynamics [7.7] (including the joint simulation...2006. [7.7] Murthy, R., Mignolet, M.P., and El-Shafei, A., "Nonparametric Stochastic Modeling of Structural Uncertainty in Rotordynamic


    Institute of Scientific and Technical Information of China (English)

    戎海武; 王向东; 孟光; 徐伟; 方同


    The principal resonance of Duffing oscillator to narrow-band random parametricexcitation was investigated. The method of multiple scales was used to determine theequations of modulation of amplitude and phase. The behavior, stability and bifurcation ofsteady state response were studied by means of qualitative analyses. The effects of damping,detuning, bandwidth and magnitudes of deterministic and random excitations wereanalyzed. The theoretical analyses were verified by numerical results. Theoretical analysesand numerical simulations show that when the intensity of the random excitation increases,the nontrivial steady state solution may change from a limit cycle to a diffused limit cycle.Under some conditions the system may have two ,steady state solutions.

  5. Superoperator representation of nonlinear response: unifying quantum field and mode coupling theories. (United States)

    Mukamel, Shaul


    Computing response functions by following the time evolution of superoperators in Liouville space (whose vectors are ordinary Hilbert space operators) offers an attractive alternative to the diagrammatic perturbative expansion of many-body equilibrium and nonequilibrium Green's functions. The bookkeeping of time ordering is naturally maintained in real (physical) time, allowing the formulation of Wick's theorem for superoperators, giving a factorization of higher order response functions in terms of two fundamental Green's functions. Backward propagations and analytic continuations using artificial times (Keldysh loops and Matsubara contours) are avoided. A generating functional for nonlinear response functions unifies quantum field theory and the classical mode coupling formalism of nonlinear hydrodynamics and may be used for semiclassical expansions. Classical response functions are obtained without the explicit computation of stability matrices.

  6. Characterizing the structure of nonlinear systems using gradual wavelet reconstruction

    Directory of Open Access Journals (Sweden)

    C. J. Keylock


    Full Text Available In this paper, classical surrogate data methods for testing hypotheses concerning nonlinearity in time-series data are extended using a wavelet-based scheme. This gives a method for systematically exploring the properties of a signal relative to some metric or set of metrics. A signal continuum is defined from a linear variant of the original signal (same histogram and approximately the same Fourier spectrum to the exact replication of the original signal. Surrogate data are generated along this continuum with the wavelet transform fixing in place an increasing proportion of the properties of the original signal. Eventually, chaotic or nonlinear behaviour will be preserved in the surrogates. The technique permits various research questions to be answered and examples covered in the paper include identifying a threshold level at which signals or models for those signals may be considered similar on some metric, analysing the complexity of the Lorenz attractor, characterising the differential sensitivity of metrics to the presence of multifractality for a turbulence time-series, and determining the amplitude of variability of the Hölder exponents in a multifractional Brownian motion that is detectable by a calculation method. Thus, a wide class of analyses of relevance to geophysics can be undertaken within this framework.

  7. Nonlinear diffraction effects around a surface-piercing structure

    Energy Technology Data Exchange (ETDEWEB)

    Lalli, F.; Mascio, A. Di; Landrini, M. [Istituto Nazionale per Studi ed Esperienze di Architettura Navale, Rome (Italy)


    In the present paper the interaction of a wave system with a submerged or surface piercing body is studied. The wave diffraction caused by a cylinder in finite depth water and by a shoal is been computed and the results are compared with analytical solutions and experimental data. The problem is analyzed numerically in the frame of irrotational incompressible flow hypothesis. Both the linearized and the fully nonlinear mathematical models are studied. The numerical solution is gained by means of a mixed panel-desingularized formulation. An explicit time-marching algorithm updates the wave elevation and the potential at the free surface. In all cases, the numerical simulation mirrors the experimental data. In the case of the diffraction around a cylinder, the simulation confirms and extends the theoretical results of the second order analysis (Kriebel 1990, 1992): the linear model yields a very good estimation of the force amplitude acting on the body, while the wave profiles are poorly predicted when compared with the fully nonlinear simulation and the experimental data.

  8. Nonlinear wave structures as exact solutions of Vlasov-Maxwell equations. (United States)

    Dasgupta, B.; Tsurutani, B. T.; Janaki, M. S.; Sharma, A. S.


    Many recent observations by POLAR and Geotail spacecraft of the low-latitudes magnetopause boundary layer (LLBL) and the polar cap boundary layer (PCBL) have detected nonlinear wave structures [Tsurutani et al, Geophys. Res. Lett., 25, 4117, 1998]. These nonlinear waves have electromagnetic signatures that are identified with Alfven and Whistler modes. Also solitary waves with mono- and bi-polar features were observed. In general such electromagnetic structures are described by the full Vlasov-Maxwell equations for waves propagating at an angle to the ambient magnetic field, but it has been a diffficult task obtaining the solutions because of the inherent nonlinearity. We have obtained an exact nonlinear solution of the full Vlasov-Maxwell equations in the presence of an electromagnetic wave propagating at an arbitrary direction with an ambient magnetic field. This is accomplished by finding the constants of motion of the charged particles in the electromagnetic field of the wave and then constructing a realistic distribution function as a function of these constants of motion. The corresponding trapping conditions for such waves are obtained, yielding the self-consistent description for the particles in the presence of the nonlinear waves. The interpretation of the observed nonlinear structures in terms of these general solutions will be presented.

  9. Nonlinear response studies and corrections for a liquid crystal spatial light modulator

    Indian Academy of Sciences (India)

    Ravinder Kumar Banyal; B Raghavendra Prasad


    The nonlinear response of light transmission characteristics of a liquid crystal (LC) spatial light modulator (SLM) is studied. The results show that the device exhibits a wide range of variations with different control parameters and input settings. Experiments were performed to obtain intensity modulation that is best described by either power-law or sigmoidal functions. Based on the inverse transformation, an appropriate pre-processing scheme for electrically addressed input gray-scale images, particularly important in several optical processing and imaging applications, is suggested. Further, the necessity to compensate the SLM image nonlinearities in a volume holographic data storage and retrieval system is demonstrated.

  10. Non-linear optical properties of molecules in heterogeneous environments: a quadratic density functional/molecular mechanics response theory. (United States)

    Rinkevicius, Zilvinas; Li, Xin; Sandberg, Jaime A R; Ågren, Hans


    We generalize a density functional theory/molecular mechanics approach for heterogeneous environments with an implementation of quadratic response theory. The updated methodology allows us to address a variety of non-linear optical, magnetic and mixed properties of molecular species in complex environments, such as combined metallic, solvent and confined organic environments. Illustrating calculations of para-nitroaniline on gold surfaces and in solution reveals a number of aspects that come into play when analyzing second harmonic generation of such systems--such as surface charge flow, coupled surface-solvent dynamics and induced geometric and electronic structure effects of the adsorbate. Some ramifications of the methodology for applied studies are discussed.

