Nonlinear Viscoelastic Characterization of Structural Adhesives.
1983-06-01
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
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)
1997-07-01
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.
Structure-induced nonlinear viscoelasticity of non-woven fibrous matrices.
Rizvi, Mohd Suhail; Pal, Anupam; Das, Sovan Lal
2016-12-01
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.
Padovan, Joe
1987-01-01
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.
Padovan, Joe
1986-01-01
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.
Nonlinear Dynamics of Coiling in Viscoelastic Jets
Majmudar, Trushant; Hartt, William; McKinley, Gareth
2010-01-01
Instabilities in free surface continuous jets of non-Newtonian fluids, although relevant for many industrial processes, remain less well understood in terms of fundamental fluid dynamics. Inviscid, and viscous Newtonian jets have been studied in great detail; buckling instability in viscous jets leads to regular periodic coiling of the jet that exhibits a non-trivial frequency dependence with the height of the fall. Very few experimental or theoretical studies exist for continuous viscoelastic jets beyond the onset of the first instability. Here, we present a systematic study of the effects of viscoelasticity on the dynamics of free surface continuous jets of surfactant solutions that form worm-like micelles. We observe complex nonlinear spatio-temporal dynamics of the jet and uncover a transition from periodic to doubly-periodic or quasi-periodic to a multi-frequency, possibly chaotic dynamics. Beyond this regime, the jet dynamics smoothly crosses over to exhibit the "leaping shampoo effect" or the Kaye effe...
A nonlinear viscoelastic constitutive equation - Yield predictions in multiaxial deformations
Shay, R. M., Jr.; Caruthers, J. M.
1987-01-01
Yield stress predictions of a nonlinear viscoelastic constitutive equation for amorphous polymer solids have been obtained and are compared with the phenomenological von Mises yield criterion. Linear viscoelasticity theory has been extended to include finite strains and a material timescale that depends on the instantaneous temperature, volume, and pressure. Results are presented for yield and the correct temperature and strain-rate dependence in a variety of multiaxial deformations. The present nonlinear viscoelastic constitutive equation can be formulated in terms of either a Cauchy or second Piola-Kirchhoff stress tensor, and in terms of either atmospheric or hydrostatic pressure.
Exposing the nonlinear viscoelastic behavior of asphalt-aggregate mixes
Levenberg, Eyal; Uzan, Jacob
2012-05-01
In this study asphalt-aggregate mixes are treated as both viscoelastic and viscoplastic. Following a damage mechanics approach, a nonlinear viscoelastic constitutive formulation is generated from a linear formulation by replacing `applied stresses' with `effective viscoelastic stresses'. A non-dimensional scalar entity called `relative viscoelastic stiffness' is introduced; it is defined as the ratio of applied to effective viscoelastic stress and encapsulates different types of nonlinearities. The paper proposes a computational scheme for exposing these nonlinearities by uncovering, through direct analysis of any test data, changes experienced by the `relative viscoelastic stiffness'. In general terms, the method is based on simultaneous application of creep and relaxation formulations while preserving the interrelationship between the corresponding time functions. The proposed scheme is demonstrated by analyzing a uniaxial tension test and a uniaxial compression test (separately). Results are presented and discussed, unveiling and contrasting the character of viscoelastic nonlinearities in both cases. A conceptual viewpoint is offered to explain the observations, illustrating the requirements from any candidate constitutive theory.
Linear and nonlinear viscoelastic arterial wall models: application on animals
Ghigo, Arthur; Armentano, Ricardo; Lagrée, Pierre-Yves; Fullana, Jose-Maria
2016-01-01
This work deals with the viscoelasticity of the arterial wall and its influence on the pulse waves. We describe the viscoelasticity by a non-linear Kelvin-Voigt model in which the coefficients are fitted using experimental time series of pressure and radius measured on a sheep's arterial network. We obtained a good agreement between the results of the nonlinear Kelvin-Voigt model and the experimental measurements. We found that the viscoelastic relaxation time-defined by the ratio between the viscoelastic coefficient and the Young's modulus-is nearly constant throughout the network. Therefore, as it is well known that smaller arteries are stiffer, the viscoelastic coefficient rises when approaching the peripheral sites to compensate the rise of the Young's modulus, resulting in a higher damping effect. We incorporated the fitted viscoelastic coefficients in a nonlinear 1D fluid model to compute the pulse waves in the network. The damping effect of viscoelasticity on the high frequency waves is clear especiall...
Institute of Scientific and Technical Information of China (English)
盛冬发; 张燕; 程昌钧
2004-01-01
Based on convolution-type constitutive equations for linear viscoelastic materials with damage and the hypotheses of Timoshenko beams with large deflections, the nonlinear equations governing dynamical behavior of Timoshenko beams with damage on viscoelastic foundation were firstly derived. By using the Galerkin method in spatial domain, the nonlinear integro-partial differential equations were transformed into a set of integro-ordinary differential equations. The numerical methods in nonlinear dynamical systems, such as the phase-trajectory diagram, Poincare section and bifurcation figure, were used to solve the simplified systems of equations. It could be seen that simplified dynamical systems possess the plenty of nonlinear dynamical properties. The influence of load and material parameters on the dynamic behavior of nonlinear system were investigated in detail.
NON-LINEAR FORCED VIBRATION OF AXIALLY MOVING VISCOELASTIC BEAMS
Institute of Scientific and Technical Information of China (English)
Yang Xiaodong; Chen Li-Qun
2006-01-01
The non-linear forced vibration of axially moving viscoelastic beams excited by the vibration of the supporting foundation is investigated. A non-linear partial-differential equation governing the transverse motion is derived from the dynamical, constitutive equations and geometrical relations. By referring to the quasi-static stretch assumption, the partial-differential non-linearity is reduced to an integro-partial-differential one. The method of multiple scales is directly applied to the governing equations with the two types of non-linearity, respectively. The amplitude of near- and exact-resonant steady state is analyzed by use of the solvability condition of eliminating secular terms. Numerical results are presented to show the contributions of foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.
VOID GROWTH AND CAVITATION IN NONLINEAR VISCOELASTIC SOLIDS
Institute of Scientific and Technical Information of China (English)
张赟; 黄筑平
2003-01-01
This paper discusses the growth of a pre-existing void in a nonlinear viscoelastic material subjected to remote hydrostatic tensions with different loading rates. The constitutive relation of this viscoelastic material is the one recently proposed by the present authors, which may be considered as a generalization of the non-Gaussian statistical theory in rubber elasticity. As the first order approximation, the above constitutive relation can be reduced to the "neo-Hookean" type viscoelastic one.Investigations of the influences of the material viscosity and the loading rate on the void growth, or on the cavitation are carried out. It is found that: (1) for generalized "inverse Langevin approximation"nonlinear viscoelastic materials, the cavitation limit does not exist, but there is a certain (remote)stress level at which the void will grow rapidly; (2) for generalized "Gaussian statistics" (neo-Hookean type) viscoelastic materials, the cavitation limit exists, and is an increasing function of the loading rate.The present discussions may be of importance in understanding the material failure process under high triaxial stress.
Swimming speeds of filaments in nonlinearly viscoelastic fluids
Fu, Henry C; Powers, Thomas R; 10.1063/1.3086320
2010-01-01
Many microorganisms swim through gels and non-Newtonian fluids in their natural environments. In this paper, we focus on microorganisms which use flagella for propulsion. We address how swimming velocities are affected in nonlinearly viscoelastic fluids by examining the problem of an infinitely long cylinder with arbitrary beating motion in the Oldroyd-B fluid. We solve for the swimming velocity in the limit in which deflections of the cylinder from its straight configuration are small relative to the radius of the cylinder and the wavelength of the deflections; furthermore, the radius of the cylinder is small compared to the wavelength of deflections. We find that swimming velocities are diminished by nonlinear viscoelastic effects. We apply these results to examine what types of swimming motions can produce net translation in a nonlinear fluid, comparing to the Newtonian case, for which Purcell's "scallop" theorem describes how time-reversibility constrains which swimming motions are effective. We find that...
Energy Technology Data Exchange (ETDEWEB)
HAMMERAND,DANIEL C.; KAPANIA,RAKESH K.
2000-05-01
A triangular flat shell element for large deformation analysis of linear viscoelastic laminated composites is presented. Hygrothermorheologically simple materials are considered for which a change in the hygrothermal environment results in a horizontal shifting of the relaxation moduli curves on a log time scale, in addition to the usual hygrothermal loads. Recurrence relations are developed and implemented for the evaluation of the viscoelastic memory loads. The nonlinear deformation process is computed using an incremental/iterative approach with the Newton-Raphson Method used to find the incremental displacements in each step. The presented numerical examples consider the large deformation and stability of linear viscoelastic structures under deformation-independent mechanical loads, deformation-dependent pressure loads, and thermal loads. Unlike elastic structures that have a single critical load value associated with a given snapping of buckling instability phenomenon, viscoelastic structures will usually exhibit a particular instability for a range of applied loads over a range of critical times. Both creep buckling and snap-through examples are presented here. In some cases, viscoelastic results are also obtained using the quasielastic method in which load-history effects are ignored, and time-varying viscoelastic properties are simply used in a series of elastic problems. The presented numerical examples demonstrate the capability and accuracy of the formulation.
Directory of Open Access Journals (Sweden)
Esfandiar, H.
2013-05-01
Full Text Available In this paper, based on the VoigtKelvin constitutive model, nonlinear dynamic modelling and state space representation of a viscoelastic beam acting as a flexible robotic manipulator is investigated. Complete nonlinear dynamic modelling of a viscoelastic beam without premature linearisation of dynamic equations is developed. The adopted method is capable of reproducing nonlinear dynamic effects, such as beam stiffening due to centrifugal and Coriolis forces induced by rotation of the joints. Structural damping effects on the models dynamic behaviour are also shown. A reliable model for a viscoelastic beam is subsequently presented. The governing equations of motion are derived using Hamiltons principle, and using the finite difference method, nonlinear partial differential equations are reduced to ordinary differential equations. For the purpose of flexible manipulator control, the standard form of state space equations for the viscoelastic link and the actuator is obtained. Simulation results indicate substantial improvements in dynamic behaviour, and a parameter sensitivity study is carried out to investigate the effect of structural damping on the vibration amplitude.
EFFECT OF DAMAGE ON NONLINEAR DYNAMIC PROPERTIES OF VISCOELASTIC RECTANGULAR PLATES
Institute of Scientific and Technical Information of China (English)
ZHENG Yu-fang; FU Yi-ming
2005-01-01
The nonlinear dynamic behaviors of viscoelastic rectangular plates including the damage effects under the action of a transverse periodic load were studied. Using the von Karman equations, Boltzmann superposition principle and continuum damage mechanics, the nonlinear dynamic equations in terms of the mid-plane displacements for the viscoelastic thin plates with damage effect were derived. By adopting the finite difference method and Newmark method, these equations were solved. The results were compared with the available data. In the numerical calculations, the effects of the external loading parameters and geometric dimensions of the plate on the nonlinear dynamic responses of the plate were discussed. Research results show that the nonlinear dynamic response of the structure will change remarkably when the damage effect is considered.
VISCOELASTIC STRUCTURAL MODEL OF ASPHALT CONCRETE
Directory of Open Access Journals (Sweden)
V. Bogomolov
2016-06-01
Full Text Available The viscoelastic rheological model of asphalt concrete based on the generalized Kelvin model is offered. The mathematical model of asphalt concrete viscoelastic behavior that can be used for calculation of asphalt concrete upper layers of non-rigid pavements for strength and rutting has been developed. It has been proved that the structural model of Burgers does not fully meet all the requirements of the asphalt-concrete.
Nonlinear dynamics of structures
Oller, Sergio
2014-01-01
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.
Nonlinear viscoelasticity and generalized failure criterion for biopolymer gels
Divoux, Thibaut; Keshavarz, Bavand; Manneville, Sébastien; McKinley, Gareth
2016-11-01
Biopolymer gels display a multiscale microstructure that is responsible for their solid-like properties. Upon external deformation, these soft viscoelastic solids exhibit a generic nonlinear mechanical response characterized by pronounced stress- or strain-stiffening prior to irreversible damage and failure, most often through macroscopic fractures. Here we show on a model acid-induced protein gel that the nonlinear viscoelastic properties of the gel can be described in terms of a 'damping function' which predicts the gel mechanical response quantitatively up to the onset of macroscopic failure. Using a nonlinear integral constitutive equation built upon the experimentally-measured damping function in conjunction with power-law linear viscoelastic response, we derive the form of the stress growth in the gel following the start up of steady shear. We also couple the shear stress response with Bailey's durability criteria for brittle solids in order to predict the critical values of the stress σc and strain γc for failure of the gel, and how they scale with the applied shear rate. This provides a generalized failure criterion for biopolymer gels in a range of different deformation histories. This work was funded by the MIT-France seed fund and by the CNRS PICS-USA scheme (#36939). BK acknowledges financial support from Axalta Coating Systems.
Three-sphere swimmer in a nonlinear viscoelastic medium
Curtis, Mark P.
2013-04-10
A simple model for a swimmer consisting of three colinearly linked spheres attached by rods and oscillating out of phase to break reciprocal motion is analyzed. With a prescribed forcing of the rods acting on the three spheres, the swimming dynamics are determined analytically in both a Newtonian Stokes fluid and a zero Reynolds number, nonlinear, Oldroyd-B viscoelastic fluid with Deborah numbers of order one (or less), highlighting the effects of viscoelasticity on the net displacement of swimmer. For instance, the model predicts that the three-sphere swimmer with a sinusoidal, but nonreciprocal, forcing cycle within an Oldroyd-B representation of a polymeric Boger fluid moves a greater distance with enhanced efficiency in comparison with its motility in a Newtonian fluid of the same viscosity. Furthermore, the nonlinear contributions to the viscoelastic constitutive relation, while dynamically nontrivial, are predicted a posteriori to have no effect on swimmer motility at leading order, given a prescribed forcing between spheres. © 2013 American Physical Society.
Ansari, R.; Faraji Oskouie, M.; Gholami, R.
2016-01-01
In recent decades, mathematical modeling and engineering applications of fractional-order calculus have been extensively utilized to provide efficient simulation tools in the field of solid mechanics. In this paper, a nonlinear fractional nonlocal Euler-Bernoulli beam model is established using the concept of fractional derivative and nonlocal elasticity theory to investigate the size-dependent geometrically nonlinear free vibration of fractional viscoelastic nanobeams. The non-classical fractional integro-differential Euler-Bernoulli beam model contains the nonlocal parameter, viscoelasticity coefficient and order of the fractional derivative to interpret the size effect, viscoelastic material and fractional behavior in the nanoscale fractional viscoelastic structures, respectively. In the solution procedure, the Galerkin method is employed to reduce the fractional integro-partial differential governing equation to a fractional ordinary differential equation in the time domain. Afterwards, the predictor-corrector method is used to solve the nonlinear fractional time-dependent equation. Finally, the influences of nonlocal parameter, order of fractional derivative and viscoelasticity coefficient on the nonlinear time response of fractional viscoelastic nanobeams are discussed in detail. Moreover, comparisons are made between the time responses of linear and nonlinear models.
Nonlinear waves in a fluid-filled thin viscoelastic tube
Zhang, Shan-Yuan; Zhang, Tao
2010-11-01
In the present paper the propagation property of nonlinear waves in a thin viscoelastic tube filled with incompressible inviscid fluid is studied. The tube is considered to be made of an incompressible isotropic viscoelastic material described by Kelvin—Voigt model. Using the mass conservation and the momentum theorem of the fluid and radial dynamic equilibrium of an element of the tube wall, a set of nonlinear partial differential equations governing the propagation of nonlinear pressure wave in the solid—liquid coupled system is obtained. In the long-wave approximation the nonlinear far-field equations can be derived employing the reductive perturbation technique (RPT). Selecting the exponent α of the perturbation parameter in Gardner—Morikawa transformation according to the order of viscous coefficient η, three kinds of evolution equations with soliton solution, i.e. Korteweg—de Vries (KdV)—Burgers, KdV and Burgers equations are deduced. By means of the method of traveling-wave solution and numerical calculation, the propagation properties of solitary waves corresponding with these evolution equations are analysed in detail. Finally, as a example of practical application, the propagation of pressure pulses in large blood vessels is discussed.
Nonlinear waves in a fluid-filled thin viscoelastic tube
Institute of Scientific and Technical Information of China (English)
Zhang Shan-Yuan; Zhang Tao
2010-01-01
In the present paper the propagation property of nonlinear waves in a thin viscoelastic tube filled with incom-pressible inviscid fluid is studied. The tube is considered to be made of an incompressible isotropic viscoelastic material described by Kelvin-Voigt model. Using the mass conservation and the momentum theorem of the fluid and radial dynamic equilibrium of an element of the tube wall, a set of nonlinear partial differential equations governing the prop-agation of nonlinear pressure wave in the solid-liquid coupled system is obtained. In the long-wave approximation the nonlinear far-field equations can be derived employing the reductive perturbation technique (RPT). Selecting the expo-η, three kinds of evolution equations with soliton solution, i.e. Korteweg-de Vries (KdV)-Burgers, KdV and Burgers equations are deduced. By means of the method of traveling-wave solution and numerical calculation, the propagation properties of solitary waves corresponding with these evolution equations are analysed in detail. Finally, as a example of practical application, the propagation of pressure pulses in large blood vessels is discussed.