  11. Nonlinear biofluvial responses to vegetation change in a semiarid environment (United States)

    Neave, Mel; Rayburg, Scott


    The desertification of grassland communities in the Jornada del Muerto Basin, southern New Mexico, USA, has occurred in association with a series of geomorphic responses that have influenced the system of vegetation change. Rainfall simulation experiments indicate that the volume of runoff generated from basin surfaces and its ability to erode are greatly affected by the distribution of vegetation, which ultimately controls processes such as rainsplash erosion, soil infiltrability and crust development. Animal activities also influence rates of sediment movement from unvegetated surfaces by disrupting soil crusts and making loose sediment available for transportation by overland flow. Shrublands in the Jornada Basin have a patchier vegetation cover than grasslands, with vegetated areas (shrubs) being separated by unvegetated (intershrub) zones. The exposed intershrub surfaces are more vulnerable to erosion than the grass and shrub surfaces. Thus, water and sediment yields, calculated using rainfall simulation experiments, were higher for vegetated (shrub and grass) plots than they were for unvegetated (intershrub) plots. The runoff and erosion model, KINEROS2, predicts that at the base of a 100 m slope, shrubland surfaces shed seven times more runoff and 25 times more sediment than grassland surfaces. Evidence to support the prediction of higher rates of erosion in the shrubland can be found in the form of the extensive rill networks that are common in this community. The contraction of grasslands has been associated with elevated rates of erosion that have altered the morphology of the surface, lowering slopes between shrubs, and increasing the amplitude of the microtopography. Overall, the viability of the exposed soils for recolonization by grasses has been reduced, reinforcing the system of shrubland invasion and lending support to the use of state-and-transition models to describe ecologic responses to change within this environment. Combined, these results



    Ebrahimian, Hamed


    Structural health monitoring (SHM) is defined as the capability to monitor the performance behavior of civil infrastructure systems as well as to detect, localize, and quantify damage in these systems. SHM technologies contribute to enhance the resilience of civil infrastructures, which are vulnerable to structural aging, degradation, and deterioration and to extreme events due to natural and man-made hazards. Given the limited financial resources available to renovate or replace them, it is ...


    Institute of Scientific and Technical Information of China (English)

    陈务军; 付功义; 何艳丽; 董石麟


    Geometrically nonlinear stiffness matrix due to large displacement-small strain was firstly formulated ex-plicitly for the basic components of pantographic foldable structures,namely, the uniplet, derived from a three-node beam element. The formulation of the uniplet stiffness matrix is based on the precise nonlinear finite elementtheory and the displacement-harmonized and internal force constraints are applied directly to the deformationmodes of the three-node beam element. The formulations were derived in general form, and can be simplified forparticular foldable structures, such as flat, cylindrical and spherical structures. Finally, two examples were pre-sented to illustrate the applications of the stiffness matrix evolved.

  14. Self-consistent photonic band structure of dielectric superlattices containing nonlinear optical materials. (United States)

    Lousse, V; Vigneron, J P


    The theory of photonic crystals is extended to include the optical Kerr effect taking place in weak third-order, nonlinear materials present in the unit cell. The influence on the dispersion relations of the illumination caused by a single Bloch mode transiting through the crystal structure is examined. Special attention is given to the modification of the photonic gap width and position. Assuming an instantaneous change of refractive index with illumination, the nonlinear band structure problem is solved as a sequence of ordinary, linear band structure calculations, carried out in a plane-wave field representation.

  15. Verification of nonlinear dynamic structural test results by combined image processing and acoustic analysis (United States)

    Tene, Yair; Tene, Noam; Tene, G.


    An interactive data fusion methodology of video, audio, and nonlinear structural dynamic analysis for potential application in forensic engineering is presented. The methodology was developed and successfully demonstrated in the analysis of heavy transportable bridge collapse during preparation for testing. Multiple bridge elements failures were identified after the collapse, including fracture, cracks and rupture of high performance structural materials. Videotape recording by hand held camcorder was the only source of information about the collapse sequence. The interactive data fusion methodology resulted in extracting relevant information form the videotape and from dynamic nonlinear structural analysis, leading to full account of the sequence of events during the bridge collapse.

  16. Nonlinear response of summer temperature to Holocene insolation forcing in Alaska. (United States)

    Clegg, Benjamin F; Kelly, Ryan; Clarke, Gina H; Walker, Ian R; Hu, Feng Sheng


    Regional climate responses to large-scale forcings, such as precessional changes in solar irradiation and increases in anthropogenic greenhouse gases, may be nonlinear as a result of complex interactions among earth system components. Such nonlinear behaviors constitute a major source of climate "surprises" with important socioeconomic and ecological implications. Paleorecords are key for elucidating patterns and mechanisms of nonlinear responses to radiative forcing, but their utility has been greatly limited by the paucity of quantitative temperature reconstructions. Here we present Holocene July temperature reconstructions on the basis of midge analysis of sediment cores from three Alaskan lakes. Results show that summer temperatures during 10,000-5,500 calibrated years (cal) B.P. were generally lower than modern and that peak summer temperatures around 5,000 were followed by a decreasing trend toward the present. These patterns stand in stark contrast with the trend of precessional insolation, which decreased by ∼10% from 10,000 y ago to the present. Cool summers before 5,500 cal B.P. coincided with extensive summer ice cover in the western Arctic Ocean, persistence of a positive phase of the Arctic Oscillation, predominantly La Niña-like conditions, and variation in the position of the Alaskan treeline. These results illustrate nonlinear responses of summer temperatures to Holocene insolation radiative forcing in the Alaskan sub-Arctic, possibly because of state changes in the Arctic Oscillation and El Niño-Southern Oscillation and associated land-atmosphere-ocean feedbacks.


    Institute of Scientific and Technical Information of China (English)



    An approximate method for analyzing the response of nonlinear systems with the Preisach hysteresis of the non-local memory under a stationary Gaussian excitation is presented based on the covariance and switching probability analysis. The covariance matrix equation of the Preisach hysteretic system response is derived. The cross correlation function of the Preisach hysteretic force and response in the covariance equation is evaluated by the switching probability analysis and the Gaussian approximation to the response process. Then an explicit expression of the correlation function is given for the case of symmetric Preisach weighting functions. The numerical result obtained is in good agreement with that from the digital simulation.

  18. Enhanced linear and nonlinear optical phase response of AlGaAs microring resonators. (United States)

    Heebner, John E; Lepeshkin, Nick N; Schweinsberg, Aaron; Wicks, G W; Boyd, Robert W; Grover, Rohit; Ho, P T


    We have constructed and characterized several optical microring resonators with scale sizes of the order of 10 microm. These devices are intended to serve as building blocks for engineerable linear and nonlinear photonic media. Light is guided vertically by an epitaxially grown structure and transversely by deeply etched air-clad sidewalls. We report on the spectral phase transfer characteristics of such resonators. We also report the observation of a pi-rad Kerr nonlinear phase shift accumulated in a single compact ring resonator evidenced by all-optical switching between output ports of a resonator-enhanced Mach-Zehnder interferometer.

  19. Pulsed second-harmonic generation in nonlinear, one-dimensional, periodic structures (United States)

    Scalora, M.; Bloemer, M. J.; Manka, A. S.; Dowling, J. P.; Bowden, C. M.; Viswanathan, R.; Haus, J. W.


    We present a numerical study of second-harmonic (SH) generation in a one-dimensional, generic, photonic band-gap material that is doped with a nonlinear χ(2) medium. We show that a 20-period, 12-μm structure can generate short SH pulses (similar in duration to pump pulses) whose energy and power levels may be 2-3 orders of magnitude larger than the energy and power levels produced by an equivalent length of a phase-matched, bulk medium. This phenomenon comes about as a result of the combination of high electromagnetic mode density of states, low group velocity, and spatial phase locking of the fields near the photonic band edge. The structure is designed so that the pump pulse is tuned near the first-order photonic band edge, and the SH signal is generated near the band edge of the second-order gap. This maximizes the density of available field modes for both the pump and SH field. Our results show that the χ(2) response is effectively enhanced by several orders of magnitude. Therefore, mm- or cm-long, quasi-phase-matched devices could be replaced by these simple layered structures of only a few micrometers in length. This has important applications to high-energy lasers, Raman-type sources, and frequency up- and down-conversion schemes.

  20. Excited-state dynamics and nonlinear optical response of Ge nanocrystals embedded in silica matrix (United States)

    Razzari, Luca; Gnoli, Andrea; Righini, Marcofabio; Dâna, Aykutlu; Aydinli, Atilla


    We use a dedicated Z-scan setup, arranged to account for cumulative effects, to study the nonlinear optical response of Ge nanocrystals embedded in silica matrix. Samples are prepared with plasma-enchanced chemical-vapor deposition and post-thermal annealing. We measure a third-order nonlinear refraction coefficient of γ =1×10-16m2/W. The nonlinear absorption shows an intensity-independent coefficient of β =4×10-10m/W related to fast processes. In addition, we measure a second β component around 10-9m /W with a relaxation time of 300μs that rises linearly with the laser intensity. We associate its origin to the absorption of excited carriers from a surface-defect state with a long depopulation time.

  1. Identifying the nonlinear mechanical behaviour of micro-speakers from their quasi-linear electrical response (United States)

    Zilletti, Michele; Marker, Arthur; Elliott, Stephen John; Holland, Keith


    In this study model identification of the nonlinear dynamics of a micro-speaker is carried out by purely electrical measurements, avoiding any explicit vibration measurements. It is shown that a dynamic model of the micro-speaker, which takes into account the nonlinear damping characteristic of the device, can be identified by measuring the response between the voltage input and the current flowing into the coil. An analytical formulation of the quasi-linear model of the micro-speaker is first derived and an optimisation method is then used to identify a polynomial function which describes the mechanical damping behaviour of the micro-speaker. The analytical results of the quasi-linear model are compared with numerical results. This study potentially opens up the possibility of efficiently implementing nonlinear echo cancellers.

  2. Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetals (United States)

    Morimoto, Takahiro; Zhong, Shudan; Orenstein, Joseph; Moore, Joel E.


    We study nonlinear magneto-optical responses of metals by a semiclassical Boltzmann equation approach. We derive general formulas for linear and second-order nonlinear optical effects in the presence of magnetic fields that include both the Berry curvature and the orbital magnetic moment. Applied to Weyl fermions, the semiclassical approach (i) captures the directional anisotropy of linear conductivity under a magnetic field as a consequence of an anisotropic B2 contribution, which may explain the low-field regime of recent experiments; and (ii) predicts strong second harmonic generation proportional to B that is enhanced as the Fermi energy approaches the Weyl point, leading to large nonlinear Kerr rotation. Moreover, we show that the semiclassical formula for the circular photogalvanic effect arising from the Berry curvature dipole is reproduced by a full quantum calculation using a Floquet approach.

  3. Experimental demonstration of non-reciprocal transmission in a nonlinear photonic-crystal Fano structure

    DEFF Research Database (Denmark)

    Yu, Yi; Chen, Yaohui; Hu, Hao;


    We suggest and experimentally demonstrate a photonic-crystal structure with more than 30 dB difference between forward and backward transmission levels. The non-reciprocity relies on the combination of ultrafast carrier nonlinearities and spatial symmetry breaking in a Fano structure employing...

  4. Expanded porphyrins as third order non-linear optical materials: Some structure-function correlations

    Indian Academy of Sciences (India)

    Sabapathi Gokulnath; Tavarekere K Chandrashekar


    In this paper, the non-linear optical properties of representative core-modified expanded porphyrins have been investigated with an emphasis on the structure-property relationship between the aromaticity and conformational behaviour. It has been shown that the measured two-photon absorption cross section (2) values depend on the structure of macrocycle, its aromaticity and the number of -electrons in conjugation.

  5. Ultrasonic nonlinear guided wave inspection of microscopic damage in a composite structure (United States)

    Zhang, Li; Borigo, Cody; Owens, Steven; Lissenden, Clifford; Rose, Joseph; Hakoda, Chris


    Sudden structural failure is a severe safety threat to many types of military and industrial composite structures. Because sudden structural failure may occur in a composite structure shortly after macroscale damage initiates, reliable early diagnosis of microdamage formation in the composite structure is critical to ensure safe operation and to reduce maintenance costs. Ultrasonic guided waves have been widely used for long-range defect detection in various structures. When guided waves are generated under certain excitation conditions, in addition to the traditional linear wave mode (known as the fundamental harmonic wave mode), a number of nonlinear higher-order harmonic wave modes are also be generated. Research shows that the nonlinear parameters of a higher-order harmonic wave mode could have excellent sensitivity to microstructural changes in a material. In this work, we successfully employed a nonlinear guided wave structural health monitoring (SHM) method to detect microscopic impact damage in a 32-layer carbon/epoxy fiber-reinforced composite plate. Our effort has demonstrated that, utilizing appropriate transducer design, equipment, excitation signals, and signal processing techniques, nonlinear guided wave parameter measurements can be reliably used to monitor microdamage initiation and growth in composite structures.

  6. Maximum Likelihood Analysis of a Two-Level Nonlinear Structural Equation Model with Fixed Covariates (United States)

    Lee, Sik-Yum; Song, Xin-Yuan


    In this article, a maximum likelihood (ML) approach for analyzing a rather general two-level structural equation model is developed for hierarchically structured data that are very common in educational and/or behavioral research. The proposed two-level model can accommodate nonlinear causal relations among latent variables as well as effects…

  7. Nonlinear response speedup in bimodal visual-olfactory object identification

    Directory of Open Access Journals (Sweden)

    Richard eHöchenberger


    Full Text Available Multisensory processes are vital in the perception of our environment. In the evaluation of foodstuff, redundant sensory inputs not only assist the identification of edible and nutritious substances, but also help avoiding the ingestion of possibly hazardous substances. While it is known that the non-chemical senses interact already at early processing levels, it remains unclear whether the visual and olfactory senses exhibit comparable interaction effects. To address this question, we tested whether the perception of congruent bimodal visual-olfactory objects is facilitated compared to unimodal stimulation. We measured response times (RT and accuracy during speeded object identification. The onset of the visual and olfactory constituents in bimodal trials was physically aligned in the first and perceptually aligned in the second experiment. We tested whether the data favored coactivation or parallel processing consistent with race models. A redundant-signals effect was observed for perceptually aligned redundant stimuli only, i.e. bimodal stimuli were identified faster than either of the unimodal components. Analysis of the RT distributions and accuracy data revealed that these observations could be explained by a race model. More specifically, visual and olfactory channels appeared to be operating in a parallel, positively dependent manner. While these results suggest the absence of early sensory interactions, future studies are needed to substantiate this interpretation.

  8. A study of non-linearity in rainfall-runoff response using 120 UK catchments (United States)

    Mathias, Simon A.; McIntyre, Neil; Oughton, Rachel H.


    This study presents a catchment characteristic sensitivity analysis concerning the non-linearity of rainfall-runoff response in 120 UK catchments. Two approaches were adopted. The first approach involved, for each catchment, regression of a power-law to flow rate gradient data for recession events only. This approach was referred to as the recession analysis (RA). The second approach involved calibrating a rainfall-runoff model to the full data set (both recession and non-recession events). The rainfall-runoff model was developed by combining a power-law streamflow routing function with a one parameter probability distributed model (PDM) for soil moisture accounting. This approach was referred to as the rainfall-runoff model (RM). Step-wise linear regression was used to derive regionalization equations for the three parameters. An advantage of the RM approach is that it utilizes much more of the observed data. Results from the RM approach suggest that catchments with high base-flow and low annual precipitation tend to exhibit greater non-linearity in rainfall-runoff response. In contrast, the results from the RA approach suggest that non-linearity is linked to low evaporative demand. The difference in results is attributed to the aggregation of storm-flow and base-flow into a single system giving rise to a seemingly more non-linear response when applying the RM approach to catchments that exhibit a strongly dual storm-flow base-flow response. The study also highlights the value and limitations in a regionlization context of aggregating storm-flow and base-flow pathways into a single non-linear routing function.