Superpressure Balloon Design Using Nonlinear Viscoelasticity
Rand, James; Rand, James; Wakefield, David
both the deployment and pressurization of a pumpkin shaped balloon, excess material should be removed. However, the stresses in the circumferential direction increase as the gore width is reduced which has led to the fear that "tertiary" creep may occur. The concept of "strain arrest" is now being introduced into the design procedure which will permit the use polyethylene film in a biaxial state of stress with confidence. This concept is based on the observation that the deformation of the material is time dependent and nonlinear. As the envelope material creeps in the circumferential direction, the film will elongate and form a lobe with a smaller radius of curvature. This will cause the stress to decrease and achieve a stable state of equilibrium. This paper will demonstrate the need for an accurate constitutive relation for the material which includes both the nonlinear and time dependent nature of the film in a biaxial stress state. In addition, analysis techniques must be able to describe the response of the system to the time dependent changes in temperature and pressure. Both of these requirements have now been accomplished and will be demonstrated.
Molecular and structural analysis of viscoelastic properties
Yapp, Rebecca D.; Kalyanam, Sureshkumar; Insana, Michael F.
2007-03-01
Elasticity imaging is emerging as an important tool for breast cancer detection and monitoring of treatment. Viscoelastic image contrast in breast lesions is generated by disease specific processes that modify the molecular structure of connective tissues. We showed previously that gelatin hydrogels exhibit mechanical behavior similar to native collagen found in breast tissue and therefore are suitable as phantoms for elasticity imaging. This paper summarizes our study of the viscoelastic properties of hydrogels designed to discover molecular-scale sources of elasticity image contrast.
Nonlinear Viscoelastic Mechanism for Aftershock Triggering and Decay
Shcherbakov, R.; Zhang, X.
2016-12-01
Aftershocks are ubiquitous in nature. They are the manifestation of relaxation phenomena observed in various physical systems. In one prominent example, they typically occur after large earthquakes. They also occur in other natural or experimental systems, for example, in solar flares, in fracture experiments on porous materials and acoustic emissions, after stock market crashes, in the volatility of stock prices returns, in internet traffic variability and e-mail spamming, to mention a few. The observed aftershock sequences usually obey several well defined non-trivial empirical laws in magnitude, temporal, and spatial domains. In many cases their characteristics follow scale-invariant distributions. The occurrence of aftershocks displays a prominent temporal behavior due to time-dependent mechanisms of stress and/or energy transfer. In this work, we consider a slider-block model to mimic the behavior of a seismogenic fault. In the model, we introduce a nonlinear viscoelastic coupling mechanism to capture the essential characteristics of crustal rheology and stress interaction between the blocks and the medium. For this purpose we employ nonlinear Kelvin-Voigt elements consisting of an elastic spring and a dashpot assembled in parallel to introduce viscoelastic coupling between the blocks and the driving plate. By mapping the model into a cellular automaton we derive the functional form of the stress transfer mechanism in the model. We show that the nonlinear viscoelasticity plays a critical role in triggering of aftershocks. It explains the functional form of the Omori-Utsu law and gives physical interpretation of its parameters. The proposed model also suggests that the power-law rheology of the fault gauge and underlying lower crust and upper mantle control the decay rate of aftershocks. To verify this, we analyze several prominent aftershock sequences to estimate their decay rates and correlate with the rheological properties of the underlying lower crust and
Blow-up of a hyperbolic equation of viscoelasticity with supercritical nonlinearities
Guo, Yanqiu; Rammaha, Mohammad A.; Sakuntasathien, Sawanya
2017-02-01
We investigate a hyperbolic PDE, modeling wave propagation in viscoelastic media, under the influence of a linear memory term of Boltzmann type, and a nonlinear damping modeling friction, as well as an energy-amplifying supercritical nonlinear source:
The role of nonlinear viscoelasticity on the functionality of laminating shortenings
Energy Technology Data Exchange (ETDEWEB)
Macias-Rodriguez, Braulio A.; Peyronel, Fernanda; Marangoni, Alejandro G.
2017-11-01
The rheology of fats is essential for the development of homogeneous and continuous layered structures of doughs. Here, we define laminating shortenings in terms of rheological behavior displayed during linear-to-nonlinear shear deformations, investigated by large amplitude oscillatory shear rheology. Likewise, we associate the rheological behavior of the shortenings with structural length scales elucidated by ultra-small angle x-ray scattering and cryo-electron microscopy. Shortenings exhibited solid-like viscoelastic and viscoelastoplastic behaviors in the linear and nonlinear regimes respectively. In the nonlinear region, laminating shortenings dissipated more viscous energy (larger normalized dynamic viscosities) than a cake bakery shortening. The fat solid-like network of laminating shortening displayed a three-hierarchy structure and layered crystal aggregates, in comparison to two-hierarchy structure and spherical-like crystal aggregates of a cake shortening. We argue that the observed rheology, correlated to the structural network, is crucial for optimal laminating performance of shortenings.
Hammerand, Daniel C.
Over the past several decades, the use of composite materials has grown considerably. Typically, fiber-reinforced polymer-matrix composites are modeled as being linear elastic. However, it is well-known that polymers are viscoelastic in nature. Furthermore, the analysis of complex structures requires a numerical approach such as the finite element method. In the present work, a triangular flat shell element for linear elastic composites is extended to model linear viscoelastic composites. Although polymers are usually modeled as being incompressible, here they are modeled as compressible. Furthermore, the macroscopic constitutive properties for fiber-reinforced composites are assumed to be known and are not determined using the matrix and fiber properties along with the fiber volume fraction. Hygrothermo-rheologically simple materials are considered for which a change in the hygrothermal environment results in a horizontal shifting of the relaxation moduli curves on a log time scale, in addition to the usual hygrothermal loads. Both the temperature and moisture are taken to be prescribed. Hence, the heat energy generated by the viscoelastic deformations is not considered. When the deformations and rotations are small under an applied load history, the usual engineering stress and strain measures can be used and the time history of a viscoelastic deformation process is determined using the original geometry of the structure. If, however, sufficiently large loads are applied, the deflections and rotations will be large leading to changes in the structural stiffness characteristics and possibly the internal loads carried throughout the structure. Hence, in such a case, nonlinear effects must be taken into account and the appropriate stress and strain measures must be used. Although a geometrically-nonlinear finite element code could always be used to compute geometrically-linear deformation processes, it is inefficient to use such a code for small deformations, due to
EXPERIMENTAL MODAL ANALYSIS OF VISCO-ELASTICALLY DAMPED STRUCTURES
Institute of Scientific and Technical Information of China (English)
1998-01-01
The form of the modal analysis of viscoelastically damped structures is simplified and this simplified form is similar to the form of the modal analysis of linear viscously damped structures. As a result of this simplified form, the experimental modal analysis methods of linear viscously damped structures are applied to the experimental modal analysis of viscoelastically damped structures.
Radially Symmetric Motions of Nonlinearly Viscoelastic Bodies Under Live Loads
Stepanov, Alexey B.; Antman, Stuart S.
2017-08-01
This paper treats radially symmetric motions of nonlinearly viscoelastic circular-cylindrical and spherical shells subjected to the live loads of centrifugal force and (time-dependent) hydrostatic pressures. The governing equations are exact versions of those for 3-dimensional continuum mechanics (so shell does not connote an approximate via some shell theory). These motions are governed by quasilinear third-order parabolic-hyperbolic equations having but one independent spatial variable. The principal part of such a partial differential equation is determined by a general family of nonlinear constitutive equations. The presence of strains in two orthogonal directions requires a careful treatment of constitutive restrictions that are physically natural and support the analysis. The interaction of geometrically exact formulations, the compatible use of general constitutive equations for material response, and the presence of live loads show how these factors play crucial roles in the behavior of solutions. In particular, for different kinds of live loads there are thresholds separating materials that produce qualitatively different dynamical behavior. The analysis (using classical methods) covers infinite-time blowup for cylindrical shells subject to centrifugal forces, infinite-time blowup for cylindrical shells subject to steady and time-dependent hydrostatic pressures, finite-time blowup for spherical shells subject to steady and time-dependent hydrostatic pressures, and the preclusion of total compression. This paper concludes with a sketch (using some modern methods) of the existence of regular solutions until the time of blowup.
Non-linear analysis and the design of Pumpkin Balloons: stress, stability and viscoelasticity
Rand, J. L.; Wakefield, D. S.
Tensys have a long-established background in the shape generation and load analysis of architectural stressed membrane structures Founded upon their inTENS finite element analysis suite these activities have broadened to encompass lighter than air structures such as aerostats hybrid air-vehicles and stratospheric balloons Winzen Engineering couple many years of practical balloon design and fabrication experience with both academic and practical knowledge of the characterisation of the non-linear viscoelastic response of the polymeric films typically used for high-altitude scientific balloons Both companies have provided consulting services to the NASA Ultra Long Duration Balloon ULDB Program Early implementations of pumpkin balloons have shown problems of geometric instability characterised by improper deployment and these difficulties have been reproduced numerically using inTENS The solution lies in both the shapes of the membrane lobes and also the need to generate a biaxial stress field in order to mobilise in-plane shear stiffness Balloons undergo significant temperature and pressure variations in flight The different thermal characteristics between tendons and film can lead to significant meridional stress Fabrication tolerances can lead to significant local hoop stress concentrations particularly adjacent to the base and apex end fittings The non-linear viscoelastic response of the envelope film acts positively to help dissipate stress concentrations However creep over time may produce lobe geometry variations that may
Institute of Scientific and Technical Information of China (English)
Shuxin Huang; Chuanjing Lu; Ron Marshall
2005-01-01
A new simple thixotropy model was proposed in the present paper to characterize the thixotropy-loop experiments and the start-up experiment of an LDPE (PE-FSB23D022/Q200) melt. The thixotropy model is a combination of a viscoelastic-component and a postulated kinetics process of structure change, which is constituted in terms of the indirect microstructural approach usually adopted in the characterization of thixotropy. The descriptions of the thixotropy model on both the thixotropy-loop tests and the startup test show good agreement with the experimental values, indicating the good capability of the model in characterizing the time-dependent nonlinear viscoelastic. The stress overshoot phenomenon and the stress relaxation after cessation of the thixotropy loop test can be described well by the model, whereas both of the typical viscoelastic phenomena could not be described in our previous work with a variant Huang model.
Institute of Scientific and Technical Information of China (English)
FuYiming; LiPing＇en; ZhengYufang
2004-01-01
Based on the Schapery three-dimensional viscoelastic constitutive relationship with growing damage, a damage model with transverse matrix cracks for the unidirectional fibre reinforced viscoelastic composite plates is developed. By using Karman theory, the nonlinear dynamic governing equations of the viscoelastic composite plates under transverse periodic loading are established. By applying the finite difference method in spatial domain and the Newton-Newmark method in time domain, and using the iterative procedure, the integral-partial differential governing equations are solved. Some examples are given and the results are compared with available data.
Aftershocks and Omori's law in a modified Carlson-Langer model with nonlinear visco-elasticity
Sakaguchi, Hidetsugu
2015-01-01
A modified Carlson-Langer model for earthquakes is proposed, which includes nonlinear visco-elasticity. Several aftershocks are generated after the main shock owing to the damping of the additional visco-elastic force. Both the Gutenberg-Richter law and Omori's law are reproduced in a numerical simulation of the modified Carlson-Langer model on a critical percolation cluster of a square lattice.
Fully coupled heat conduction and deformation analyses of nonlinear viscoelastic composites
Khan, Kamran
2012-05-01
This study presents an integrated micromechanical model-finite element framework for analyzing coupled heat conduction and deformations of particle-reinforced composite structures. A simplified micromechanical model consisting of four sub-cells, i.e., one particle and three matrix sub-cells is formulated to obtain the effective thermomechanical properties and micro-macro field variables due to coupled heat conduction and nonlinear thermoviscoelastic deformation of a particulate composite that takes into account the dissipation of energy from the viscoelastic constituents. A time integration algorithm for simultaneously solving the equations that govern heat conduction and thermoviscoelastic deformations of isotropic homogeneous materials is developed. The algorithm is then integrated to the proposed micromechanical model. A significant temperature generation due to the dissipation effect in the viscoelastic matrix was observed when the composite body is subjected to cyclic mechanical loadings. Heat conduction due to the dissipation of the energy cannot be ignored in predicting the factual temperature and deformation fields within the composite structure, subjected to cyclic loading for a long period. A higher creep resistant matrix material or adding elastic particles can lower the temperature generation. Our analyses suggest that using particulate composites and functionally graded materials can reduce the heat generation due to energy dissipation. © 2012 Elsevier Ltd.
Nonlinear electroelastic vibration analysis of NEMS consisting of double-viscoelastic nanoplates
Ebrahimy, Farzad; Hosseini, S. Hamed S.
2016-10-01
The nonlinear electroelastic vibration behavior of viscoelastic nanoplates is investigated based on nonlocal elasticity theory. Employing nonlinear strain-displacement relations, the geometrical nonlinearity is modeled while governing equations are derived through Hamilton's principle and they are solved applying semi-analytical generalized differential quadrature (GDQ) method. Eringen's nonlocal elasticity theory takes into account the effect of small size, which enables the present model to become effective in the analysis and design of nanosensors and nanoactuators. Based on Kelvin-Voigt model, the influence of the viscoelastic coefficient is also discussed. It is demonstrated that the GDQ method has high precision and computational efficiency in the vibration analysis of viscoelastic nanoplates. The good agreement between the results of this article and those available in literature validated the presented approach. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as electric voltage, small-scale effects, van der Waals interaction, Winkler and Pasternak elastic coefficients, the viscidity and aspect ratio of the nanoplate on its nonlinear vibrational characteristics. It is explicitly shown that the electroelastic vibration behavior of viscoelastic nanoplates is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of viscoelastic nanoplates which are fundamental elements in nanoelectromechanical systems.
Nonlinear shear wave in a non Newtonian visco-elastic medium
Energy Technology Data Exchange (ETDEWEB)
Banerjee, D.; Janaki, M. S.; Chakrabarti, N. [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Calcutta 700 064 (India); Chaudhuri, M. [Max-Planck-Institut fuer extraterrestrische Physik, 85741 Garching (Germany)
2012-06-15
An analysis of nonlinear transverse shear wave has been carried out on non-Newtonian viscoelastic liquid using generalized hydrodynamic model. The nonlinear viscoelastic behavior is introduced through velocity shear dependence of viscosity coefficient by well known Carreau-Bird model. The dynamical feature of this shear wave leads to the celebrated Fermi-Pasta-Ulam problem. Numerical solution has been obtained which shows that initial periodic solutions reoccur after passing through several patterns of periodic waves. A possible explanation for this periodic solution is given by constructing modified Korteweg de Vries equation. This model has application from laboratory to astrophysical plasmas as well as in biological systems.
Nonlinear Shear Wave in a Non Newtonian Visco-elastic Medium
Janaki, D Banerjee M S; Chaudhuri, M
2013-01-01
An analysis of nonlinear transverse shear wave has been carried out on non-Newtonian viscoelastic liquid using generalized hydrodynamic(GH) model. The nonlinear viscoelastic behavior is introduced through velocity shear dependence of viscosity coefficient by well known Carreau -Bird model. The dynamical feature of this shear wave leads to the celebrated Fermi-Pasta-Ulam (FPU) problem. Numerical solution has been obtained which shows that initial periodic solutions reoccur after passing through several patterns of periodic waves. A possible explanation for this periodic solution is given by constructing modified Korteweg de Vries (mKdV) equation. This model has application from laboratory to astrophysical plasmas as well as biological systems.
A Distortion-Modified Free Volume Theory for Nonlinear Viscoelastic Behavior
Popelar, C. F.; Liechti, K. M.
2003-06-01
Many polymeric materials, including structural adhesives, exhibit anonlinear viscoelastic response. The nonlinear theory of Knauss and Emri(Polym. Engrg. Sci. 27, 1987, 87 100) is based on the Doolittle conceptthat the ‘free volume’ controls the mobility of polymer molecules and,thus, the inherent time scale of the material. It then follows thatfactors such as temperature and moisture, which change the free volume,will influence the time scale. Furthermore, stress-induced dilatationwill also affect the free volume and, hence, the time scale. However,during this investigation, dilatational effects alone were found to beinsufficient for describing the response of near pure shear tests of abisphenol A epoxy with amido amine hardener. Thus, the free volumeapproach presented here has been modified to include distortionaleffects in the inherent time scale of the material. The same was foundto be true for a urethane adhesive.
Estimation of piezoelastic and viscoelastic properties in laminated structures
DEFF Research Database (Denmark)
Araujo, A. L.; Soares, C. M. Mota; Herskovits, J.;
2009-01-01
An inverse method for material parameter estimation of elastic, piezoelectric and viscoelastic laminated plate structures is presented. The method uses a gradient based optimization technique in order to solve the inverse problem, through minimization of an error functional which expresses...... the difference between experimental free vibration data and corresponding numerical data produced by a finite element model. The complex modulus approach is used to model the viscoelastic material behavior, assuming hysteretic type damping. Applications that illustrate the influence of adhesive material...
Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.
1989-01-01
In response to the tremendous growth in the development of advanced materials, such as fiber-reinforced plastic (FRP) composite materials, a new numerical method is developed to analyze and predict the time-dependent properties of these materials. Basic concepts in viscoelasticity, laminated composites, and previous viscoelastic numerical methods are presented. A stable numerical method, called the nonlinear differential equation method (NDEM), is developed to calculate the in-plane stresses and strains over any time period for a general laminate constructed from nonlinear viscoelastic orthotropic plies. The method is implemented in an in-plane stress analysis computer program, called VCAP, to demonstrate its usefulness and to verify its accuracy. A number of actual experimental test results performed on Kevlar/epoxy composite laminates are compared to predictions calculated from the numerical method.
Nonlinear wave breaking in self-gravitating viscoelastic quantum fluid
Energy Technology Data Exchange (ETDEWEB)
Mitra, Aniruddha, E-mail: anibabun@gmail.com [Center for Plasma Studies, Department of Instrumentation Science, Jadavpur University, Kolkata, 700 032 (India); Roychoudhury, Rajkumar, E-mail: rajdaju@rediffmail.com [Advanced Centre for Nonlinear and Complex Phenomena, 1175 Survey Park, Kolkata 700075 (India); Department of Mathematics, Bethune College, Kolkata 700006 (India); Bhar, Radhaballav [Center for Plasma Studies, Department of Instrumentation Science, Jadavpur University, Kolkata, 700 032 (India); Khan, Manoranjan, E-mail: mkhan.ju@gmail.com [Center for Plasma Studies, Department of Instrumentation Science, Jadavpur University, Kolkata, 700 032 (India)
2017-02-12
The stability of a viscoelastic self-gravitating quantum fluid has been studied. Symmetry breaking instability of solitary wave has been observed through ‘viscosity modified Ostrovsky equation’ in weak gravity limit. In presence of strong gravitational field, the solitary wave breaks into shock waves. Response to a Gaussian perturbation, the system produces quasi-periodic short waves, which in terns predicts the existence of gravito-acoustic quasi-periodic short waves in lower solar corona region. Stability analysis of this dynamical system predicts gravity has the most prominent effect on the phase portraits, therefore, on the stability of the system. The non-existence of chaotic solution has also been observed at long wavelength perturbation through index value theorem. - Highlights: • In weak gravitational field, viscoelastic quantum fluid exhibits symmetry breaking instability. • Gaussian perturbation produces quasi-periodic gravito-acoustic waves into the system. • There exists no chaotic state of the system against long wavelength perturbations.
Institute of Scientific and Technical Information of China (English)
CHEN Liqun; Jean W.ZU; WU Jun
2004-01-01
To investigate the principal resonance in transverse nonlinear parametric vibration of an axially accelerating viscoelastic string, the method of multiple scales is applied directly to the nonlinear partial differential equation that governs the transverse vibration of the string. To derive the governing equation, Newton's second law, Lagrangean strain, and Kelvin's model are respectively used to account the dynamical relation, geometric nonlinearity and the viscoelasticity of the string material.Based on the solvability condition of eliminating the secular terms, closed form solutions are obtained for the amplitude and the existence conditions of nontrivial steady-state response of the principal parametric resonance. The Lyapunov linearized stability theory is employed to analyze the stability of the trivial and nontrivial solutions in the principal parametric resonance. Some numerical examples are presented to show the effects of the mean transport speed, the amplitude and the frequency of speed variation.
Relationship Between Structure and Viscoelastic Properties of Geosynthetics
Directory of Open Access Journals (Sweden)
Loginova Irina
2016-01-01
Full Text Available In this work, a study on viscoelastic properties of geosynthetic materials used in civil engineering is presented. Six samples of geofabrics and geogrids with different structures including woven geotextile fabric, nonwoven geotextile fabrics, warp-knitted geogrids and extruded geogrid were investigated. The tensile properties of geosynthetics including tensile strength, strain at maximum load and tensile load at specified strain have been determined. The creep and relaxation tests were carried out. The structure type was found to significantly affect the viscoelastic properties of the geosynthetics materials. In the article some results of numerous conducted tests are presented, analyzed and may be used to preselection of geosynthetics materials.
Creep characterization of gels and nonlinear viscoelastic material model
Ishikawa, Kiyotaka; Fujikawa, Masaki; Makabe, Chobin; Tanaka, Kou
2016-07-01
In this paper, we examine gel creep behavior and develop a material model for useful and simple numerical simulation of this behavior. This study has three stages and aims: (1) gel creep behavior is examined; (2) the material model is determined and the material constants are identified; and (3) the versatility of the material model and the constants are evaluated. The creep behavior is found to be independent of the initial stress level in the present experiment. Thus, the viscoelastic model proposed by Simo is selected, and its material constants are identified using the results of creep tests. Moreover, from the results of numerical calculations and experiments, it is found that the chosen material model has good reproducibility, predictive performance and high versatility.
Nonlinear wave breaking in self-gravitating viscoelastic quantum fluid
Mitra, Aniruddha; Roychoudhury, Rajkumar; Bhar, Radhaballav; Khan, Manoranjan
2017-02-01
The stability of a viscoelastic self-gravitating quantum fluid has been studied. Symmetry breaking instability of solitary wave has been observed through 'viscosity modified Ostrovsky equation' in weak gravity limit. In presence of strong gravitational field, the solitary wave breaks into shock waves. Response to a Gaussian perturbation, the system produces quasi-periodic short waves, which in terns predicts the existence of gravito-acoustic quasi-periodic short waves in lower solar corona region. Stability analysis of this dynamical system predicts gravity has the most prominent effect on the phase portraits, therefore, on the stability of the system. The non-existence of chaotic solution has also been observed at long wavelength perturbation through index value theorem.
Institute of Scientific and Technical Information of China (English)
Hu Ding; Li-Qun Chen
2011-01-01
Steady-state periodical response is investigated for an axially moving viscoelastic beam with hybrid supports via approximate analysis with numerical confirmation.It is assumed that the excitation is spatially uniform and temporally harmonic. The transverse motion of axially moving beams is governed by a nonlinear partial-differential equation and a nonlinear integro-partial-differential equation. The material time derivative is used in the viscoelastic constitutive relation. The method of multiple scales is applied to the governing equations to investigate primary resonances under general boundary conditions. It is demonstrated that the mode uninvolved in the resonance has no effect on the steady-state response. Numerical examples are presented to demonstrate the effects of the boundary constraint stiffness on the amplitude and the stability of the steady-state response. The results derived for two governing equations are qualitatively the same, but quantitatively different. The differential quadrature schemes are developed to verify those results via the method of multiple scales.
Nonlinear static and dynamic responses of an electrically actuated viscoelastic microbeam
Institute of Scientific and Technical Information of China (English)
Y. M. Fu; J. Zhang
2009-01-01
On the basis of the Euler-Bernoulli hypothesis,nonlinear static and dynamic responses of a viscoelastic microbeam under two kinds of electric forces [a purely direct current (DC) and a combined current composed of a DC and an alternating current] are studied. By using Taylor series expansion, a governing equation of nonlinear integro-differential type is derived, and numerical analyses are performed.When a purely DC is applied, there exist an instantaneous pull-in voltage and a durable pull-in voltage of which the physical meanings are also given, whereas under an applied combined current, the effect of the element relaxation coefficient on the dynamic pull-in phenomenon is observed where the largest Lyapunov exponent is taken as a criterion for the dynamic pull-in instability of viscoelastic microbeams.
Nonlinear thermal convection in a viscoelastic nanofluid saturated porous medium under gravity mod
Directory of Open Access Journals (Sweden)
Palle Kiran
2016-06-01
Full Text Available This paper carried out a nonlinear thermal convection in a porous medium saturated with viscoelastic nanofluid under vibrations. The Darcy model has been used for the porous medium, while the nanofluid layer incorporates the effect of Brownian motion along with thermophoresis. An Oldroyd-B type constitutive equation was used to describe the rheological behavior of viscoelastic nanofluids. The non-uniform vertical vibrations of the system, which can be realized by oscillating the system vertically, is considered to vary sinusoidally with time. In order to find the heat and mass transports for unsteady state, a nonlinear analysis, using a minimal representation of the truncated Fourier series of two terms, has been performed. Effect of various parameters has been investigated on heat and mass transport and then presented graphically. It is found that gravity modulation can be used effectively to regulate either heat or mass transports in the system.
ON TRANSMISSION PROBLEM FOR VISCOELASTIC WAVE EQUATION WITH A LOCALIZED A NONLINEAR DISSIPATION
Institute of Scientific and Technical Information of China (English)
Jeong Ja BAE; Seong Sik KIM
2013-01-01
In this article,we consider the global existence and decay rates of solutions for the transmission problem of Kirchhoff type wave equations consisting of two physically different types of materials,one component being a Kirchhoff type wave equation with time dependent localized dissipation which is effective only on a neighborhood of certain part of boundary,while the other being a Kirchhoff type viscoelastic wave equation with nonlinear memory.
LARGE TIME BEHAVIOR OF SOLUTIONS TO NONLINEAR VISCOELASTIC MODEL WITH FADING MEMORY
Institute of Scientific and Technical Information of China (English)
Yanni Zeng
2012-01-01
We study the Cauchy problem of a one-dimensional nonlinear viscoelastic model with fading memory. By introducing appropriate new variables we convert the integro-partial differential equations into a hyperbolic system of balance laws.When it is a perturbation of a constant state,the solution is shown time asymptotically approaching to predetermined diffusion waves.Pointwise estimates on the convergence details are obtained.
Institute of Scientific and Technical Information of China (English)
Feng Yu-Lin; Liu Xiao-Zhou; Liu Jie-Hui; Ma Li
2009-01-01
Based on an equivalent medium approach,this paper presents a model describing the nonlinear propagation of acoustic waves in a viscoelastic medium containing cylindrical micropores. The influences of pores' nonlinear oscillations on sound attenuation,sound dispersion and an equivalent acoustic nonlinearity parameter are discussed. The calculated results show that the attenuation increases with an increasing volume fraction of mieropores. The peak of sound velocity and attenuation occurs at the resonant frequency of the micropores while the peak of the equivalent acoustic nonlinearity parameter occurs at the half of the resonant frequency of the micropores. Furthermore,multiple scattering has been taken into account,which leads to a modification to the effective wave number in the equivalent medium approach. We find that these linear and nonlinear acoustic parameters need to be corrected when the volume fraction of micropores is larger than 0.1%.
Yang, Zhi
2015-12-01
We have investigated the linear and nonlinear rheology of various gelatine-multiwalled carbon nanotube (gel-MWNT) composites, namely physically-crosslinked-gelatine gel-MWNT composites, chemically-crosslinked-gelatine gel-MWNT composites, and chemically-physically-crosslinked-gelatine gel-MWNT composites. Further, the internal structures of these gel-MWNT composites were characterized by ultra-small angle neutron scattering and scanning electron microscopy. The adsorption of gelatine onto the surface of MWNT is also investigated to understand gelatine-assisted dispersion of MWNT during ultrasonication. For all gelatine gels, addition of MWNT increases their complex modulus. The dependence of storage modulus with frequency for gelatine-MWNT composites is similar to that of the corresponding neat gelatine matrix. However, by incorporating MWNT, the dependence of the loss modulus on frequency is reduced. The linear viscoelastic region is decreased approximately linearly with the increase of MWNT concentration. The pre-stress results demonstrate that the addition of MWNT does not change the strain-hardening behaviour of physically-crosslinked gelatine gel. However, the addition of MWNT can increase the strain-hardening behaviour of chemically-crosslinked gelatine gel, and chemically-physically crosslinked gelatine gel. Results from light microscopy, cryo-SEM, and USANS demonstrate the hierarchical structures of MWNT, including that tens-of-micron scale MWNT agglomerates are present. Furthermore, the adsorption curve of gelatine onto the surface of MWNT follows two-stage pseudo-saturation behaviour.
Nonlinear rheological models for structured interfaces
Sagis, L.M.C.
2010-01-01
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
Experimental Characterization of Nonlinear Viscoelastic and Adhesive Properties of Elastomers
2006-07-27
constant strain rate " = 7rn,, / L was imposed over the entire rod. The material was modeled as a hypoelastic material derived from Storen and Rice (1975...constitutive models that are based on free volume or enthalpy for their nonlinear contribution. The confined compression experiment provides an appropriate...the need to test the evolving constitutive model on physically well described and experimentally well documented situations that are not overshadowed
Khan, Kamran
2012-11-09
We formulate a constitutive framework for biodegradable polymers that accounts for nonlinear viscous behavior under regimes with large deformation. The generalized Maxwell model is used to represent the degraded viscoelastic response of a polymer. The large-deformation, time-dependent behavior of viscoelastic solids is described using an Ogden-type hyperviscoelastic model. A deformation-induced degradation mechanism is assumed in which a scalar field depicts the local state of the degradation, which is responsible for the changes in the material\\'s properties. The degradation process introduces another timescale (the intrinsic material clock) and an entropy production mechanism. Examples of the degradation of a polymer under various loading conditions, including creep, relaxation and cyclic loading, are presented. Results from parametric studies to determine the effects of various parameters on the process of degradation are reported. Finally, degradation of an annular cylinder subjected to pressure is also presented to mimic the effects of viscoelastic arterial walls (the outer cylinder) on the degradation response of a biodegradable stent (the inner cylinder). A general contact analysis is performed. As the stiffness of the biodegradable stent decreases, stress reduction in the stented viscoelastic arterial wall is observed. The integration of the proposed constitutive model with finite element software could help a designer to predict the time-dependent response of a biodegradable stent exhibiting finite deformation and under complex mechanical loading conditions. © 2012 Springer-Verlag Wien.
Fully non-linear hyper-viscoelastic modeling of skeletal muscle in compression.
Wheatley, Benjamin B; Pietsch, Renée B; Haut Donahue, Tammy L; Williams, Lakiesha N
2016-01-01
Understanding the behavior of skeletal muscle is critical to implementing computational methods to study how the body responds to compressive loading. This work presents a novel approach to studying the fully nonlinear response of skeletal muscle in compression. Porcine muscle was compressed in both the longitudinal and transverse directions under five stress relaxation steps. Each step consisted of 5% engineering strain over 1 s followed by a relaxation period until equilibrium was reached at an observed change of 1 g/min. The resulting data were analyzed to identify the peak and equilibrium stresses as well as relaxation time for all samples. Additionally, a fully nonlinear strain energy density-based Prony series constitutive model was implemented and validated with independent constant rate compressive data. A nonlinear least squares optimization approach utilizing the Levenberg-Marquardt algorithm was implemented to fit model behavior to experimental data. The results suggested the time-dependent material response plays a key role in the anisotropy of skeletal muscle as increasing strain showed differences in peak stress and relaxation time (p 0.05). The optimizing procedure produced a single set of hyper-viscoelastic parameters which characterized compressive muscle behavior under stress relaxation conditions. The utilized constitutive model was the first orthotropic, fully nonlinear hyper-viscoelastic model of skeletal muscle in compression while maintaining agreement with constitutive physical boundaries. The model provided an excellent fit to experimental data and agreed well with the independent validation in the transverse direction.
On a shock problem involving a nonlinear viscoelastic bar
Directory of Open Access Journals (Sweden)
Tran Ngoc Diem
2005-11-01
Full Text Available We treat an initial boundary value problem for a nonlinear wave equation uttÃ¢ÂˆÂ’uxx+K|u|ÃŽÂ±u+ÃŽÂ»|ut|ÃŽÂ²ut=f(x,t in the domain 0
Fereidoon, A.; Andalib, E.; Mirafzal, A.
2016-07-01
This article studies the nonlinear vibration of viscoelastic embedded nano-sandwich structures containing of a double walled carbon nanotube (DWCNT) integrated with two piezoelectric Zinc oxide (ZnO) layers. DWCNT and ZnO layers are subjected to magnetic and electric fields, respectively. This system is conveying viscous fluid and the related force is calculated by modified Navier-Stokes relation considering slip boundary condition and Knudsen number. Visco-Pasternak model with three parameters of the Winkler modulus, shear modulus, and damp coefficient is used for simulation of viscoelastic medium. The nano-structure is simulated as an orthotropic Timoshenko beam (TB) and the effects of small scale, structural damping and surface stress are considered based on Eringen's, Kelvin-voigt and Gurtin-Murdoch theories. Energy method and Hamilton's principle are employed to derive motion equations which are then solved using differential quadrature method (DQM). The detailed parametric study is conducted, focusing on the combined effects of small scale effect, fluid velocity, thickness of piezoelectric layer, boundary condition, surface effects, van der Waals (vdW) force on the frequency and critical velocity of nano-structure. Results indicate that the frequency and critical velocity increases with assume of surface effects.
Viscoelastic fluid-structure interaction between a non-Newtonian fluid flow and flexible cylinder
Dey, Anita; Modarres-Sadeghi, Yahya; Rothstein, Jonathan
2016-11-01
It is well known that when a flexible or flexibly-mounted structure is placed perpendicular to the flow of a Newtonian fluid, it can oscillate due to the shedding of separated vortices at high Reynolds numbers. If the same flexible object is placed in non-Newtonian flows, however, the structure's response is still unknown. Unlike Newtonian fluids, the flow of viscoelastic fluids can become unstable at infinitesimal Reynolds numbers due to a purely elastic flow instability. In this talk, we will present a series of experiments investigating the response of a flexible cylinder placed in the cross flow of a viscoelastic fluid. The elastic flow instabilities occurring at high Weissenberg numbers can exert fluctuating forces on the flexible cylinder thus leading to nonlinear periodic oscillations of the flexible structure. These oscillations are found to be coupled to the time-dependent state of viscoelastic stresses in the wake of the flexible cylinder. The static and dynamic responses of the flexible cylinder will be presented over a range of flow velocities, along with measurements of velocity profiles and flow-induced birefringence, in order to quantify the time variation of the flow field and the state of stress in the fluid.