  9. Axisymmetric nonlinear waves and structures in Hall plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Islam, Tanim [Lawrence Livermore National Laboratory, P. O. Box 808, Livermore, California 94551-0808 (United States)


    In this paper, a general equation for the evolution of an axisymmetric magnetic field in a Hall plasma is derived, with an integral similar to the Grad-Shafranov equation. Special solutions arising from curvature-whistler drift modes that propagate along the electron drift as a Burger's shock and nonlinear periodic and soliton-like solutions to the generalized Grad-Shafranov integral-are analyzed. We derive analytical and numerical solutions in a classical electron-ion Hall plasma, in which electrons and ions are the only species in the plasmas. Results may then be applied to the following low-ionized astrophysical plasmas: in protostellar disks, in which the ions may be coupled to the motion of gases; and in molecular clouds and protostellar jets, in which the much heavier charged dust in a dusty Hall plasma may be collisionally coupled to the gas.

  10. Anisotropies in the microwave sky due to nonlinear structures

    Energy Technology Data Exchange (ETDEWEB)

    Martinez-Gonzalez, E.; Sanz, J.L.; Silk, J. (California Univ., Berkeley (USA))


    The propagation of light in a nonstatic linear gravitational potential associated with nonlinear density fluctuations is studied. A potential approximation to Einstein's field equations makes it possible to derive simple expressions for the anisotropies induced in the temperature of the microwave background radiation, associated in particular with angular distortions induced by the time-varying gravitational potential along the line of sight to the surface of last scattering. These results are applied to two examples of interest: a compensated void in the thin-shell approximation and a compensated lump in the Swiss cheese approach, obtaining the same results, with regard to temperature profiles, as those obtained using a general-relativistic treatment. 20 refs.

  11. Axisymmetric Nonlinear Waves And Structures in Hall Plasmas

    CERN Document Server

    Islam, Tanim


    A Hall plasma consists of a plasma with not all species frozen into the magnetic field. In this paper, a general equation for the evolution of an axisymmetric magnetic field in a Hall plasma is derived, with an integral similar to the Grad-Shafranov equation. Special solutions arising from curvature -- whistler drift modes that propagate along the electron drift as a Burger's shock, and nonlinear periodic and soliton-like solutions to the generalized Grad-Shafranov integral -- are analyzed. We derive analytical and numerical solutions in an electron-ion Hall plasma, in which electrons and ions are the only species in the plasmas. Results may then be applied to electron-ion-gas Hall plasmas, in which the ions are coupled to the motion of gases in low ionized plasmas (lower ionosphere and protostellar disks), and to dusty Hall plasmas (such as molecular clouds), in which the much heavier charged dust may be collisionally coupled to the gas.

  12. Nonlinear dynamics of breathers in the spiral structures of magnets

    Energy Technology Data Exchange (ETDEWEB)

    Kiselev, V. V., E-mail:; Raskovalov, A. A. [Russian Academy of Sciences, Mikheev Institute of Metal Physics, Ural Branch (Russian Federation)


    The structure and properties of pulsating solitons (breathers) in the spiral structures of magnets are analyzed within the sine-Gordon model. The breather core pulsations are shown to be accompanied by local shifts and oscillations of the spiral structure with the formation of “precursors” and “tails” in the moving soliton. The possibilities for the observation and excitation of breathers in the spiral structures of magnets and multiferroics are discussed.

  13. Measurement of nonlinear elastic response in rock by the resonant bar method

    Energy Technology Data Exchange (ETDEWEB)

    Johnson, P.A. (Los Alamos National Lab., NM (United States)); Rasolofosaon, P.; Zinszner, B. (Institut Francais du Petrole (IFP), 92 - Rueil-Malmaison (France))


    In this work we are studying the behavior of the fundamental (Young's) mode resonant peak as a function of drive amplitude in rock samples. Our goal from these studies is to obtain nonlinear moduli for many rock types, and to study the nonlinear moduli as a function of water saturation and other changes in physical properties. Measurements were made on seven different room dry rock samples. For one sample measurements were taken at 16 saturation levels between 1 and 98%. All samples display a softening'' nonlinearity, that is, the resonant frequency shifts downward with increasing drive amplitude. In extreme cases, the resonant frequency changes by as much as 25% over a strain interval of 10[sup [minus]7] to [approximately]4 [times] 10[sup [minus]5]. Measurements indicate that the nonlinear response is extremely sensitive to saturation. Estimates of a combined cubic and quartic nonlinear parameter [Gamma] range from approximately [minus]300 to [minus]10[sup 9] for the rock samples.

  14. Non-linear magnetohydrodynamic modeling of plasma response to resonant magnetic perturbations

    Energy Technology Data Exchange (ETDEWEB)

    Orain, F.; Bécoulet, M.; Dif-Pradalier, G.; Nardon, E.; Passeron, C.; Latu, G.; Grandgirard, V.; Fil, A.; Ratnani, A. [CEA, IRFM, F-13108 Saint-Paul-Lez-Durance (France); Huijsmans, G. [ITER Organization, Route de Vinon, F-13115 Saint-Paul-Lez-Durance (France); Pamela, S. [IIFS-PIIM. Aix Marseille Université - CNRS, 13397 Marseille Cedex20 (France); Chapman, I.; Kirk, A.; Thornton, A. [EURATOM/CCFE Fusion Association, Culham Science Centre, Oxon OX14 3DB (United Kingdom); Hoelzl, M. [Max-Planck-Institut für Plasmaphysik, EURATOM Association, Garching (Germany); Cahyna, P. [Association EURATOM/IPP.CR, Prague (Czech Republic)


    The interaction of static Resonant Magnetic Perturbations (RMPs) with the plasma flows is modeled in toroidal geometry, using the non-linear resistive MHD code JOREK, which includes the X-point and the scrape-off-layer. Two-fluid diamagnetic effects, the neoclassical poloidal friction and a source of toroidal rotation are introduced in the model to describe realistic plasma flows. RMP penetration is studied taking self-consistently into account the effects of these flows and the radial electric field evolution. JET-like, MAST, and ITER parameters are used in modeling. For JET-like parameters, three regimes of plasma response are found depending on the plasma resistivity and the diamagnetic rotation: at high resistivity and slow rotation, the islands generated by the RMPs at the edge resonant surfaces rotate in the ion diamagnetic direction and their size oscillates. At faster rotation, the generated islands are static and are more screened by the plasma. An intermediate regime with static islands which slightly oscillate is found at lower resistivity. In ITER simulations, the RMPs generate static islands, which forms an ergodic layer at the very edge (ψ≥0.96) characterized by lobe structures near the X-point and results in a small strike point splitting on the divertor targets. In MAST Double Null Divertor geometry, lobes are also found near the X-point and the 3D-deformation of the density and temperature profiles is observed.

  15. Non-linear magnetohydrodynamic modeling of plasma response to resonant magnetic perturbations (United States)

    Orain, F.; Bécoulet, M.; Dif-Pradalier, G.; Huijsmans, G.; Pamela, S.; Nardon, E.; Passeron, C.; Latu, G.; Grandgirard, V.; Fil, A.; Ratnani, A.; Chapman, I.; Kirk, A.; Thornton, A.; Hoelzl, M.; Cahyna, P.