Institute of Scientific and Technical Information of China (English)
侯之超; 祖武争
2004-01-01
Nonlinear dynamic analysis is performed on moving belts subjected to geometric nonlinearity and initial tension fluctuation.To incorporate more accurately the damping mechanism of belt material, linear viscoelastic models are adopted in a unified form of differential operators.To circumvent high-order differential vibration equation of time-varying coefficients and with gyroscopic and nonlinear terms, where analytical solution is almost impossible, a systematic approach is presented by reforming the motion equation and directly using the method of multiple scales.To exemplify the procedure, the solutions at principal resonance are obtained and their stability conditions are derived for employing a Kelvin-Voigt model to reflect the property of the belt material.The solutions and stability conditions successfully reduce to those for using Kelvin model and elastic model, which validate the present approaches.Numerical simulations highlight the effects of tension fluctuations and translating speeds on the stability of the belt vibration.
General decay of solutions of a nonlinear system of viscoelastic wave equations
Said-Houari, Belkacem
2011-04-16
This work is concerned with a system of two viscoelastic wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we prove that, for certain class of relaxation functions and for some restrictions on the initial data, the rate of decay of the total energy depends on those of the relaxation functions. This result improves many results in the literature, such as the ones in Messaoudi and Tatar (Appl. Anal. 87(3):247-263, 2008) and Liu (Nonlinear Anal. 71:2257-2267, 2009) in which only the exponential and polynomial decay rates are considered. © 2011 Springer Basel AG.
Sunbuloglu, Emin; Bozdag, Ergun; Toprak, Tuncer; Islak, Civan
2013-01-01
This study is aimed at setting a method of experimental parameter estimation for large-deforming nonlinear viscoelastic continuous fibre-reinforced composite material model. Specifically, arterial tissue was investigated during experimental research and parameter estimation studies, due to medical, scientific and socio-economic importance of soft tissue research. Using analytical formulations for specimens under combined inflation/extension/torsion on thick-walled cylindrical tubes, in vitro experiments were carried out with fresh sheep arterial segments, and parameter estimation procedures were carried out on experimental data. Model restrictions were pointed out using outcomes from parameter estimation. Needs for further studies that can be developed are discussed.
Viscoelastic Characterization of a Nonlinear, Glass/Epoxy Composite Including the Effects of Damage
1974-10-01
Compliac Figue 12. oparion o exerimnta initliancorn 58-8R pox rsin. 6 270 11 Co CII (1a) V Q) 0 ) CD CJ. CL ~4-) ~ CU 4 0 ; &-* S- C ’L - SL 4- LL ) I C)C...34 Brown University, Technical Report No. 3, January 1968. 114. W. G. Gottenberg, J. 0. Bird and G. L. Agrawal, " An Experimental Study of Nonlinear...the Society of Rheology, Vol. 12 (1968), p. 155. 126. H. B3. Bird and B. 0. Marsh, "Viscoelastic Hysteresis Part 1, Model Prediction; Part II
Khan, Kamran
2012-11-10
We formulate a variational constitutive framework that accounts for nonlinear viscous behavior of electrically sensitive polymers, specifically Dielectric Elastomers (DEs), under large deformation. DEs are highly viscoelastic and their actuation response is greatly affected in dynamic applications. We used the generalized Maxwell model to represent the viscoelastic response of DE allowing the material to relax with multiple mechanisms. The constitutive updates at each load increment are obtained by minimizing an objective function formulated using the free energy and electrostatic energy of the elastomer, in addition to the viscous dissipation potential of the dashpots in each Maxwell branch. The model is then used to predict the electromechanical instability (EMI) of DE. The electro-elastic response of the DE is verified with available analytical solutions in the literature and then the material parameters are calibrated using experimental data. The model is integrated with finite element software to perform a variety of simulations on different types of electrically driven actuators under various electromechanical loadings. The electromechanical response of the DE and the critical conditions at which EMI occurs were found to be greatly affected by the viscoelasticity. Our model predicts that under a dead load EMI can be avoided if the DE operates at a high voltage rate. Subjected to constant, ramp and cyclic voltage, our model qualitatively predicts responses similar to the ones obtained from the analytical solutions and experimental data available in the literature. © 2012 Springer-Verlag Berlin Heidelberg.
Electrically actuated MEMS resonators: Effects of fringing field and nonlinear viscoelasticity
Farokhi, Hamed; Ghayesh, Mergen H.
2017-10-01
This paper studies the nonlinear electromechanical response of a MEMS resonator numerically. A nonlinear continuous multi-physics model of the MEMS resonator is developed taking into account the effects of fringing field, size, residual axial load, and viscoelasticity. Moreover, both longitudinal and transverse motions are accounted for in the system modelling and simulations. The equations of motion of the MEMS resonator are obtained employing Hamilton's principle together with the modified version of the couple stress based theory (to account for size effects) and the Kelvin-Voigt model (to account for nonlinear energy dissipation). The Meijs-Fokkema electrostatic load formula is used to reliably model the fringing field effects. The continuous multi-physics model, consisting of geometrical, electrical, and viscos nonlinearities is discretised via a weighted-residual method, yielding a set of nonlinearly coupled ordinary differential equations (ODEs). The resultant set of ODEs is solved numerically when the microresonator is actuated by a biased DC voltage and an AC voltage. The results of the numerical simulations are presented in the form of DC voltage-deflection, DC voltage-natural frequency, and AC frequency-displacement diagrams. The effects of fringing field, residual axial load, small-scale, and nonlinear energy dissipation are highlighted. It is shown that fringing field effects are significant on both static and dynamic electromechanical responses of the MEMS resonator.
NONLINEAR TRANSIENT RESPONSE OF STAY CABLE WITH VISCOELASTICITY DAMPER IN CABLE-STAYED BRIDGE
Institute of Scientific and Technical Information of China (English)
陈水生; 孙炳楠; 冯义卿
2004-01-01
Taking the bending stiffness,static sag,and geometric non-linearity into consideration,the space nonlinear vibration partial differential equations were derived.The partical differential equations were discretized in space by finite center difference approximation,then the nonlinear ordinal differential equations were obtained.A hybrid method involving the combination of the Newmark method and the pseudo-force strategy was proposed to analyze the nonlinear transient response of the inclined cable-dampers system subjected to arbitrary dynamic loading.As an example,two typical stay cables were calculated by the present method.The results reveal both the validity and the deficiency of the viscoelasticity damper for vibration control of stay cables.The efficiency and accuracy of the proposed method is also verified by comparing the results with those obtained by using Runge-Kutta direct integration technique.A new time history analysis method is provided for the research on the stay cable vibration control.
Energy Technology Data Exchange (ETDEWEB)
Hayat, T. [Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000 (Pakistan); Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589 (Saudi Arabia); Muhammad, Taseer, E-mail: taseer_qau@yahoo.com [Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000 (Pakistan); Alsaedi, A.; Alhuthali, M.S. [Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589 (Saudi Arabia)
2015-07-01
Magnetohydrodynamic (MHD) three-dimensional flow of couple stress nanofluid in the presence of thermophoresis and Brownian motion effects is analyzed. Energy equation subject to nonlinear thermal radiation is taken into account. The flow is generated by a bidirectional stretching surface. Fluid is electrically conducting in the presence of a constant applied magnetic field. The induced magnetic field is neglected for a small magnetic Reynolds number. Mathematical formulation is performed using boundary layer analysis. Newly proposed boundary condition requiring zero nanoparticle mass flux is employed. The governing nonlinear mathematical problems are first converted into dimensionless expressions and then solved for the series solutions of velocities, temperature and nanoparticles concentration. Convergence of the constructed solutions is verified. Effects of emerging parameters on the temperature and nanoparticles concentration are plotted and discussed. Skin friction coefficients and Nusselt number are also computed and analyzed. It is found that the thermal boundary layer thickness is an increasing function of radiative effect. - Highlights: • Three-dimensional boundary layer flow of viscoelastic nanofluid is examined. • Nonlinear thermal radiation is analyzed. • Brownian motion and thermophoresis effects are present. • Recently developed condition requiring zero nanoparticle mass flux is implemented. • Construction of convergent solutions of nonlinear flow is possible.
Energy Technology Data Exchange (ETDEWEB)
Adolf, D.
1997-11-01
Butyl rubber, unfortunately, has pronounced nonlinear viscoelastic behavior, which may be modelled by a separable KBKZ formalism. While these effects seem to have minimal impact on accelerated sealing force measurements, they do severely impact compression set tests. Therefore, a new test is suggested for evaluating field-return o-rings which is free from such confounding effects.
Directory of Open Access Journals (Sweden)
Haitao Che
2011-01-01
Full Text Available We investigate a H1-Galerkin mixed finite element method for nonlinear viscoelasticity equations based on H1-Galerkin method and expanded mixed element method. The existence and uniqueness of solutions to the numerical scheme are proved. A priori error estimation is derived for the unknown function, the gradient function, and the flux.
Directory of Open Access Journals (Sweden)
T McMillen
2008-08-01
Full Text Available Locomotion provides superb examples of cooperation among neuromuscular systems, environmental reaction forces, and sensory feedback. As part of a program to understand the neuromechanics of locomotion, here we construct a model of anguilliform (eel-like swimming in slender fishes. Building on a continuum mechanical representation of the body as an viscoelastic rod, actuated by a traveling wave of preferred curvature and subject to hydrodynamic reaction forces, we incorporate a new version of a calcium release and muscle force model, fitted to data from the lamprey Ichthyomyzon unicuspis, that interactively generates the curvature wave. We use the model to investigate the source of the difference in speeds observed between electromyographic waves of muscle activation and mechanical waves of body curvature, concluding that it is due to a combination of passive viscoelastic and geometric properties of the body and active muscle properties. Moreover, we find that nonlinear force dependence on muscle length and shortening velocity may reduce the work done by the swimming muscles in steady swimming.
Analysis of steady-state and dynamical radially-symmetric problems of nonlinear viscoelasticity
Stepanov, Alexey B.
This thesis treats radially symmetric steady states and radially symmetric motions of nonlinearly elastic and viscoelastic plates and shells subject to dead-load and hydrostatic pressures on their boundaries and with the plate subject to centrifugal force. The plates and shells are described by specializations of the exact (nonlinear) equations of three-dimensional continuum mechanics. The treatment in every case is very general and encompasses large classes of constitutive functions (characterizing the material response). We first treat the radially symmetric steady states of plates and shells and the radially symmetric steady rotations of plates. We show that the existence, multiplicity, and qualitative behavior of solutions for problems accounting for the live loads due to hydrostatic pressure and centrifugal force depend critically on the material properties of the bodies, physically reasonable refined descriptions of which are given and examined here with great care, and on the nature of boundary conditions. he treatment here, giving new and sharp results, employs several different mathematical tools, ranging from phase-plane analysis to the mathematically more sophisticated direct methods of the Calculus of Variations, fixed-point theorems, and global continuation methods, each of which has different strengths and weaknesses for handling intrinsic difficulties in the mechanics. We then treat the initial-boundary-value problems for the radially symmetric motions of annular plates and spherical shells that consist of a nonlinearly viscoelastic material of strain-rate type. We discuss a range of physically natural constitutive equations. We first show that when the material is strong in a suitable sense relative to externally applied loads, solutions exist for all time, depend continuously on the data, and consequently are unique. We study the role of the constitutive restrictions and that of the regularity of the data in ensuring the preclusion of a total
Nonlinear Forced Vibration of a Viscoelastic Buckled Beam with 2 : 1 Internal Resonance
Directory of Open Access Journals (Sweden)
Liu-Yang Xiong
2014-01-01
Full Text Available Nonlinear dynamics of a viscoelastic buckled beam subjected to primary resonance in the presence of internal resonance is investigated for the first time. For appropriate choice of system parameters, the natural frequency of the second mode is approximately twice that of the first providing the condition for 2 : 1 internal resonance. The ordinary differential equations of the two mode shapes are established using the Galerkin method. The problem is replaced by two coupled second-order differential equations with quadratic and cubic nonlinearities. The multiple scales method is applied to derive the modulation-phase equations. Steady-state solutions of the system as well as their stability are examined. The frequency-amplitude curves exhibit the steady-state response in the directly excited and indirectly excited modes due to modal interaction. The double-jump, the saturation phenomenon, and the nonperiodic region phenomena are observed illustrating the influence of internal resonance. The validity range of the analytical approximations is assessed by comparing the analytical approximate results with a numerical solution by the Runge-Kutta method. The unstable regions in the internal resonance are explored via numerical simulations.
Said-Houari, Belkacem
2012-09-01
The goal of this work is to study a model of the viscoelastic wave equation with nonlinear boundary/interior sources and a nonlinear interior damping. First, applying the Faedo-Galerkin approximations combined with the compactness method to obtain existence of regular global solutions to an auxiliary problem with globally Lipschitz source terms and with initial data in the potential well. It is important to emphasize that it is not possible to consider density arguments to pass from regular to weak solutions if one considers regular solutions of our problem where the source terms are locally Lipschitz functions. To overcome this difficulty, we use an approximation method involving truncated sources and adapting the ideas in [13] to show that the existence of weak solutions can still be obtained for our problem. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term, then the solution ceases to exist and blows up in finite time provided that the initial data are large enough.
Directory of Open Access Journals (Sweden)
Gang Li
2013-01-01
Full Text Available This paper deals with the initial boundary value problem for the nonlinear viscoelastic Petrovsky equation utt+Δ2u−∫0tgt−τΔ2ux,τdτ−Δut−Δutt+utm−1ut=up−1u. Under certain conditions on g and the assumption that m
Liang Fei; Gao Hongjun
2011-01-01
Abstract In this paper, we consider the system of nonlinear viscoelastic equations u t t - Δ u + ∫ 0 t g 1 ( t - τ ) Δ u ( τ ) d τ - Δ u t = f 1 ( u , v ) , ( x , t ) ∈ Ω × ( 0 , T ) , v t t - Δ v + ∫ 0 t g 2 ( t - τ ) Δ v ( τ ) d τ - Δ v t = f 2 ( u , v ) , ( x , t ) ∈ Ω...
Institute of Scientific and Technical Information of China (English)
LIM; C.W.
2010-01-01
Nonlinear combination parametric resonance is investigated for an axially accelerating viscoelastic string.The governing equation of in-planar motion of the string is established by introducing a coordinate transform in the Eulerian equation of a string with moving boundaries.The string under investigation is constituted by the standard linear solid model in which the material,not partial,time derivative was used.The governing equation leads to the Mote model for transverse vibration by omitting the longitudinal component and higher order terms.The Kirchhoff model is derived from the Mote model by replacing the tension with the averaged tension over the string.The two models are respectively analyzed via the method of multiple scales for principal parametric resonance.The amplitudes and the existence conditions of steady-state response and its stability can be numerically determined.Numerical calculations demonstrate the effects of the string material parameters,the initial tension,and the axial speed fluctuation amplitude.The outcomes of the two models are qualitatively and quantitatively compared.
Interaction model between capsule robot and intestine based on nonlinear viscoelasticity.
Zhang, Cheng; Liu, Hao; Tan, Renjia; Li, Hongyi
2014-03-01
Active capsule endoscope could also be called capsule robot, has been developed from laboratory research to clinical application. However, the system still has defects, such as poor controllability and failing to realize automatic checks. The imperfection of the interaction model between capsule robot and intestine is one of the dominating reasons causing the above problems. A model is hoped to be established for the control method of the capsule robot in this article. It is established based on nonlinear viscoelasticity. The interaction force of the model consists of environmental resistance, viscous resistance and Coulomb friction. The parameters of the model are identified by experimental investigation. Different methods are used in the experiment to obtain different values of the same parameter at different velocities. The model is proved to be valid by experimental verification. The achievement in this article is the attempted perfection of an interaction model. It is hoped that the model can optimize the control method of the capsule robot in the future.
非线性粘弹性梁的混沌运动%Chaotic Motions of Nonlinear Viscoelastic Beams
Institute of Scientific and Technical Information of China (English)
陈立群; 程昌; 张能辉
2000-01-01
The integro-partial-differential equation that governs the dynamical behavior of homogeneous viscoelastic beams with geometric and material nonlinearities is established. The material of the beams obeys the Leaderman nonlinear constitutive relation. In the case of simple supported ends, the Galerkin method is applied to simplify the integro-partial-differential equation to a integro -differential equation. The equation is further simplified to a set of ordinary differential equations by introducing an additional variable. Finally, the numerical method is applied to investigate the dynamical behavior of the beam, and results show that chaos occurs in the motion of the beam.
非线性粘弹性梁的混沌运动%Chaotic Motions of Nonlinear Viscoelastic Beams
Institute of Scientific and Technical Information of China (English)
陈立群; 程昌; 张能辉
2001-01-01
The integro-partial-differential equation that governs the dynamical behavior of homogeneous viscoelastic beams with geometric and material nonlinearities is established. The material of the beams obeys the Leaderman nonlinear constitutive relation. In the case of simple supported ends, the Galerkin method is applied to simplify the integro-partial-differential equation to a integro -differential equation. The equation is further simplified to a set of ordinary differential equations by introducing an additional variable. Finally, the numerical method is applied to investigate the dynamical behavior of the beam, and results show that chaos occurs in the motion of the beam.
Energy Technology Data Exchange (ETDEWEB)
Meili, G.; Dubroca, G.; Pasquier, M.; Thepenier, J.