    The interaction of static Resonant Magnetic Perturbations (RMPs) with the plasma flows is modeled in toroidal geometry, using the non-linear resistive MHD code JOREK, which includes the X-point and the scrape-off-layer. Two-fluid diamagnetic effects, the neoclassical poloidal friction and a source of toroidal rotation are introduced in the model to describe realistic plasma flows. RMP penetration is studied taking self-consistently into account the effects of these flows and the radial electric field evolution. JET-like, MAST, and ITER parameters are used in modeling. For JET-like parameters, three regimes of plasma response are found depending on the plasma resistivity and the diamagnetic rotation: at high resistivity and slow rotation, the islands generated by the RMPs at the edge resonant surfaces rotate in the ion diamagnetic direction and their size oscillates. At faster rotation, the generated islands are static and are more screened by the plasma. An intermediate regime with static islands which slightly oscillate is found at lower resistivity. In ITER simulations, the RMPs generate static islands, which forms an ergodic layer at the very edge (ψ ≥0.96) characterized by lobe structures near the X-point and results in a small strike point splitting on the divertor targets. In MAST Double Null Divertor geometry, lobes are also found near the X-point and the 3D-deformation of the density and temperature profiles is observed.

  16. A computer program for predicting nonlinear uniaxial material responses using viscoplastic models (United States)

    Chang, T. Y.; Thompson, R. L.


    A computer program was developed for predicting nonlinear uniaxial material responses using viscoplastic constitutive models. Four specific models, i.e., those due to Miller, Walker, Krieg-Swearengen-Rhode, and Robinson, are included. Any other unified model is easily implemented into the program in the form of subroutines. Analysis features include stress-strain cycling, creep response, stress relaxation, thermomechanical fatigue loop, or any combination of these responses. An outline is given on the theoretical background of uniaxial constitutive models, analysis procedure, and numerical integration methods for solving the nonlinear constitutive equations. In addition, a discussion on the computer program implementation is also given. Finally, seven numerical examples are included to demonstrate the versatility of the computer program developed.

  17. A hybrid method based upon nonlinear Lamb wave response for locating a delamination in composite laminates. (United States)

    Yelve, Nitesh P; Mitra, Mira; Mujumdar, P M; Ramadas, C


    A new hybrid method based upon nonlinear Lamb wave response in time and frequency domains is introduced to locate a delamination in composite laminates. In Lamb wave based nonlinear method, the presence of damage is shown by the appearance of higher harmonics in the Lamb wave response. The proposed method not only uses this spectral information but also the corresponding temporal response data, for locating the delamination. Thus, the method is termed as a hybrid method. The paper includes formulation of the method and its application to locate a Barely Visible Impact Damage (BVID) induced delamination in a Carbon Fiber Reinforced Polymer (CFRP) laminate. The method gives the damage location fairly well. It is a baseline free method, as it does not need data from the pristine specimen.

  18. Nonlinearity and Strain-Rate Dependence in the Deformation Response of Polymer Matrix Composites Modeled (United States)

    Goldberg, Robert K.


    There has been no accurate procedure for modeling the high-speed impact of composite materials, but such an analytical capability will be required in designing reliable lightweight engine-containment systems. The majority of the models in use assume a linear elastic material response that does not vary with strain rate. However, for containment systems, polymer matrix composites incorporating ductile polymers are likely to be used. For such a material, the deformation response is likely to be nonlinear and to vary with strain rate. An analytical model has been developed at the NASA Glenn Research Center at Lewis Field that incorporates both of these features. A set of constitutive equations that was originally developed to analyze the viscoplastic deformation of metals (Ramaswamy-Stouffer equations) was modified to simulate the nonlinear, rate-dependent deformation of polymers. Specifically, the effects of hydrostatic stresses on the inelastic response, which can be significant in polymers, were accounted for by a modification of the definition of the effective stress. The constitutive equations were then incorporated into a composite micromechanics model based on the mechanics of materials theory. This theory predicts the deformation response of a composite material from the properties and behavior of the individual constituents. In this manner, the nonlinear, rate-dependent deformation response of a polymer matrix composite can be predicted.

  19. Robust identification method for nonlinear model structures and its application to high-performance aircraft (United States)

    Shi, Zhong-Ke; Wu, Fang-Xiang


    A common assumption is that the model structure is known for modelling high performance aircraft. In practice, this is not the case. Actually, structure identification plays the most important role in the processing of nonlinear system modelling. The integration of mode structure identification and parameter estimation is an efficient method to construct the model for high performance aircraft, which is nonlinear and also contains uncertainties. This article presents an efficient method for identifying nonlinear model structure and estimating parameters for high-performance aircraft model, which contains uncertainties. The parameters associated with nonlinear terms are considered one after the other if they should be included in the nonlinear model until a stopping criterion is met, which is based on Akaike's information criterion. A numerically efficient U-D factorisation is presented to avoid complex computation of high-order matrices. The proposed method is applied to flight test data of a high-performance aircraft. The results demonstrate that the proposed method could obtain the good aircraft model with a reasonably good fidelity based on the comparison with flight test data.

  20. Curved Displacement Transfer Functions for Geometric Nonlinear Large Deformation Structure Shape Predictions (United States)

    Ko, William L.; Fleischer, Van Tran; Lung, Shun-Fat


    For shape predictions of structures under large geometrically nonlinear deformations, Curved Displacement Transfer Functions were formulated based on a curved displacement, traced by a material point from the undeformed position to deformed position. The embedded beam (depth-wise cross section of a structure along a surface strain-sensing line) was discretized into multiple small domains, with domain junctures matching the strain-sensing stations. Thus, the surface strain distribution could be described with a piecewise linear or a piecewise nonlinear function. The discretization approach enabled piecewise integrations of the embedded-beam curvature equations to yield the Curved Displacement Transfer Functions, expressed in terms of embedded beam geometrical parameters and surface strains. By entering the surface strain data into the Displacement Transfer Functions, deflections along each embedded beam can be calculated at multiple points for mapping the overall structural deformed shapes. Finite-element linear and nonlinear analyses of a tapered cantilever tubular beam were performed to generate linear and nonlinear surface strains and the associated deflections to be used for validation. The shape prediction accuracies were then determined by comparing the theoretical deflections with the finiteelement- generated deflections. The results show that the newly developed Curved Displacement Transfer Functions are very accurate for shape predictions of structures under large geometrically nonlinear deformations.


    Institute of Scientific and Technical Information of China (English)

    徐旭; 曹志远


    In light of the characteristics of the interactions between flexible structure and wind in three directions, and based on the rational mechanical section-model of structure, a new aerodynamic force model is accepted, i. e. the coefficients of three component forces are the functions of the instantaneous attack angle and rotational speed Ci = Ci(β(t),θ),(i = D, L, M). So, a new method to formulate the linear and nonlinear aerodynamic items of wind and structure interacting has been put forward in accordance with "strip theory"and modified "quasi-static theory ", and then the linear and nonlinear coupled theory of super-slender structure for civil engineering analyzing are converged in one model. For the linear aerodynamic-force parts, the semi-analytical expressions of the items so-called "flutter derivatives" corresponding to the one in the classic equations have been given here,and so have the nonlinear parts. The study of the stability of nonlinear aerodynamic-coupled torsional vibration of the old Tacoma bridge shows that the form and results of the nonlinear control equation in rotational direction are in agreement with that of V. F. Bohm's.

  2. Molecular structure-property correlations from optical nonlinearity and thermal-relaxation dynamics. (United States)

    Bhattacharyya, Indrajit; Priyadarshi, Shekhar; Goswami, Debabrata


    We apply ultrafast single beam Z-scan technique to measure saturation absorption coefficients and nonlinear-refraction coefficients of primary alcohols at 1560 nm. The nonlinear effects result from vibronic transitions and cubic nonlinear-refraction. To measure the pure total third-order nonlinear susceptibility, we removed thermal effects with a frequency optimized optical-chopper. Our measurements of thermal-relaxation dynamics of alcohols, from 1560 nm thermal lens pump and 780 nm probe experiments revealed faster and slower thermal-relaxation timescales, respectively, from conduction and convection. The faster timescale accurately predicts thermal-diffusivity, which decreases linearly with alcohol chain-lengths since thermal-relaxation is slower in heavier molecules. The relation between thermal-diffusivity and alcohol chain-length confirms structure-property relationship.

  3. Structure Detection of Nonlinear Aeroelastic Systems with Application to Aeroelastic Flight Test Data. Part 2 (United States)

    Kukreja, Sunil L.; Brenner, martin J.


    This viewgraph presentation reviews the 1. Motivation for the study 2. Nonlinear Model Form 3. Structure Detection 4. Least Absolute Shrinkage and Selection Operator (LASSO) 5. Objectives 6. Results 7. Assess LASSO as a Structure Detection Tool: Simulated Nonlinear Models 8. Applicability to Complex Systems: F/A-18 Active Aeroelastic Wing Flight Test Data. The authors conclude that 1. this is a novel approach for detecting the structure of highly over-parameterised nonlinear models in situations where other methods may be inadequate 2. that it is a practical significance in the analysis of aircraft dynamics during envelope expansion and could lead to more efficient control strategies and 3. this could allow greater insight into the functionality of various systems dynamics, by providing a quantitative model which is easily interpretable

  4. Cosmology emerging as the gauge structure of a nonlinear quantum system

    CERN Document Server

    Kam, Chon-Fai


    Berry phases and gauge structures in parameter spaces of quantum systems are the foundation of a broad range of quantum effects such as quantum Hall effects and topological insulators. The gauge structures of interacting many-body systems, which often present exotic features, are particularly interesting. While quantum systems are intrinsically linear due to the superposition principle, nonlinear quantum mechanics can arise as an effective theory for interacting systems (such as condensates of interacting bosons). Here we show that gauge structures similar to curved spacetime can arise in nonlinear quantum systems where the superposition principle breaks down. In the canonical formalism of the nonlinear quantum mechanics, the geometric phases of quantum evolutions can be formulated as the classical geometric phases of a harmonic oscillator that represents the Bogoliubov excitations. We find that the classical geometric phase can be described by a de Sitter universe. The fundamental frequency of the harmonic o...

  5. Global stabilization of high-energy response of a nonlinear wideband electromagnetic energy harvester (United States)

    Sato, T.; Kato, S.; Masuda, A.


    This paper presents a resonance-type vibration energy harvester with a Duffing-type nonlinear oscillator which is designed to perform effectively in a wide frequency band. For the conventional linear vibration energy harvester, the maximum performance of the power generation and its bandwidth are in a relation of trade-off. Introducing a Duffing-type nonlinearity can expand the resonance frequency band and enable the harvester to generate larger electric power in a wider frequency range. However, since such nonlinear oscillator may have coexisting multiple steady-state solutions in the resonance band, it is difficult for the nonlinear harvester to maintain the high performance of the power generation constantly. The principle of self-excitation and entrainment has been utilized to give global stability to the high-energy orbit by destabilizing other unexpected low-energy orbits by introducing a switching circuit of the load resistance between positive and the negative values depending on the response amplitude of the oscillator. In this paper, an improved control law that switches the load resistance according to a frequency-dependent threshold is proposed to ensure the oscillator to respond in the high-energy orbit without ineffective power consumption. Numerical study shows that the steady-state responses of the harvester with the proposed control low are successfully kept on the high-energy orbit without repeating activation of the excitationmode.

  6. Stable response of low-gravity liquid non-linear sloshing in a circle cylindrical tank

    Institute of Scientific and Technical Information of China (English)


    Under pitch excitation, the sloshing of liquid in circular cylindrical tank includes planar motion, rotary motion and rotary motion inside planar motion. The boundaries between stable motion and unstable motion depend on the radius of the tank, the liquid height, the gravitational intension, the surface tensor and the sloshing damping. In this article, the differential equations of nonlinear sloshing are built first.And by variational principle, the Lagrange function of liquid pressure is constructed in volume intergration form. Then the velocity potential function is expanded in series by wave height function at the free surface. The nonlinear equations with kinematics and dynamics free surface boundary conditions through variation are derived. At last, these equations are solved by multiple-scales method. The influence of Bond number on the global stable response of nonlinear liquid sloshing in circular cylinder tank is analyzed in detail. The result indicates that variation of amplitude frequency response characteristics of the system with Bond, jump, lag and other nonlinear phenomena of liquid sloshing are investigated.

  7. A displacement-based approach for determining non-linear effects on pre-tensioned-cable cross-braced structures (United States)

    Giaccu, Gian Felice; Caracoglia, Luca


    Pre-tensioned-cable bracing systems are widely employed in structural engineering to limit lateral deflections and stabilize structures. A suitable configuration of the pre-tensioned-cable bracing systems in a structure is an important issue since the internal force distribution, emerging from the interaction with the existing structure, significantly affects the structural dynamic behavior. The design, however, is often based on the intuition and the previous experience of the engineer. In recent years, the authors have been investigating the non-linear dynamic response of cable systems, installed on cable-stayed bridges, and in particular the so-called ;cable-cross-tie systems; forming a cable network. The bracing cables (cross-ties) can exhibit slackening or snapping. Therefore, a non-linear unilateral model, combined with the taut-cable theory, is required to simulate the incipient slackening conditions in the stays. Capitalizing from this work on non-linear cable dynamics, this paper proposes a new approach to analyze, in laterally- braced truss structures, the unilateral effects and dynamic response accounting for the loss in the pre-tensioning force imparted to the bracing cables. This effect leads to non-linear vibration of the structure. In this preliminary study, the free vibrations of the structure are investigated by using the ;Equivalent Linearization Method;. A performance coefficient, a real positive number between 0.5 and 1.0, is defined and employed to monitor the relative reduction in the apparent stiffness of the braces during structural vibration, ;mode by mode;. It is shown that the system can exhibit alternate unilateral behavior of the cross-braces. A reduction of the performance coefficient close to fifty percent is observed in the braces when the initial pre-tensioning force is small. On the other hand the performance coefficient tends to one in the case of a high level of pre-stress. It is concluded that the performance coefficient may

  8. Evaluation on Stability of Stope Structure Based on Nonlinear Dynamics of Coupling Artificial Neural Network

    Institute of Scientific and Technical Information of China (English)


    The nonlinear dynamical behaviors of artificial neural network (ANN) and their application to science and engineering were summarized. The mechanism of two kinds of dynamical processes, i.e. weight dynamics and activation dynamics in neural networks, and the stability of computing in structural analysis and design were stated briefly. It was successfully applied to nonlinear neural network to evaluate the stability of underground stope structure in a gold mine. With the application of BP network, it is proven that the neuro-computing is a practical and advanced tool for solving large-scale underground rock engineering problems.