1982-06-01
The paper discusses a method for the mechanical testing of casebonded composite modified double base charges (CMDB) subjected to thermal cycling. The method proposed to determine stresses and safety margins takes into account the non-linear viscoelastic behaviour and the compressibility of the propellant. The non-linear behaviour is derived from tensile testing. The equations of equilibrium are solved numerically by deviding the grain web into many layers. The nonlinearities mainly concern the modulus; a multiaxial criterion and the time-temperature shift factors are used. At each time-step and for each layer the temperature, the reduced time, the non-linear factor, the Poisson's ratio and the damage according to the concept of Farris are calculated. Different charges (star, wagon wheel, finocyl) were subjected to various types of thermal cycles. The comparison between prediction and experimentation is acceptable even for complex histories in strain and temperature.
Explicit solution for the natural frequency of structures with partial viscoelastic treatment
DEFF Research Database (Denmark)
Høgsberg, Jan Becker
2016-01-01
the influence from residual vibration modes. The correction term is eliminated in terms of the corresponding natural frequency associated with the high-frequency stiffness of the viscoelastic treatment, whereby an expression is obtained for the complex-valued natural frequency, which only requires the solution......The free vibration characteristics of structures with viscoelastic treatment are represented by the complex-valued natural frequencies. The assumed single mode representation associated with the low-frequency stiffness of the viscoelastic treatment is modified by a correction term representing...
Institute of Scientific and Technical Information of China (English)
盛冬发; 张燕; 程昌钧
2004-01-01
Based on convolution-type constitutive equations for linear viscoelastic materials with damage and the hypotheses of Timoshenko beams with large deflections, the nonlinear equations governing dynamical behavior of Timoshenko beams with damage on viscoelastic foundation were firstly derived. By using the Galerkin method in spatial domain, the nonlinear integro-partial differential equations were transformed into a set of integro-ordinary differential equations. The numerical methods in nonlinear dynamical systems, such as the phase-trajectory diagram, Poincare section and bifurcation figure, were used to solve the simplified systems of equations. It could be seen that simplified dynamical systems possess the plenty of nonlinear dynamical properties. The influence of load and material parameters on the dynamic behavior of nonlinear system were investigated in detail.
Tuttle, M. E.; Brinson, H. F.
1986-01-01
The impact of flight error in measured viscoelastic parameters on subsequent long-term viscoelastic predictions is numerically evaluated using the Schapery nonlinear viscoelastic model. Of the seven Schapery parameters, the results indicated that long-term predictions were most sensitive to errors in the power law parameter n. Although errors in the other parameters were significant as well, errors in n dominated all other factors at long times. The process of selecting an appropriate short-term test cycle so as to insure an accurate long-term prediction was considered, and a short-term test cycle was selected using material properties typical for T300/5208 graphite-epoxy at 149 C. The process of selection is described, and its individual steps are itemized.
Energy Technology Data Exchange (ETDEWEB)
Hashemabadi, S.H. [Iran Univ. of Science and Technology, Dept. of Chemical Engineering, Tehran (Iran); Etemad, S.Gh. [Isfahan Univ. of Technology, Dept. of Chemical Engineering, Isfahan (Israel); Thibault, J. [Ottawa Univ., Dept. of Chemical Engineering, Ottawa, ON (Canada)
2004-08-01
Heat transfer to viscoelastic fluids is frequently encountered in various industrial processing. In this investigation an analytical solution was obtained to predict the fully developed, steady and laminar heat transfer of viscoelastic fluids between parallel plates. One of the plates was stationary and was subjected to a constant heat flux. The other plate moved with constant velocity and was insulated. The simplified Phan-Thien-Tanner (SPTT) model, believed to be a more realistic model for viscoelastic fluids, was used to represent the rheological behavior of the fluid. The energy equation was solved for a wide range of Brinkman number, dimensionless viscoelastic group, and dimensionless pressure drop. Results highlight the strong effects of these parameters on the heat transfer rate. (Author)
Řehoř, Martin; Pr&oring; ša, Vít; T&oring; ma, Karel
2016-10-01
Rigorous analysis of the response of nonlinear materials to step inputs requires one to simultaneously handle the discontinuity, differentiation, and nonlinearity. This task is however beyond the reach of the standard theories such as the classical theory of distributions and presents a considerable mathematical difficulty. New advanced mathematical tools are necessary to handle the challenge. An elegant and relatively easy-to-use framework capable of accomplishing the task is provided by the Colombeau algebra, which is a generalisation of the classical theory of distributions to the nonlinear setting. We use the Colombeau algebra formalism and derive explicit formulae describing the response of incompressible Maxwell viscoelastic fluid subject to step load/deformation in the lubricated squeeze flow setting.
Acoustic-gravity nonlinear structures
Directory of Open Access Journals (Sweden)
D. Jovanović
2002-01-01
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.
Viscoelasticity of Axisymmetric Composite Structures: Analysis and Experimental Validation
2013-02-01
are currently used for lightweight pressure vessels and highly efficient rotors for energy storage . For both applications, pre-stresses are built in...analysis can be applied to composite pressure vessels, gun barrels, and flywheels . 15. SUBJECT TERMS viscoelasticity, creep, composite, gun barrel... flywheel 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18. NUMBER OF PAGES 28 19a. NAME OF RESPONSIBLE PERSON Jerome T
Gutierrez-Lemini, Danton
2014-01-01
Engineering Viscoelasticity covers all aspects of the thermo- mechanical response of viscoelastic substances that a practitioner in the field of viscoelasticity would need to design experiments, interpret test data, develop stress-strain models, perform stress analyses, design structural components, and carry out research work. The material in each chapter is developed from the elementary to the advanced, providing the background in mathematics and mechanics that are central to understanding the subject matter being presented. The book examines how viscoelastic materials respond to the application of loads, and provides practical guidelines to use them in the design of commercial, military and industrial applications. This book also: · Facilitates conceptual understanding by progressing in each chapter from elementary to challenging material · Examines in detail both differential and integral constitutive equations, devoting full chapters to each type and using both forms in ...
Institute of Scientific and Technical Information of China (English)
Wang Xinjun; Feng Zhenzhou; Wang Fusheng; Yue Zhufeng
2007-01-01
Damage-modified nonlinear viscoelastic constitutive equation and failure criterion are introduced and the three-dimensional incremental forms are deduced based on the updated Lagrangian approach. A simple tensile test model and a split Hopkinson pressure bar model are built to verify the accuracy of the subroutine implemented within the non-linear finite element program LS-DYNA. A numerical model of bird strike on windshield is established to study the responses of windshield under three different bird velocities at three sites. The bird is represented by a cylinder with a hemisphere at each end and the contact-impact coupling algorithm is used in this study. It is found that the implemented subroutine can properly describe the mechanical behavior of polymethyl methacrylate under low and high strain rates and large deformation, and can be used validly.
Nonlinear dynamics aspects of subcritical transitions and singular flows in viscoelastic fluids
Becherer, Paul
2008-01-01
Recently, there has been a renewed interest in theoretical aspects of flows of viscoelastic fluids (such as dilute polymer solutions). This thesis addresses two distinct issues related to such flows. Motivated by the possible occurrence of subcritical (finite-amplitude) instabilities in parallel flo
DEFF Research Database (Denmark)
van Ruymbeke, E.; Nielsen, J.; Hassager, Ole
2010-01-01
In this manuscript, we extend the tube-based model that we developed for predicting the linear viscoelasticity of entangled polymers [van Ruymbeke et al., J. Non-Newtonian Fluid Mech. 128, 7-22 (2005)] to the prediction of the extensional rheology of monodisperse and bidisperse linear polymers...
A structurally based viscoelastic model for passive myocardium in finite deformation
Shen, Jing Jin
2016-09-01
This paper discusses the finite-deformation viscoelastic modeling for passive myocardium tissue. The formulations established can also be applied to model other fiber-reinforced soft tissue. Based on the morphological structure of the myocardium, a specific free-energy function is constructed to reflect its orthotropicity. After deriving the stress-strain relationships in the simple shear deformation, a genetic algorithm is used to optimally estimate the material parameters of the myocardial constitutive equation. The results show that the proposed myocardial model can well fit the shear experimental data. To validate the viscoelastic model, it is used to predict the creep and the dynamic responses of a cylindrical model of the left ventricle. Upon comparing the results calculated by the proven myocardial elastic model with those by the viscoelastic model, the merits of the latter are discussed.
Directory of Open Access Journals (Sweden)
Yury A. Rossikhin
2015-01-01
Full Text Available In the previous analysis, the dynamic behaviour of a nonlinear plate embedded into a fractional derivative viscoelastic medium has been studied by the method of multiple time scales under the conditions of the internal resonances two-to-one and one-to-one, as well as the internal combinational resonances for the case when the linear parts of nonlinear equations of motion occur to be coupled. A new approach proposed in this paper allows one to uncouple the linear parts of equations of motion of the plate, while the same method, the method of multiple time scales, has been utilized for solving nonlinear equations. The influence of viscosity on the energy exchange mechanism between interacting nonlinear modes has been analyzed. It has been shown that for some internal resonances there exist such particular cases when it is possible to obtain two first integrals, namely, the energy integral and the stream function, which allows one to reduce the problem to the calculation of elliptic integrals. The new approach enables one to solve the problems of vibrations of thin bodies more efficiently.
Institute of Scientific and Technical Information of China (English)
叶昆; 李黎; 唐家祥
2003-01-01
Viscoelastic dampers, as supplementary energy dissipation devices, have been used in building structures under seismic excitation or wind loads. Different analytical models have been proposed to describe their dynamic force deformation characteristics. Among these analytical models, the fractional derivative models have attracted more attention as they can capture the frequency dependence of the material stiffness and damping properties observed from tests very well. In this paper, a Fourier-transform-based technique is presented to obtain the fractional unit impulse function and the response of structures with added viscoelastic dampers whose force-deformation relationship is described by a fractional derivative model. Then, a Duhamel integral-type expression is suggested for the response analysis of a fractional damped dynamic system subjected to deterministic or random excitation. Through numerical verification, it is shown that viscoelastic dampers are effective in reducing structural responses over a wide frequency range, and the proposed schemes can be used to accurately predict the stochastic seismic response of structures with added viscoelastic dampers described by a Kelvin model with fractional derivative.
Qu, Jinxiu; Zhang, Zhousuo; Wen, Jinpeng; Guo, Ting; Luo, Xue; Sun, Chuang; Li, Bing
2014-08-01
The viscoelastic sandwich structure is widely used in mechanical equipment, yet the structure always suffers from damage during long-term service. Therefore, state recognition of the viscoelastic sandwich structure is very necessary for monitoring structural health states and keeping the equipment running with high reliability. Through the analysis of vibration response signals, this paper presents a novel method for this task based on the adaptive redundant second generation wavelet packet transform (ARSGWPT), permutation entropy (PE) and the wavelet support vector machine (WSVM). In order to tackle the non-linearity existing in the structure vibration response, the PE is introduced to reveal the state changes of the structure. In the case of complex non-stationary vibration response signals, in order to obtain more effective information regarding the structural health states, the ARSGWPT, which can adaptively match the characteristics of a given signal, is proposed to process the vibration response signals, and then multiple PE features are extracted from the resultant wavelet packet coefficients. The WSVM, which can benefit from the conventional SVM as well as wavelet theory, is applied to classify the various structural states automatically. In this study, to achieve accurate and automated state recognition, the ARSGWPT, PE and WSVM are combined for signal processing, feature extraction and state classification, respectively. To demonstrate the effectiveness of the proposed method, a typical viscoelastic sandwich structure is designed, and the different degrees of preload on the structure are used to characterize the various looseness states. The test results show that the proposed method can reliably recognize the different looseness states of the viscoelastic sandwich structure, and the WSVM can achieve a better classification performance than the conventional SVM. Moreover, the superiority of the proposed ARSGWPT in processing the complex vibration response
A BEM formulation applied in the mechanical material modelling of viscoelastic cracked structures
Oliveira, Hugo Luiz; Leonel, Edson Denner
2016-12-01
The present study aims at performing a mechanical analysis of 2D viscoelastic cracked structural materials using the Boundary Element Method (BEM). The mesh dimensionality reduction provided by the BEM and its accuracy in representing high gradient fields make this numerical method robust to solve fracture mechanics problems. Viscoelastic models address phenomena that provide changes on the mechanical material properties along time. Well-established viscoelastic models such as Maxwell, Kelvin-Voigt and Boltzmann are used in this study. The numerical viscoelastic scheme, which is based on algebraic BEM equations, utilizes the Euler method for time derivative evaluation. Therefore, the unknown variables at the structural boundary and its variations along time are determined through an ordinary linear system of equations. Moreover, time-dependent boundary conditions may be considered, which represent loading phases. The dual BEM formulation is adopted for modelling the mechanical structural behaviour of cracks bodies. Three examples are considered to illustrate the robustness of the adopted formulation. The results achieved by the BEM are in good agreement with reported data and numerical stability is observed.
Directory of Open Access Journals (Sweden)
Liang Fei
2011-01-01
Full Text Available Abstract In this paper, we consider the system of nonlinear viscoelastic equations u t t - Δ u + ∫ 0 t g 1 ( t - τ Δ u ( τ d τ - Δ u t = f 1 ( u , v , ( x , t ∈ Ω × ( 0 , T , v t t - Δ v + ∫ 0 t g 2 ( t - τ Δ v ( τ d τ - Δ v t = f 2 ( u , v , ( x , t ∈ Ω × ( 0 , T with initial and Dirichlet boundary conditions. We prove that, under suitable assumptions on the functions gi , fi (i = 1, 2 and certain initial data in the stable set, the decay rate of the solution energy is exponential. Conversely, for certain initial data in the unstable set, there are solutions with positive initial energy that blow up in finite time. 2000 Mathematics Subject Classifications: 35L05; 35L55; 35L70.
An Optimum Analysis Method of Sandwich Structures Made from Elastic-viscoelastic Materials
Institute of Scientific and Technical Information of China (English)
CHEN Ying-bo; XIA Yu; REN Zhi-gang; LU Zhe-an; WANG Er-lei
2004-01-01
Due to a viscoelastic damping middle layer,sandwich structures have the capacity of energy consumption.In this paper,we describe the frequency-dependent property of viscoelastic materials using complex modulus model,and iterative modal strain energy method and iterative complex eigenvalue method are presented to obtain frequency and loss factor of sandwich structures.The two methods are effective and exact for the large-scale complex composite sandwich structures.Then an optimum analysis method is suggested to apply to sandwich structures.Finally,as an example,an optimum analysis of a clamped-clamped sandwich beams is conducted,theoretical closed-form solution and numerical predictions are studied comparatively,and the results agree well.
Hassan, M A; Hamdi, M; Noma, A
2012-01-01
The mechanical behavior of the heart muscle tissues is the central problem in finite element simulation of the heart contraction, excitation propagation and development of an artificial heart. Nonlinear elastic and viscoelastic passive material properties of the left ventricular papillary muscle of a guinea pig heart were determined based on in-vitro precise uniaxial and relaxation tests. The nonlinear elastic behavior was modeled by a hypoelastic model and different hyperelastic strain energy functions such as Ogden and Mooney-Rivlin. Nonlinear least square fitting and constrained optimization were conducted under MATLAB and MSC.MARC in order to obtain the model material parameters. The experimental tensile data was used to get the nonlinear elastic mechanical behavior of the heart muscle. However, stress relaxation data was used to determine the relaxation behavior as well as viscosity of the tissues. Viscohyperelastic behavior was constructed by a multiplicative decomposition of a standard Ogden strain energy function, W, for instantaneous deformation and a relaxation function, R(t), in a Prony series form. The study reveals that hypoelastic and hyperelastic (Ogden) models fit the tissue mechanical behaviors well and can be safely used for heart mechanics simulation. Since the characteristic relaxation time (900 s) of heart muscle tissues is very large compared with the actual time of heart beating cycle (800 ms), the effect of viscosity can be reasonably ignored. The amount and type of experimental data has a strong effect on the Ogden parameters. The in vitro passive mechanical properties are good initial values to start running the biosimulation codes for heart mechanics. However, an optimization algorithm is developed, based on clinical intact heart measurements, to estimate and re-correct the material parameters in order to get the in vivo mechanical properties, needed for very accurate bio-simulation and for the development of new materials for the
Nonlinear visco-elastic finite element analysis of different porcelain veneers configuration.
Sorrentino, Roberto; Apicella, Davide; Riccio, Carlo; Gherlone, Enrico; Zarone, Fernando; Aversa, Raffaella; Garcia-Godoy, Franklin; Ferrari, Marco; Apicella, Antonio
2009-11-01
This study is aimed at evaluating the biomechanical behavior of feldspathic versus alumina porcelain veneers. A 3D numerical model of a maxillary central incisor, with the periodontal ligament (PDL) and the alveolar bone was generated. Such model was made up of four main volumes: dentin, enamel, cement layer and veneer. Incisors restored with alumina and feldspathic porcelain veneers were compared with a natural sound tooth (control). Enamel, cementum, cancellous and cortical bone were considered as isotropic elastic materials; on the contrary, the tubular structure of dentin was designed as elastic orthotropic. The nonlinear visco-elatic behavior of the PDL was considered. The veneer volumes were coupled with alumina and feldspathic porcelain mechanical properties. The adhesive layers were modeled in the FE environment using spring elements. A 50N load applied at 60 degrees angle with tooth longitudinal axis was applied and validated. Compressive stresses were concentrated on the external surface of the buccal side of the veneer close to the incisal margin; such phenomenon was more evident in the presence of alumina. Tensile stresses were negligible when compared to compressive ones. Alumina and feldspathic ceramic were characterized by a different biomechanical behavior in terms of elastic deformations and stress distributions. The ultimate strength of both materials was not overcome in the performed analysis.
Viscoelastic behaviour of pumpkin balloons
Gerngross, T.; Xu, Y.; Pellegrino, S.
2008-11-01
The lobes of the NASA ULDB pumpkin-shaped super-pressure balloons are made of a thin polymeric film that shows considerable time-dependent behaviour. A nonlinear viscoelastic model based on experimental measurements has been recently established for this film. This paper presents a simulation of the viscoelastic behaviour of ULDB balloons with the finite element software ABAQUS. First, the standard viscoelastic modelling capabilities available in ABAQUS are examined, but are found of limited accuracy even for the case of simple uniaxial creep tests on ULDB films. Then, a nonlinear viscoelastic constitutive model is implemented by means of a user-defined subroutine. This approach is verified by means of biaxial creep experiments on pressurized cylinders and is found to be accurate provided that the film anisotropy is also included in the model. A preliminary set of predictions for a single lobe of a ULDB is presented at the end of the paper. It indicates that time-dependent effects in a balloon structure can lead to significant stress redistribution and large increases in the transverse strains in the lobes.
Viscoelastic flow simulations in model porous media
De, S.; Kuipers, J. A. M.; Peters, E. A. J. F.; Padding, J. T.
2017-05-01
We investigate the flow of unsteadfy three-dimensional viscoelastic fluid through an array of symmetric and asymmetric sets of cylinders constituting a model porous medium. The simulations are performed using a finite-volume methodology with a staggered grid. The solid-fluid interfaces of the porous structure are modeled using a second-order immersed boundary method [S. De et al., J. Non-Newtonian Fluid Mech. 232, 67 (2016), 10.1016/j.jnnfm.2016.04.002]. A finitely extensible nonlinear elastic constitutive model with Peterlin closure is used to model the viscoelastic part. By means of periodic boundary conditions, we model the flow behavior for a Newtonian as well as a viscoelastic fluid through successive contractions and expansions. We observe the presence of counterrotating vortices in the dead ends of our geometry. The simulations provide detailed insight into how flow structure, viscoelastic stresses, and viscoelastic work change with increasing Deborah number De. We observe completely different flow structures and different distributions of the viscoelastic work at high De in the symmetric and asymmetric configurations, even though they have the exact same porosity. Moreover, we find that even for the symmetric contraction-expansion flow, most energy dissipation is occurring in shear-dominated regions of the flow domain, not in extensional-flow-dominated regions.
Energy Technology Data Exchange (ETDEWEB)
Qi, M.; Wegner, J.; Ganzer, L. [Technische Univ. Clausthal, Clausthal-Zellerfeld (Germany). ITE
2013-08-01
Polymer flooding, as an EOR method, has become one of the most important driving forces after water flooding. The conventional believe is that polymer flooding can only improve sweep efficiency, but it has no contribution to residual oil saturation reduction. However, experimental studies indicated that polymer solution can also improve displacement efficiency and decrease residual oil saturation. To get a better understanding of the mechanism to increase the microscopic sweep efficiency and the displacement efficiency, theoretical studies are required. In this paper, we studied the viscoelasticity effect of polymer by using a numerical simulator, which is based on Finite Element Analysis. Since it is showed experimentally that the first normal stress difference of viscoelastic polymer solution is higher than the second stress difference, the Oldroyd-B model was selected as the constitutive equation in the simulation. Numerical modelling of Oldroyd-B viscoelastic fluids is notoriously difficult. Standard Galerkin finite element methods are prone to numerical oscillations, and there is no convergence as the elasticity of fluid increases. Therefore, we use a stabilised finite element model. In order to verify our model, we first built up a model with the same geometry and fluid properties as presented in literature and compared the results. Then, with the tested model we simulated the effect of viscoelastic polymer fluid on dead pores in three simplified pore structures, which are contraction structure, expansion structure and expansion-contraction structure. Correspondingly, the streamlines and velocity contours of polymer solution, with different Reynolds numbers (Re) and Weissenberg numbers (We), flowing in these three structures are showed. The simulation results indicate that the viscoelasticity of polymer solution is the main contribution to increase the micro-scale sweep efficiency. With higher elasticity, the velocity of polymer solution is getting bigger at
Modeling the Non-linear Viscoelastic Response of High Temperature Polyimides
Karra, Satish
2010-01-01
A constitutive model is developed to predict the viscoelastic response of polyimide resins that are used in high temperature applications. This model is based on a thermodynamic framework that uses the notion that the `natural configuration' of a body evolves as the body undergoes a process and the evolution is determined by maximizing the rate of entropy production in general and the rate of dissipation within purely mechanical considerations. We constitutively prescribe forms for the specific Helmholtz potential and the rate of dissipation (which is the product of density, temperature and the rate of entropy production), and the model is derived by maximizing the rate of dissipation with the constraint of incompressibility, and the reduced energy dissipation equation is also regarded as a constraint in that it is required to be met in every process that the body undergoes. The efficacy of the model is ascertained by comparing the predictions of the model with the experimental data for PMR-15 and HFPE-II-52 ...
Brands, Dave W A; Bovendeerd, Peter H M; Wismans, Jac S H M
2002-11-01
In current Finite Element (FE) head models, brain tissue is commonly assumed to display linear viscoelastic material behaviour. However, brain tissue behaves like a non-linear viscoelastic solid for shear strains above 1%. The main objective of this study was to study the effect of non-linear material behaviour on the predicted brain response. We used a non-linear viscoelastic constitutive model, developed on the basis of experimental shear data presented elsewere. First we tested the numerical implementation of the constitutive model by simulating the response of a silicone gel (Sylgard 572 A&B) filled cylindrical cup, subjected to a transient rotational acceleration. The experimental results could be reproduced within 9%. Subsequently, the effect of non-linear material modelling on computed brain response was investigated in an existing three-dimensional head model subjected to an eccentric rotation. At the applied external load strains in the brain were approximately ten times larger than was expected on the basis of published data. This is probably caused by the values of the shear moduli applied in the model. These are at least a factor of ten lower than the ones used in head models in literature but comparable to material data in recent literature. Non-linear material behaviour was found to influence the levels of predicted strains (+20%) and stresses (-11%) but not their temporal and spatial distribution. The pressure response was independent of non-linear material behaviour. In fact it could be predicted by the equilibrium of momentum, and thus it is independent of the choice of the brain constitutive model.
Viscoelasticity, nonlinear shear start-up, and relaxation of entangled star polymers
Snijkers, Frank
2013-07-23
We report on a detailed rheological investigation of well-defined symmetric entangled polymer stars of low functionality with varying number of arms, molar mass of the arms, and solvent content. Emphasis is placed on the response of the stars in simple shear, during start-up, and for relaxation upon flow cessation. To reduce experimental artifacts associated with edge fracture (primarily) and wall slip, we employ a homemade cone-partitioned plate fixture which was successfully implemented in recent studies. Reliable data for these highly entangled stars could be obtained for Weissenberg numbers below 300. The appearance of a stress overshoot during start-up with a corresponding strain approaching a value of 2 suggests that in the investigated shear regime the stars orient but do not stretch. This is corroborated by the fact that the empirical Cox-Merx rule appears to be validated, within experimental error. On the other hand, the (shear) rate dependent steady shear viscosity data exhibit a slope smaller than the convective constraint release slope of -1 (for linear polymers) for the investigated range of rates. The broadness of the stress overshoot reflects the broad linear relaxation spectrum of the stars. The initial stress relaxation rate, reflecting the initial loss of entanglements due to the action of convective constraint release in steady shear flow, increases with Weissenberg number. More importantly, when compared against the relevant rates for comb polymers with relatively short arms, the latter are slower at larger Weissenberg numbers. At long times, the relaxation data are consistent with the linear viscoelastic data on these systems. © 2013 American Chemical Society.
Buckling and Multiple Equilibrium States of Viscoelastic Rectangular Plates
Institute of Scientific and Technical Information of China (English)
无
1999-01-01
On the basis of Karman's theory of thin plates with large deflection, the Boltzmann law on linear viscoelastic materials and the mathematical model of dynamic analysis on viscoelastic thin plates, a set of nonlinear integro-partial-differential equations is first presented by means of a structural function introduced in this paper. Then,by using the Galerkin technique in spatial field and a backward difference scheme in temporal field, the set of nonlinear integro-partial-differential equations reduces to a system of nonlinear algebraic equations. After solving the algebraic equations, the buckling behavior and multiple equilibrium states can be obtained.
Pollitz, F.; Banerjee, P.; Grijalva, K.; Nagarajan, B.; Burgmann, R.
2008-01-01
The 2004 M=9.2 Sumatra-Andaman earthquake profoundly altered the state of stress in a large volume surrounding the ???1400 km long rupture. Induced mantle flow fields and coupled surface deformation are sensitive to the 3-D rheology structure. To predict the post-seismic motions from this earthquake, relaxation of a 3-D spherical viscoelastic earth model is simulated using the theory of coupled normal modes. The quasi-static deformation basis set and solution on the 3-D model is constructed using: a spherically stratified viscoelastic earth model with a linear stress-strain relation; an aspherical perturbation in viscoelastic structure; a 'static'mode basis set consisting of Earth's spheroidal and toroidal free oscillations; a "viscoelastic" mode basis set; and interaction kernels that describe the coupling among viscoelastic and static modes. Application to the 2004 Sumatra-Andaman earthquake illustrates the profound modification of the post-seismic flow field at depth by a slab structure and similarly large effects on the near-field post-seismic deformation field at Earth's surface. Comparison with post-seismic GPS observations illustrates the extent to which viscoelastic relaxation contributes to the regional post-seismic deformation. ?? Journal compilation ?? 2008 RAS.
Internal structure and thermo-viscoelastic properties of agar ionogels.
Sharma, Anshu; Rawat, Kamla; Solanki, Pratima R; Aswal, V K; Kohlbrecher, J; Bohidar, H B
2015-12-10
Ionic liquids (IL) can alter the physical properties of agar hydrogels. Rheology studies show that gels with wide range of storage moduli (gel strength) G0 values ranging from 1 to 20 KPa could be made in imidazolium based IL solutions where the IL concentration may not exceed 5% (w/v). Gelation and gel melting temperatures (tgel and Tm) could be altered by as much as ≈ 10 °C. Small angle neutron scattering studies revealed the presence of fibre bundles of agar double helices having typical length of 120 nm that increased to ≈ 180 nm under favorable conditions. These structures gain flexibility from the cladding of the agar bundles by IL molecules which in turn caused partial charge neutralization of its surface. Raman spectroscopy revealed differential hydration of these bundles. It was found that IL molecules with longer alkyl chain (more hydrophobic) altered the gel homogeneity, and changed its thermal and mechanical properties significantly. Therefore, customization of agar hydrogels in green solvent medium (IL solutions) widens the scope of its application potential that may include sensing.
Nonlinear structural analysis using integrated force method
Indian Academy of Sciences (India)
N R B Krishnam Raju; J Nagabhushanam
2000-08-01
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.
Snijkers, F.
2016-03-31
We report upon the characterization of the steady-state shear stresses and first normal stress differences as a function of shear rate using mechanical rheometry (both with a standard cone and plate and with a cone partitioned plate) and optical rheometry (with a flow-birefringence setup) of an entangled solution of asymmetric exact combs. The combs are polybutadienes (1,4-addition) consisting of an H-skeleton with an additional off-center branch on the backbone. We chose to investigate a solution in order to obtain reliable nonlinear shear data in overlapping dynamic regions with the two different techniques. The transient measurements obtained by cone partitioned plate indicated the appearance of overshoots in both the shear stress and the first normal stress difference during start-up shear flow. Interestingly, the overshoots in the start-up normal stress difference started to occur only at rates above the inverse stretch time of the backbone, when the stretch time of the backbone was estimated in analogy with linear chains including the effects of dynamic dilution of the branches but neglecting the effects of branch point friction, in excellent agreement with the situation for linear polymers. Flow-birefringence measurements were performed in a Couette geometry, and the extracted steady-state shear and first normal stress differences were found to agree well with the mechanical data, but were limited to relatively low rates below the inverse stretch time of the backbone. Finally, the steady-state properties were found to be in good agreement with model predictions based on a nonlinear multimode tube model developed for linear polymers when the branches are treated as solvent.
Sun, Hong-xiang; Zhang, Shu-yi; Xia, Jian-ping
2015-06-01
The propagation characteristics of laser-generated Rayleigh waves in coating-substrate structures with anisotropic and viscoelastic properties have been investigated quantitatively. Based on the plane strain theory, finite element models for simulating laser-generated Rayleigh waves in coating-substrate structures are established, in which the carbon fiber-reinforced epoxy matrix composite and aluminum are used as the coating and/or the substrate alternately. The numerical results exhibit that the characteristics of the laser-generated Rayleigh waves, including attenuation, velocity, and dispersion, are mainly and closely related to the anisotropic and viscoelastic properties of the composite in the coating-substrate structures.
Viscoelastic polymer flows and elastic turbulence in three-dimensional porous structures.
Mitchell, Jonathan; Lyons, Kyle; Howe, Andrew M; Clarke, Andrew
2016-01-14
Viscoelastic polymer solutions flowing through reservoir rocks have been found to improve oil displacement efficiency when the aqueous-phase shear-rate exceeds a critical value. A possible mechanism for this enhanced recovery is elastic turbulence that causes breakup and mobilization of trapped oil ganglia. Here, we apply nuclear magnetic resonance (NMR) pulsed field gradient (PFG) diffusion measurements in a novel way to detect increased motion of disconnected oil ganglia. The data are acquired directly from a three-dimensional (3D) opaque porous structure (sandstone) when viscoelastic fluctuations are expected to be present in the continuous phase. The measured increase in motion of trapped ganglia provides unequivocal evidence of fluctuations in the flowing phase in a fully complex 3D system. This work provides direct evidence of elastic turbulence in a realistic reservoir rock - a measurement that cannot be readily achieved by conventional laboratory methods. We support the NMR data with optical microscopy studies of fluctuating ganglia in simple two-dimensional (2D) microfluidic networks, with consistent apparent rheological behaviour of the aqueous phase, to provide conclusive evidence of elastic turbulence in the 3D structure and hence validate the proposed flow-fluctuation mechanism for enhanced oil recovery.
RESEARCH ON NONLINEAR PROBLEMS IN STRUCTURAL DYNAMICS.
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
Vadiraja, G. K.; Mahapatra, D. Roy
2009-03-01
In this paper we incorporate a novel approach to synthesize a class of closed-loop feedback control, based on the variational structure assignment. Properties of a viscoelastic system are used to design an active feedback controller for an undamped structural system with distributed sensor, actuator and controller. Wave dispersion properties of onedimensional beam system have been studied. Efficiency of the chosen viscoelastic model in enhancing damping and stability properties of one-dimensional viscoelastic bar have been analyzed. The variational structure is projected on a solution space of a closed-loop system involving a weakly damped structure with distributed sensor and actuator with controller. These assign the phenomenology based internal strain rate damping parameter of a viscoelastic system to the usual elastic structure but with active control. In the formulation a model of cantilever beam with non-collocated actuator and sensor has been considered. The formulation leads to the matrix identification problem of two dynamic stiffness matrices. The method has been simplified to obtain control system gains for the free vibration control of a cantilever beam system with collocated actuator-sensor, using quadratic optimal control and pole-placement methods.
Structural optimization for nonlinear dynamic response.
Dou, Suguang; Strachan, B Scott; Shaw, Steven W; Jensen, Jakob S
2015-09-28
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.
BRST structure of non-linear superalgebras
Asorey, M; Radchenko, O V; Sugamoto, A
2008-01-01
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.
基于ABAQUS的非线性粘弹性本构模型二次开发%Developing of Nonlinear Viscoelastic Constitutive Model Based on ABAQUS
Institute of Scientific and Technical Information of China (English)
彭云
2011-01-01
基于大型非线性有限元软件ABAQUS/EXPLICIT所提供的用户材料子程序接口VUMAT,对非线性粘弹性本构模型进行二次开发.通过标准犬骨单轴拉伸算例,验证了子程序的有效性,弥补了ABAQUS仅含线性粘弹性本构模型的不足.文中详述了材料子程序开发流程,探讨了涉及的诸多实用技术,可为用户扩充ABAQUS的材料模型提供参考.%Based on the subroutine VUMAT, user - defined material model in the nonlinear FEM software ABAQUS/EXPIiCIT, a nonlinear viscoelastic constitutive model is developed. The validity of the subroutine has been proven through the standard uniaxial ten-sile model. The shortage of ABAQUS which only has linear viscoelastic constitutive model is remedied. This paper presents the process of developing a material constitutive model and some useful technology. It can be referred for extending the material constitutive model in ABAQUS.
Embedding viscoelastic damping materials in low-cost VARTM composite structures
Robinson, M. J.; Kosmatka, J. B.