  9. Reduced-order computational model in nonlinear structural dynamics for structures having numerous local elastic modes in the low-frequency range. Application to fuel assemblies

    Energy Technology Data Exchange (ETDEWEB)

    Batou, A., E-mail: [Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallee (France); Soize, C., E-mail: [Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallee (France); Brie, N., E-mail: [EDF R and D, Département AMA, 1 avenue du général De Gaulle, 92140 Clamart (France)


    Highlights: • A ROM of a nonlinear dynamical structure is built with a global displacements basis. • The reduced order model of fuel assemblies is accurate and of very small size. • The shocks between grids of a row of seven fuel assemblies are computed. -- Abstract: We are interested in the construction of a reduced-order computational model for nonlinear complex dynamical structures which are characterized by the presence of numerous local elastic modes in the low-frequency band. This high modal density makes the use of the classical modal analysis method not suitable. Therefore the reduced-order computational model is constructed using a basis of a space of global displacements, which is constructed a priori and which allows the nonlinear dynamical response of the structure observed on the stiff part to be predicted with a good accuracy. The methodology is applied to a complex industrial structure which is made up of a row of seven fuel assemblies with possibility of collisions between grids and which is submitted to a seismic loading.

  10. Parametric system identification of resonant micro/nanosystems operating in a nonlinear response regime (United States)

    Sabater, A. B.; Rhoads, J. F.


    The parametric system identification of macroscale resonators operating in a nonlinear response regime can be a challenging research problem, but at the micro- and nanoscales, experimental constraints add additional complexities. For example, due to the small and noisy signals micro/nanoresonators produce, a lock-in amplifier is commonly used to characterize the amplitude and phase responses of the systems. While the lock-in enables detection, it also prohibits the use of established time-domain, multi-harmonic, and frequency-domain methods, which rely upon time-domain measurements. As such, the only methods that can be used for parametric system identification are those based on fitting experimental data to an approximate solution, typically derived via perturbation methods and/or Galerkin methods, of a reduced-order model. Thus, one could view the parametric system identification of micro/nanosystems operating in a nonlinear response regime as the amalgamation of four coupled sub-problems: nonparametric system identification, or proper experimental design and data acquisition; the generation of physically consistent reduced-order models; the calculation of accurate approximate responses; and the application of nonlinear least-squares parameter estimation. This work is focused on the theoretical foundations that underpin each of these sub-problems, as the methods used to address one sub-problem can strongly influence the results of another. To provide context, an electromagnetically transduced microresonator is used as an example. This example provides a concrete reference for the presented findings and conclusions.

  11. Nonlinear response of soil respiration to increasing nitrogen additions in a Tibetan alpine steppe (United States)

    Peng, Yunfeng; Li, Fei; Zhou, Guoying; Fang, Kai; Zhang, Dianye; Li, Changbin; Yang, Guibiao; Wang, Guanqin; Wang, Jun; Mohammat, Anwar; Yang, Yuanhe


    Nitrogen (N) availability is a key regulator of carbon (C) cycling in terrestrial ecosystems. Anthropogenic N input, such as N deposition and fertilization, increases N availability in soil, which has important implications for an ecosystem’s C storage and loss. Soil respiration (Rs), which is the second largest C flux from terrestrial ecosystems to the atmosphere, plays an important role in terrestrial C cycles. The direction and magnitude of the responses of Rs and its components to N addition have been widely evaluated, but it remains unclear how these processes change across multiple N addition levels. Here we conducted a two-year field experiment to examine the changes of Rs and its autotrophic respiration (Ra) and heterotrophic respiration (Rh) components along a gradient of eight N levels (0, 1 2, 4, 8, 16, 24, 32 g m‑2 yr‑1) in a Tibetan alpine steppe, and used structural equation modeling (SEM) to explore the relative contributions of biotic and abiotic variables and their direct and indirect pathways regulating the Ra and Rh. Our results indicated that both Rs and Ra exhibited first increasing and then subsequent decreasing trends at the threshold of 8 g N m‑2 yr‑1. In contrast, the Rh declined linearly with the N addition rate continuously increasing. SEM analysis revealed that, among various environmental factors, soil temperature was the most important one modulating Rs, which not only had a direct effect on the two Rs components, but also indirectly regulated the Ra and Rh via root and microbial biomass. These findings suggest that the nonlinear response patterns of Rs should be considered for better predicting terrestrial C balance, given that anthropogenic N input to the terrestrial ecosystems is increasing continuously.

  12. Nonlinear seismic response analysis of a high-strength concrete frame structure reinforced with high-strength bars%高强钢筋高强混凝土框架结构非线性地震反应分析

    Institute of Scientific and Technical Information of China (English)

    阎石; 陈鑫; 季保建


    研究配有高强钢筋的高强混凝土框架结构的抗震性能.采用OpenSees开放式软件对配有高强钢筋的高强混凝土框架结构进行了地震作用下的非线性有限元分析,并将计算结果与同等参数条件下的结构拟动力试验进行了对比.得到不同峰值加速度情况下的结构层间反应时程曲线,层间位移滞回曲线,以及破坏模式等,数值计算结果与试验吻合程度较好.研究结果表明利用基于OpenSees的有限元分析方法,能够有效地分析配有高强钢筋的高强混凝土框架结构的地震响应,可以辅助研究该结构的抗震性能.%The nonlinear seismic response analysis of a two-story high-strength concrete frame structure is completed by using OpenSees software, which installed high-strength transverse and partly longitudinal reinforcement. The placement of the high-strength bars is to increase the ductility of the frame by effectively confining the core concrete to a three dimensional compression state. The results of the FEM simulation are compared with those of pseudo-dynamic model test with the same parameters, so the relative time history responses for the stories, hysteretic loops and failure modes of the frame under different peak acceleration are obtained, results between numerical computation and test are matched well. The FEM based on OpenSees software can effectively analyze the seismic responses of the high-strength concrete frame structure reinforced with high-strength bars and can additionally study the seismic performance of the kind of structures.

  13. Structural and nonlinear optical properties of as-grown and annealed metallophthalocyanine thin films

    Energy Technology Data Exchange (ETDEWEB)

    Zawadzka, A., E-mail: [Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Torun (Poland); Płóciennik, P.; Strzelecki, J. [Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Torun (Poland); Pranaitis, M.; Dabos-Seignon, S.; Sahraoui, B. [LUNAM Université, Université d' Angers, CNRS UMR 6200, Laboratoire MOLTECH-Anjou, 2 bd Lavoisier, 49045 Angers cedex (France)


    The paper presents the Third Harmonic Generation investigation of four metallophtalocyanine (MPc, M = Cu, Co, Mg and Zn) thin films. The investigated films were fabricated by Physical Vapor Deposition in high vacuum onto quartz substrates. MPc thin films were annealed after fabrication in ambient atmosphere for 12 h at the temperature equal to 150 °C or 250 °C. The Third Harmonic Generation spectra were measured to investigate the nonlinear optical properties and their dependence on the structure of the thin film after the annealing process. This approach allowed us to determine the electronic contribution of the third-order nonlinear optical susceptibility χ{sup <3>}{sub elec} of these MPc films and to investigate two theoretical models for explanation of the observed results. We find that the annealing process significantly changes the optical and structural properties of MPc thin films. - Highlights: • Metallophtalocyanine thin films were grown by Physical Vapor Deposition technique. • MPcs thin films were undergone an annealing process in ambient atmosphere. • Third Harmonic spectra were measured to investigate nonlinear optical properties. • The third order nonlinear optical susceptibility χ{sup <3>}{sub elec} was determined. • We report changing both nonlinear optical and structural properties of thin films.