2005-05-01
It has been well established that using viscoelastic damping materials in structural applications can greatly reduce the dynamic response and thus improve structural fatigue life. Previously these materials have been used to solve vibration problems in metallic structures, where the damping material is attached to the structure and then a stiff outer layer is attached to promote shear deformation in the damping material. More recently, these materials have been used successfully in expensive aerospace composite structures, where the damping material is embedded between plies of prepreg graphite/epoxy prior to being cured in a high-temperature, high-pressure autoclave. The current research involves embedding these damping layers into low-cost composite structures fabricated using the Vacuum Assisted Resin Transfer Molding (VARTM) process. The damping layers are perforated with a series of small holes to allow the resin to flow through the damping layer and completely wet-out the structure. Experimental fabrication, vibration testing, and stiffness testing investigate the effect of hole diameter versus hole spacing. Results show that the damping and stiffness can be very sensitive to perforation spacing and size. It is shown that for closely spaced perforations (95% damping area) that damping increases by only a factor of 2.2 over the undamped plate. However, for greater perforation spacing (99.7% damping area) the damping is increased by a factor of 14.3. Experimental results as well as practical design considerations for fabricating damped composite structures using the VARTM process are presented.
Structural optimization for nonlinear dynamic response
DEFF Research Database (Denmark)
Dou, Suguang; Strachan, B. Scott; Shaw, Steven W.
2015-01-01
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...
Nonlinear Dynamics of Structures with Material Degradation
Soltani, P.; Wagg, D. J.; Pinna, C.; Whear, R.; Briody, C.
2016-09-01
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.
Khan, Sabeel M.; Hammad, M.; Sunny, D. A.
2017-08-01
In this article, the influence of thermal relaxation time and chemical reaction is studied on the MHD upper-convected viscoelastic fluid with internal structure using the Cattaneo-Christov heat flux equation for the first time in the literature. The flow-governing equations are formulated and are converted into their respective ordinary differential equations (ODEs) with the application of similarity functions. The resulting system of coupled nonlinear ODEs is solved along with the prescribed conditions at boundary using a finite-difference code in MATLAB. Influence of chemical reaction, thermal relaxation time and internal material parameter on the macroscopic and micropolar velocities as well as on the temperature and concentration profiles is examined along with other physical parameters ( e.g., magnetic parameter, Eckert number, Prandtl number and fluid relaxation time). The accuracy of the obtained numerical solution is shown by comparing the physical parameters of interest with particular cases of existing results in the literature.
Supratransmission in a disordered nonlinear periodic structure
Yousefzadeh, B.; Phani, A. Srikantha
2016-10-01
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.
2012-06-09
these formulations employ some form of either the Euler-Bernoulli or Timoshenko beam theories and are mostly restricted to small strain analysis. The...and Kadioglu [1], wherein a Timoshenko beam element is de- veloped using mixed variational principles. In their work, the finite element model...method in their analysis of cylindrical helical rods (based on the Timoshenko beam hypotheses). Additional numerical formulations for viscoelastic beams
Nonlinear Dynamics and Control of Flexible Structures
1991-03-01
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
Optimal arrangement of viscoelastic dampers for seismic control of adjacent shear-type structures
Institute of Scientific and Technical Information of China (English)
Xiao HUANG; Hong-ping ZHU
2013-01-01
The optimal arrangement of viscoelastic dampers (VEDs) used to link two adjacent shear-type structures under seismic excitation was investigated.A two-step optimal design method is proposed.First,optimal parameter expressions of the Kelvin model are used to calculate the optimal stiffness and damping coefficient of the VEDs.Then,using the two-step optimal design method,taking the quadratic performance index as the optimization objective,the optimal arrangement of the dampers is determined.General rules about the optimal arrangement of the VEDs were obtained.The results show that the placement of only one damper between two adjacent shear-type structures should be avoided; if more than one damper is used,they should be distributed on the top and lower floors of the structures.Optimization of the number of dampers had little effect on response reduction.The most important factor was the optimization of the placement of the dampers.Through comparative study,for buildings of equal and unequal heights,the optimal parameters of dampers from parametric studies were shown to match the theoretical results for different numbers and placements of dampers.The level of response reduction was shown to be sensitive to the damping coefficient of the dampers.
Structure, viscoelasticity, and interfacial dynamics of a model polymeric bicontinuous microemulsion
Energy Technology Data Exchange (ETDEWEB)
Hickey, Robert J.; Gillard, Timothy M.; Irwin, Matthew T.; Lodge, Timothy P.; Bates, Frank S.
2016-01-01
We have systematically studied the equilibrium structure and dynamics of a polymeric bicontinuous microemulsion (BμE) composed of poly(cyclohexylethylene) (PCHE), poly(ethylene) (PE), and a volumetrically symmetric PCHE–PE diblock copolymer, using dynamic mechanical spectroscopy, small angle X-ray and neutron scattering, and transmission electron microscopy. The BμE was investigated over an 80 °C temperature range, revealing a structural evolution and a rheological response not previously recognized in such systems. As the temperature is reduced below the point associated with the lamellar-disorder transition at compositions adjacent to the microemulsion channel, the interfacial area per chain of the BμE approaches that of the neat (undiluted) lamellar diblock copolymer. With increasing temperature, the diblock-rich interface swells through homopolymer infiltration. Time–temperature-superposed linear dynamic data obtained as a function of frequency show that the viscoelastic response of the BμE is strikingly similar to that of the fluctuating pure diblock copolymer in the disordered state, which we associate with membrane undulations and the breaking and reforming of interfaces. This work provides new insights into the structure and dynamics that characterize thermodynamically stable BμEs in the limits of relatively weak and strong segregation.
Soil-structure interaction including nonlinear soil
Gicev, Vlado
2008-01-01
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.
Structural investigation of viscoelastic micellar water/CTAB/NaNO3 solutions
Indian Academy of Sciences (India)
K Kuperkar; L Abezgauz; D Danino; G Verma; P A Hassan; V K Aswal; D Varade; P Bahadur
2008-11-01
A highly viscoelastic worm-like micellar solution is formed in hexa-decyltrimethylammonium bromide (CTAB) in the presence of sodium nitrate (NaNO3). A gradual increase in micellar length with increasing NaNO3 was assumed from the rheological measurements where the zero-shear viscosity (0) versus NaNO3 concentration curve exhibits a maximum. However, upon increase in temperature, the viscosity decreases. Changes in the structural parameters of the micelles with addition of NaNO3 were inferred from small angle neutron scattering measurements (SANS). The intensity of scattered neutrons in the low region was found to increase with increasing NaNO3 concentration. This suggests an increase in the size of the micelles and/or decrease of intermicellar interaction with increasing salt concentration. Analysis of the SANS data using prolate ellipsoidal structure and Yukawa form of interaction potential between mi-celles indicate that addition of NaNO3 leads to a decrease in the surface charge of the ellipsoidal micelles which induces micellar growth. Cryo-TEM measurements support the presence of thread-like micelles in CTAB and NaNO3.
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)
1995-08-01
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.
Nonlinearities in Periodic Structures and Metamaterials
Denz, Cornelia; Kivshar, Yuri S
2010-01-01
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.
Sciumè, Giuseppe; Benboudjema, Farid
2016-09-01
A post-processing technique which allows computing crack width in concrete is proposed for a viscoelastic damage model. Concrete creep is modeled by means of a Kelvin-Voight cell while the damage model is that of Mazars in its local form. Due to the local damage approach, the constitutive model is regularized with respect to finite element mesh to avoid mesh dependency in the computed solution (regularization is based on fracture energy). The presented method is an extension to viscoelasticity of the approach proposed by Matallah et al. (Int. J. Numer. Anal. Methods Geomech. 34(15):1615-1633, 2010) for a purely elastic damage model. The viscoelastic Unitary Crack-Opening (UCO) strain tensor is computed accounting for evolution with time of surplus of stress related to damage; this stress is obtained from decomposition of the effective stress tensor. From UCO the normal crack width is then derived accounting for finite element characteristic length in the direction orthogonal to crack. This extension is quite natural and allows for accounting of creep impact on opening/closing of cracks in time dependent problems. A graphical interpretation of the viscoelastic UCO using Mohr's circles is proposed and application cases together with a theoretical validation are presented to show physical consistency of computed viscoelastic UCO.
Control of nonlinear flexible space structures
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
CISM course on exploiting nonlinear behaviour in structural dynamics
Virgin, Lawrence; Exploiting Nonlinear Behavior in Structural Dynamics
2012-01-01
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.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The viscoelastic multi-dimensional earthquake isolation and mitigation device is a new kind of passive control device, which can perform its "name-giving" task of earthquake isolation and earthquake mitigation simultaneously. In order to quantify its vertical earthquake isolation and mitigation effect on structures, firstly, shaking table tests on steel frame structures with and without the devices were carried out; secondly, analysis on dynamic characteristics and dynamic responses of the structures was also performed; furthermore, the finite element analytical results and the experimental results were compared. It can be shown from the analytical and experimental results that the devices have noticeable earthquake isolation and mitigation effect in the vertical direction.
Nonlinear frequency response analysis of structural vibrations
Weeger, Oliver; Wever, Utz; Simeon, Bernd
2014-12-01
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.
Nonlinear transient analysis of joint dominated structures
Chapman, J. M.; Shaw, F. H.; Russell, W. C.
1987-01-01
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.
Wientjes, R.H.W.; Duits, M.H.G.; Bakker, J.W.P.; Jongschaap, R.J.J.; Mellema, J.
2001-01-01
To gain more insight into the mechanisms of stress relaxation in aqueous guar gum solutions, we investigated the effect of chemical modifications of the polymer and of the solvent on the linear viscoelastic behavior in different regions of the frequency domain. Interchain bonding could be ruled out
An Updated Analytical Structural Pounding Force Model Based on Viscoelasticity of Materials
Directory of Open Access Journals (Sweden)
Qichao Xue
2016-01-01
Full Text Available Based on the summary of existing pounding force analytical models, an updated pounding force analysis method is proposed by introducing viscoelastic constitutive model and contact mechanics method. Traditional Kelvin viscoelastic pounding force model can be expanded to 3-parameter linear viscoelastic model by separating classic pounding model parameters into geometry parameters and viscoelastic material parameters. Two existing pounding examples, the poundings of steel-to-steel and concrete-to-concrete, are recalculated by utilizing the proposed method. Afterwards, the calculation results are compared with other pounding force models. The results show certain accuracy in proposed model. The relative normalized errors of steel-to-steel and concrete-to-concrete experiments are 19.8% and 12.5%, respectively. Furthermore, a steel-to-polymer pounding example is calculated, and the application of the proposed method in vibration control analysis for pounding tuned mass damper (TMD is simulated consequently. However, due to insufficient experiment details, the proposed model can only give a rough trend for both single pounding process and vibration control process. Regardless of the cheerful prospect, the study in this paper is only the first step of pounding force calculation. It still needs a more careful assessment of the model performance, especially in the presence of inelastic response.
Zhu, Shengyang; Cai, Chengbiao; Spanos, Pol D.
2015-01-01
A nonlinear and fractional derivative viscoelastic (FDV) model is used to capture the complex behavior of rail pads. It is implemented into the dynamic analysis of coupled vehicle-slab track (CVST) systems. The vehicle is treated as a multi-body system with 10 degrees of freedom, and the slab track is represented by a three layer Bernoulli-Euler beam model. The model for the rail pads is one dimensional, and the force-displacement relation is based on a superposition of elastic, friction, and FDV forces. This model takes into account the influences of the excitation frequency and of the displacement amplitude through a fractional derivative element, and a nonlinear friction element, respectively. The Grünwald representation of the fractional derivatives is employed to numerically solve the fractional and nonlinear equations of motion of the CVST system by means of an explicit integration algorithm. A dynamic analysis of the CVST system exposed to excitations of rail harmonic irregularities is carried out, pointing out the stiffness and damping dependence on the excitation frequency and the displacement amplitude. The analysis indicates that the dynamic stiffness and damping of the rail pads increase with the excitation frequency while they decrease with the displacement amplitude. Furthermore, comparisons between the proposed model and ordinary Kelvin model adopted for the CVST system, under excitations of welded rail joint irregularities and of random track irregularities, are conducted in the time domain as well as in the frequency domain. The proposed model is shown to possess several modeling advantages over the ordinary Kelvin element which overestimates both the stiffness and damping features at high frequencies.
Ultrafast Structure Switching through Nonlinear Phononics
Juraschek, D. M.; Fechner, M.; Spaldin, N. A.
2017-02-01
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.
Identification of Nonlinearities in Joints of a Wing Structure
Sani M.S.M.; Ouyang H
2016-01-01
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...
Uniform Decay for Solutions of an Axially Moving Viscoelastic Beam
Energy Technology Data Exchange (ETDEWEB)
Kelleche, Abdelkarim, E-mail: kellecheabdelkarim@gmail.com [Université des Sciences et de la Technologie Houari Boumediene, Faculté des Mathématiques (Algeria); Tatar, Nasser-eddine, E-mail: tatarn@Kfupm.edu.sa [King Fahd University of Petroleum and Minerals, Department of Mathematics and Statistics (Saudi Arabia)
2017-06-15
The paper deals with an axially moving viscoelastic structure modeled as an Euler–Bernoulli beam. The aim is to suppress the transversal displacement (transversal vibrations) that occur during the axial motion of the beam. It is assumed that the beam is moving with a constant axial speed and it is subject to a nonlinear force at the right boundary. We prove that when the axial speed of the beam is smaller than a critical value, the dissipation produced by the viscoelastic material is sufficient to suppress the transversal vibrations. It is shown that the rate of decay of the energy depends on the kernel which arise in the viscoelastic term. We consider a general kernel and notice that solutions cannot decay faster than the kernel.
Linear viscoelastic characterization from filament stretching rheometry
DEFF Research Database (Denmark)
Wingstrand, Sara Lindeblad; Alvarez, Nicolas J.; Hassager, Ole
viscoelasticity well into the nonlinear regime. Therefore at present, complete rheological characterization of a material requires two apparatuses: a shear and an extensional rheometer. This work is focused on developing a linear viscoelastic protocol for the filament stretching rheometer (FSR) in order...
Manzhirov, A. V.; Parshin, D. A.
2016-11-01
The process of erection an object under the action of gravity forces in the absence of additional loads is studied together with the technology of application of prestressed structure elements. The mathematically two-dimensional engineering problem of mechanics of gradual building of a heavy semicircular vault from a prestressed viscoelastic homogeneously aging material is solved analytically. The vault fixation on a rigid horizontal base by sliding fixation, which ensures continuous smooth contact between the vault foot and the base, is considered. The performed computations permit demonstrating high efficiency of preliminary stress creation in the material elements added to the vault in the process of its building in order to control its technological stress state. It is shown that this measure permits significantly decreasing the final values of the separating contact stresses on the foot of the built vault and obtaining the final state of the whole structure which is safer with respect to the level of tensile stresses than that obtain by using unstressed elements.
Earthquake analysis of structures using nonlinear models
Cemalovic, Miran
2015-01-01
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...
Gurbatov, S N; Saichev, A I
2012-01-01
"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...
Nonlinear helicons bearing multi-scale structures
Abdelhamid, Hamdi M.; Yoshida, Zensho
2017-02-01
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.
Conditions on Structural Controllability of Nonlinear Systems: Polynomial Method
Directory of Open Access Journals (Sweden)
Qiang Ma
2011-03-01
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.
Khurana, Meenakshi; Rana, Puneet; Srivastava, Sangeet
2016-12-01
In the present paper, we present both linear and nonlinear analyses to investigate thermal instability on a rotating non-Newtonian viscoelastic nanofluid layer under the influence of a magnetic field. In the linear stability analysis, the stationary and oscillatory modes of convection are obtained for various controlling parameters using the normal mode technique. Both Nusselt and Sherwood numbers are calculated after employing the minimal truncated Fourier series to steady and unsteady state. The main findings conclude that rotation and strain retardation parameter increase the value of the critical Rayleigh number in the neutral stability curve which delays the onset of convection in the nanofluid layer while the stress relaxation parameter enhances the convection. The magnetic field stabilizes the system for low values of the Taylor number (rotation) but an inverse trend is observed for high Taylor number. Both Nusselt and Sherwood numbers initially oscillate with time until the steady state prevails and they decrease with both Chandrasekhar and Taylor numbers. The magnitude of the streamlines and the contours of both isotherms and iso-nanohalines concentrate near the boundaries for large values of Ra, indicating an increase in convection.
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...
Nonlinear and Variable Structure Excitation Controller for Power System Stability
Institute of Scientific and Technical Information of China (English)
Wang Ben; Ronnie Belmans
2006-01-01
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.
DEFF Research Database (Denmark)
Chen, X.; Cui, W.; Jensen, Jørgen Juncher
2003-01-01
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 ...
Arzoumanidis, Alexis Gerasimos
A four point bend, mixed-mode, reinforced, cracked lap shear specimen experimentally simulated adhesive joints between load bearing composite parts in automotive components. The experiments accounted for fatigue, solvent and temperature effects on a swirled glass fiber composite adherend/urethane adhesive system. Crack length measurements based on compliance facilitated determination of da/dN curves. A digital image processing technique was also utilized to monitor crack growth from in situ images of the side of the specimen. Linear elastic fracture mechanics and finite elements were used to determine energy release rate and mode-mix as a function of crack length for this specimen. Experiments were conducted in air and in a salt water bath at 10, 26 and 90°C. Joints tested in the solvent were fully saturated. In air, both increasing and decreasing temperature relative to 26°C accelerated crack growth rates. In salt water, crack growth rates increased with increasing temperature. Threshold energy release rate is shown to be the most appropriate design criteria for joints of this system. In addition, path of the crack is discussed and fracture surfaces are examined on three length scales. Three linear viscoelastic properties were measured for the neat urethane adhesive. Dynamic tensile compliance (D*) was found using a novel extensometer and results were considerably more accurate and precise than standard DMTA testing. Dynamic shear compliance (J*) was determined using an Arcan specimen. Dynamic Poisson's ratio (nu*) was extracted from strain gage data analyzed to include gage reinforcement. Experiments spanned three frequency decades and isothermal data was shifted by time-temperature superposition to create master curves spanning thirty decades. Master curves were fit to time domain Prony series. Shear compliance inferred from D* and nu* compared well with measured J*, forming a basis for finding the complete time dependent material property matrix for this
Model updating of nonlinear structures from measured FRFs
Canbaloğlu, Güvenç; Özgüven, H. Nevzat
2016-12-01
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
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
2005-01-01
@@ 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.