  14. Nonlinear Response of Unbiased and Biased Bilayer Graphene at Terahertz Frequencies (United States)

    McGouran, Riley

    The main focus of this thesis is the investigation of the nonlinear response of unbiased and biased bilayer graphene to incident radiation at terahertz frequencies. We present a tight-binding model of biased and unbiased bilayer graphene that is used to calculate the nonlinear terahertz response. Dynamic equations are developed for the electron density matrix within the length gauge. These equations facilitate the calculation of interband and intraband carrier dynamics. We then obtain nonlinear transmitted and reflected terahertz fields using the calculated nonlinear interband and intraband current densities. We examine the nonlinear response of unbiased bilayer graphene as a function of the incident field amplitude. In this case the sample is taken to be undoped. In the reflected field, we find the maximum third harmonic amplitude to be approximately 30% of the fundamental frequency for an incident field of 1.5 kV cm-1, which is greater than that found in undoped monolayer graphene at the same field amplitude. To examine the nonlinear response of biased bilayer graphene, we investigate two different scenarios. In the first scenario, we consider an undoped sample at fixed temperature. We find that when the external bias has a value of 2 meV, the generated third harmonic in the reflected field is approximately 45% of the fundamental for an incident field amplitude of 2 kV cm-1 . When we increase the external bias further to 8 meV, we find the generated third harmonic field is approximately 38% of the fundamental for an incident field amplitude of 1 kV cm-1. For both of these bias values, the generated third harmonic is greater than that found in undoped monolayer graphene. In that system, the generated third harmonic field is approximately 32% of the fundamental for an incident field amplitude of 200 V cm-1. In the second scenario, we consider doped biased bilayer graphene. We fix the carrier density at 2x1012 cm-2, the incident field amplitude at 50 kV cm-1, and

  15. Effect of nonlinearity of connecting dampers on vibration control of connected building structures

    Directory of Open Access Journals (Sweden)

    Masatoshi eKasagi


    Full Text Available The connection of two building structures with dampers is one of effective vibration control systems. In this vibration control system, both buildings have to possess different vibration properties in order to provide a higher vibration reduction performance. In addition to such condition of different vibration properties of both buildings, the connecting dampers also play an important role in the vibration control mechanism. In this paper, the effect of nonlinearity of connecting dampers on the vibration control of connected building structures is investigated in detail. A high-damping rubber damper and an oil damper with and without relief mechanism are treated. It is shown that, while the high-damping rubber damper is effective in a rather small deformation level, the linear oil damper is effective in a relatively large deformation level. It is further shown that, while the oil dampers reduce the response in the same phase as the case without dampers, the high-damping rubber dampers change the phase. The merit is that the high-damping rubber can reduce the damper deformation and keep the sufficient space between both buildings. This can mitigate the risk of building pounding.

  16. Study of the Performance of an All-Optical Half-Adder Based on Three-Core Non-Linear Directional Fiber Coupler Under Delayed and Instantaneous Non-Linear Kerr Responses (United States)

    Menezes, J. W. M.; Fraga, W. B.; Lima, F. T.; Guimarães, G. F.; Ferreira, A. C.; Lyra, M. L.; Sombra, A. S. B.


    Recently, much attention has been given to the influence of the relaxation process of the non-linear response, because the usual assumption of instantaneous non-linear response fails for ultra-short pulses, and additional contributions coming from non-linear dispersion and delayed non-linearity have to be taken into account. This article presents a numerical analysis of the symmetric planar and asymmetric planar three-core non-linear directional fiber couplers operating with a soliton pulse, where effects of both delayed and instantaneous non-linear Kerr responses are analyzed for implementation of an all-optical half-adder. To implement this all-optical half-adder, eight configurations were analyzed for the non-linear directional fiber coupler, with two symmetric and six asymmetric configurations. The half-adder is the key building block for many digital processing functions, such as shift register, binary counter, and serial parallel data converters. The optical coupler is an important component for applications in optical-fiber telecommunication systems and all integrated optical circuit because of its very high switching speeds. In this numerical simulation, the symmetric/asymmetric planar presents a structure with three cores in a parallel equidistant arrangement, three logical inputs, and two output energy. To prove the effectiveness of the theoretical model for generation of the all-optical half-adder, the best phase to be applied to the control pulse was sought, and a study was done of the extinction ratio level as a function of the Δ > parameter, the normalized time duration, and the Sum and Carry outputs of the (symmetric planar/asymmetric planar) non-linear directional fiber coupler. In this article, the interest is in transmission characteristics, extinction ratio level, normalized time duration, and pulse evolution along the non-linear directional fiber coupler. To compare the performance of the all-optical half-adders, the figure of merit of the

  17. Beyond the perturbative description of the nonlinear optical response of low-index materials. (United States)

    Reshef, Orad; Giese, Enno; Zahirul Alam, M; De Leon, Israel; Upham, Jeremy; Boyd, Robert W


    We show that standard approximations in nonlinear optics are violated for situations involving a small value of the linear refractive index. Consequently, the conventional equation for the intensity-dependent refractive index, n(I)=n0+n2I, becomes inapplicable in epsilon-near-zero and low-index media, even in the presence of only third-order effects. For the particular case of indium tin oxide, we find that the χ((3)), χ((5)), and χ((7)) contributions to refraction eclipse the linear term; thus, the nonlinear response can no longer be interpreted as a perturbation in these materials. Although the response is non-perturbative, we find no evidence that the power series expansion of the material polarization diverges.

  18. The horizontal angular vestibulo-ocular reflex: a nonlinear mechanism for context-dependent responses. (United States)

    Ranjbaran, Mina; Galiana, Henrietta L


    Studies of the vestibulo-ocular reflex (VOR) have revealed that this type of involuntary eye movement is influenced by viewing distance. This paper presents a bilateral model for the horizontal angular VOR in the dark based on realistic physiological mechanisms. It is shown that by assigning proper nonlinear neural computations at the premotor level, the model is capable of replicating target-distance-dependent VOR responses that are in agreement with geometrical requirements. Central premotor responses in the model are also shown to be consistent with experimental observations. Moreover, the model performance after simulated unilateral canal plugging also reproduces experimental observations, an emerging property. Such local nonlinear computations could similarly generate context-dependent behaviors in other more complex motor systems.

  19. Electron vortex magnetic holes: a nonlinear coherent plasma structure

    CERN Document Server

    Haynes, Christopher T; Camporeale, Enrico; Sundberg, Torbjorn


    We report the properties of a novel type of sub-proton scale magnetic hole found in two dimensional PIC simulations of decaying turbulence with a guide field. The simulations were performed with a realistic value for ion to electron mass ratio. These structures, electron vortex magnetic holes (EVMHs), have circular cross-section. The magnetic field depression is associated with a diamagnetic azimuthal current provided by a population of trapped electrons in petal-like orbits. The trapped electron population provides a mean azimuthal velocity and since trapping preferentially selects high pitch angles, a perpendicular temperature anisotropy. The structures arise out of initial perturbations in the course of the turbulent evolution of the plasma, and are stable over at least 100 electron gyroperiods. We have verified the model for the EVMH by carrying out test particle and PIC simulations of isolated structures in a uniform plasma. It is found that (quasi-)stable structures can be formed provided that there is ...

  20. Simulating Nonlinear Dynamics of Deployable Space Structures Project (United States)

    National Aeronautics and Space Administration — To support NASA's vital interest in developing much larger solar array structures over the next 20 years, MotionPort LLC's Phase I SBIR project will strengthen...