Identification of Non-Linear Structures using Recurrent Neural Networks
DEFF Research Database (Denmark)
Kirkegaard, Poul Henning; Nielsen, Søren R. K.; Hansen, H. I.
1995-01-01
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....
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....
Identification of Non-Linear Structures using Recurrent Neural Networks
DEFF Research Database (Denmark)
Kirkegaard, Poul Henning; Nielsen, Søren R. K.; Hansen, H. I.
1995-01-01
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....
Lutz-Bueno, Viviane; Pasquino, Rossana; Liebi, Marianne; Kohlbrecher, Joachim; Fischer, Peter
2016-05-03
During the anisotropic growth from globular to wormlike micelles, the basic interactions among distinct parts of the surfactant monomer, its counterion, and additives are fundamental to tune molecular self-assembly. We investigate the addition of sodium salicylate (NaSal) to hexadecyltrimethylammonium chloride and bromide (CTAC and CTAB), 1-hexadecylpyridinium chloride and bromide (CPyCl and CPyBr), and benzyldimethylhexadecylammonium chloride (BDMC), which have the same hydrophobic tail. Their potential to enhance viscoelasticity by anisotropic micellar growth upon salt addition was compared in terms of (i) the influence of the headgroup structure, and (ii) the influence of surfactant counterion type. Employing proton nuclear magnetic resonance ((1)H NMR), we focused on the molecular conformation of surfactant monomers in the core and polar shell regions of the micelles and their interactions with increasing concentration of NaSal. The viscoelastic response was investigated by rotational and oscillatory rheology. We show that micellar growth rates can be tuned by varying the flexibility and size of the surfactant headgroup as well as the dissociation degree of the surfactant counterion, which directly influences the strength of headgroup-counterion pairing. As a consequence, the morphological transitions depend directly on charge neutralization by electrostatic screening. For example, the amount of salt necessary to start the rodlike-to-wormlike micelle growth depends directly on the number of dissociated counterions in the polar shell.
Energy Technology Data Exchange (ETDEWEB)
Tehrani, Mehran; Al-Haik, Marwan; Garmestani, Hamid; Li, Dongsheng
2012-01-01
In this study the effect of moderate magnetic fields on the microstructure of a structural epoxy system was investigated. The changes in the microstructure have been quantitatively investigated using wide angle x-ray diffraction (WAXD) and pole figure analysis. The mechanical properties (modulus, hardness and strain rate sensitivity parameter) of the epoxy system annealed in the magnetic field were probed with the aid of instrumented nanoindentation and the results are compared to the reference epoxy sample. To further examine the creep response of the magnetically annealed and reference samples, short 45 min duration creep tests were carried out. An equivalent to the macro scale creep compliance was calculated using the aforementioned nano-creep data. Using the continuous complex compliance (CCC) analysis, the phase lag angle, tan (δ), between the displacement and applied force in an oscillatory nanoindentation test was measured for both neat and magnetically annealed systems through which the effect of low magnetic fields on the viscoelastic properties of the epoxy was invoked. The comparison of the creep strain rate sensitivity parameter , A/d(0), from short term(80 ), creep tests and the creep compliance J(t) from the long term(2700 s) creep tests with the tan(δ) suggests that former parameter is a more useful comparative creep parameter than the creep compliance. The results of this investigation reveal that under low magnetic fields both the quasi-static and viscoelastic mechanical properties of the epoxy have been improved.
Li, Dongna; Li, Xudong; Dai, Jianfeng
2017-08-01
In this paper, two kinds of transient models, the viscoelastic model and the linear elastic model, are established to analyze the curing deformation of the thermosetting resin composites, and are calculated by COMSOL Multiphysics software. The two models consider the complicated coupling between physical and chemical changes during curing process of the composites and the time-variant characteristic of material performance parameters. Subsequently, the two proposed models are implemented respectively in a three-dimensional composite laminate structure, and a simple and convenient method of local coordinate system is used to calculate the development of residual stresses, curing shrinkage and curing deformation for the composite laminate. Researches show that the temperature, degree of curing (DOC) and residual stresses during curing process are consistent with the study in literature, so the curing shrinkage and curing deformation obtained on these basis have a certain referential value. Compared the differences between the two numerical results, it indicates that the residual stress and deformation calculated by the viscoelastic model are more close to the reference value than the linear elastic model.
Yamasaki, Tadashi; Houseman, Gregory; Hamling, Ian; Postek, Elek
2010-05-01
We have developed a new parallelized 3-D numerical code, OREGANO_VE, for the solution of the general visco-elastic problem in a rectangular block domain. The mechanical equilibrium equation is solved using the finite element method for a (non-)linear Maxwell visco-elastic rheology. Time-dependent displacement and/or traction boundary conditions can be applied. Matrix assembly is based on a tetrahedral element defined by 4 vertex nodes and 6 nodes located at the midpoints of the edges, and within which displacement is described by a quadratic interpolation function. For evaluating viscoelastic relaxation, an explicit time-stepping algorithm (Zienkiewicz and Cormeau, Int. J. Num. Meth. Eng., 8, 821-845, 1974) is employed. We test the accurate implementation of the OREGANO_VE by comparing numerical and analytic (or semi-analytic half-space) solutions to different problems in a range of applications: (1) equilibration of stress in a constant density layer after gravity is switched on at t = 0 tests the implementation of spatially variable viscosity and non-Newtonian viscosity; (2) displacement of the welded interface between two blocks of differing viscosity tests the implementation of viscosity discontinuities, (3) displacement of the upper surface of a layer under applied normal load tests the implementation of time-dependent surface tractions (4) visco-elastic response to dyke intrusion (compared with the solution in a half-space) tests the implementation of all aspects. In each case, the accuracy of the code is validated subject to use of a sufficiently small time step, providing assurance that the OREGANO_VE code can be applied to a range of visco-elastic relaxation processes in three dimensions, including post-seismic deformation and post-glacial uplift. The OREGANO_VE code includes a capability for representation of prescribed fault slip on an internal fault. The surface displacement associated with large earthquakes can be detected by some geodetic observations
Nonlinear excitations in two-dimensional molecular structures with impurities
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Rasmussen, Kim; Christiansen, Peter Leth
1995-01-01
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....
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)
1994-09-01
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.
Institute of Scientific and Technical Information of China (English)
Liu Bing-Can; Yu Li; Lu Zhi-Xin
2011-01-01
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.
Identification of Nonlinearities in Joints of a Wing Structure
Directory of Open Access Journals (Sweden)
Sani M.S.M.
2016-01-01
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.
Itoh, Yuji; Nishimura, Takuya
2016-09-01
Postseismic deformation of the 2003 Tokachi-oki earthquake ( M w 8.0) has been observed by GNSS. We analyzed the deformation observed in Hokkaido in the 2nd to the 7th year following the 2003 Tokachi-oki earthquake and examined the effect of two major mechanisms (i.e., afterslip and viscoelastic relaxation) for the observed postseismic deformation by fitting it with a model consisting of afterslip and viscoelastic relaxation. The thickness of the lithosphere, the viscosity of the asthenosphere, and the time decaying constant of afterslip were estimated to be 50 km, 2.0 × 1019 Pa s, and 0.110 year, respectively, which are concordant with those in the Tohoku region estimated in previous studies. The revealed characteristics of postseismic deformation are as follows. At most of the used stations, afterslip played the dominant role in the 2nd year and was still sustained near the coseismic area even in the 7th year. However, the calculated velocity due to viscoelastic relaxation was comparable to that due to afterslip at the stations in northern Hokkaido after the 5th year. Because the calculated velocity due to viscoelastic relaxation was landward near the coseismic slip area, afterslip near the coseismic slip area will be biased to be smaller if viscoelastic relaxation is ignored. A systematic spatial pattern of the residuals considering afterslip only highlights an importance for explaining the observation data. We also examined the effect of viscoelastic relaxation due to afterslip for the parameter estimation and found that it was too small to affect the estimated structure parameters.[Figure not available: see fulltext.
Robust stabilization of general nonlinear systems with structural uncertainty
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
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.
Akbarov, Surkay
2013-01-01
This book investigates stability loss and buckling delamination problems of the viscoelastic composite materials and structural members made from these materials within the framework of the Three-Dimensional Linearized Theory of Stability (TDLTS). The investigation of stability loss problems is based on the study of an evolution of the initial infinitesimal imperfection in the structure of the material or of the structural members with time (for viscoelastic composites) or with external compressing forces (for elastic composites). This study is made within the scope of the Three-Dimensional Geometrically Non-Linear Theory of the Deformable Solid Body Mechanics. The solution to the corresponding boundary-value problems is presented in the series form in a small parameter which characterizes the degree of the initial imperfection. The boundary form perturbation technique is employed and nonlinear problems for the domains bounded by noncanonical surfaces are reduced to the same nonlinear problem for the correspo...
Nonlinear structural damage detection using support vector machines
Xiao, Li; Qu, Wenzhong
2012-04-01
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.
Nonlinear damage detection in composite structures using bispectral analysis
Ciampa, Francesco; Pickering, Simon; Scarselli, Gennaro; Meo, Michele
2014-03-01
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.
Nonlinear structural finite element model updating and uncertainty quantification
Ebrahimian, Hamed; Astroza, Rodrigo; Conte, Joel P.
2015-04-01
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.
Nonlinear structure formation in Nonlocal Gravity
Barreira, Alexandre; Hellwing, Wojciech A; Baugh, Carlton M; Pascoli, Silvia
2014-01-01
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...
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)
2015-10-01
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.
Nonlinear normal modes and their application in structural dynamics
Directory of Open Access Journals (Sweden)
2006-01-01
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.
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)
1997-12-01
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}
Sinou, Jean-Jacques; Thouverez, Fabrice; Jezequel, Louis
2006-01-01
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...
Bykov, D. L.; Konovalov, D. N.
2007-12-01
Material fracture experiments on specimens and structures testify that materials can resist greater stresses in local stress concentration regions than in regions with a nearly homogeneous stress state. Taking this fact into account in design stress analysis permits one to reveal additional structure loading and/or service life margins. One approach aimed at taking into account the increased strength in local stress concentration regions is to use averaged limit characteristics parametrically depending on the characteristic size L of the averaging region. One version of this approach is the concept of "elementary block" of a material [1, 2]. The averaged limit characteristics are determined by an experiment-calculation method involving the analysis of the stress-strain state of a material specimen with a stress concentrator at the time when the specimen attains the limit state preceding macrofracture. In [3], the dependence of the averaged limit separation stresses on the size of the averaging region was determined on the basis of numerical analysis of the singular stress state of the specimen used to determine the standard characteristics of the adhesion strength of a filled polymer material. In the present paper, we generalize the above approach to the case of a viscoelastic material. For the limit characteristics of the material in the local stress concentration region we take the volume-averaged components of the specific work of internal forces [4, 5] (the averaged specific absorbed energy and the averaged specific instantaneously reversible energy). The introduction of two limit energies originates from the fact that, to initiate the process of macrofracture, it is necessary to satisfy the following two conditions simultaneously: the material must be "damaged" sufficiently strongly by the preceding loading, and the "damaged" material must be loaded sufficiently strongly. As an example of determining the material averaged limit energy characteristics in a
Prolongation Structure of Semi-discrete Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
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.
Non-linear finite element analysis in structural mechanics
Rust, Wilhelm
2015-01-01
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.
Relativistic viscoelastic fluid mechanics.
Fukuma, Masafumi; Sakatani, Yuho
2011-08-01
A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.
Towards homoscedastic nonlinear cointegration for structural health monitoring
Zolna, Konrad; Dao, Phong B.; Staszewski, Wieslaw J.; Barszcz, Tomasz
2016-06-01
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.
Bhatti, Abdul Qadir
2013-08-01
A number of studies have been carried out to investigate the performance of viscoelastic dampers (VEDs) and magnetorheological dampers (MRDs) in controlling the seismic response of buildings, but very few of them regarding the effect of temperature on the behavior of those dampers. The energy absorption properties of the VEDs are dependent on the ambient temperature, excitation frequency and strain amplitude. Several mathematical models have been investigated for reproducing the experimental behavior of single degree of freedom VEDs and MEDs. Of these, only the fractional derivative model can reflect the influence of temperature which is, however, so complex that it is difficult to apply in structural analysis. In order to verify the effect of temperature, two case studies of structural element have been conducted: once using VED and once using MRD. Kelvin-Voigt mathematical model applied, they were investigated and after analyzing the results, the force vs. displacement showed that MRD achieved a high force capacity and a better performance than VED. Furthermore, the effect of the temperature in case of VED observed via plotting the dissipated energy hysteresis at different temperatures. These results validate the effect of the temperature as the lower the temperature the more viscous the dashpot element becomes, hence improving damping, but this is up to a specific low temperature.
Nonlinear and stochastic dynamics of coherent structures
DEFF Research Database (Denmark)
Rasmussen, Kim
1997-01-01
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...
Nonlinear Phononic Periodic Structures and Granular Crystals
2012-02-10
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
Crystalline structure and symmetry dependence of acoustic nonlinearity parameters
Cantrell, John H.
1994-01-01
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.
Shape recovery of viscoelastic beams after stowage
DEFF Research Database (Denmark)
Kwok, Kawai
2015-01-01
The deployment of viscoelastic structures that have been held stowed for a given time duration can be formulated as a viscoelastic boundary value problem in which the prescribed condition switches from constant displacement to constant traction. This paper presents closed-form expressions...
Coupled parametric processes in binary nonlinear photonic structures
Saygin, M Yu
2016-01-01
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...
International Conference on Structural Nonlinear Dynamics and Diagnosis
CSNDD 2012; CSNDD 2014
2015-01-01
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...
Multiwave nonlinear couplings in elastic structures
Directory of Open Access Journals (Sweden)
2006-01-01
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.
Yan, Wang; Zhang, Zhousou; Qu, Jinxiu; Sun, Chuang
2016-07-01
In general, a vibration signal consists of several frequency modulation (FM) components. Every component contains different information, and can be characterized by its instantaneous amplitude (IA) and instantaneous phase (IP). In engineering applications, conventional time-frequency analysis methods and signal decomposition methods have shown their power in investigating features of the vibration signal. However, they are limited in resolution and it is hard to analyze these FM components individually. To overcome these deficiencies, a novel signal decomposition algorithm, named time-frequency distribution decomposition (TFDD), is proposed in this paper, which reconstructs one FM component of the signal at a time by estimating its IP and IA. The IA and IP are approximated by two polynomial functions respectively. One important advantage of TFDD is that it can directly extract the component we are interested in. Therefore, we can analyze the key component of the signal with little influence from other components. This will help us to characterize the vibration signal more deeply. Furthermore, it is very stable to noise. This is conductive to protecting the information of the vibration signal. The effectiveness of the TFDD is validated by a numerical simulation and the study of the vibration response signal collected from a viscoelastic sandwich structure (VSS). From the value of permutation entropy of the component extracted by TFDD, the looseness state of the VSS is recognized.
SEISMIC RANDOM VIBRATION ANALYSIS OF LOCALLY NONLINEAR STRUCTURES
Institute of Scientific and Technical Information of China (English)
ZhaoYan; LinJiahao; ZhangYahui; AnWei
2003-01-01
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.
Parametric localized modes in quadratic nonlinear photonic structures
DEFF Research Database (Denmark)
Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole;
2001-01-01
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....
Numerical solution methods for viscoelastic orthotropic materials
Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.
1988-01-01
Numerical solution methods for viscoelastic orthotropic materials, specifically fiber reinforced composite materials, are examined. The methods include classical lamination theory using time increments, direction solution of the Volterra Integral, Zienkiewicz's linear Prony series method, and a new method called Nonlinear Differential Equation Method (NDEM) which uses a nonlinear Prony series. The criteria used for comparison of the various methods include the stability of the solution technique, time step size stability, computer solution time length, and computer memory storage. The Volterra Integral allowed the implementation of higher order solution techniques but had difficulties solving singular and weakly singular compliance function. The Zienkiewicz solution technique, which requires the viscoelastic response to be modeled by a Prony series, works well for linear viscoelastic isotropic materials and small time steps. The new method, NDEM, uses a modified Prony series which allows nonlinear stress effects to be included and can be used with orthotropic nonlinear viscoelastic materials. The NDEM technique is shown to be accurate and stable for both linear and nonlinear conditions with minimal computer time.
Nonlinear vibration with control for flexible and adaptive structures
Wagg, David
2015-01-01
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 ...
Geometric and material nonlinear analysis of tensegrity structures
Institute of Scientific and Technical Information of China (English)
Hoang Chi Tran; Jaehong Lee
2011-01-01
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.
Observability and Information Structure of Nonlinear Systems,
1985-10-01
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
Nonlinear Quantum Optics in Artificially Structured Media
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
Fessel, Gion; Snedeker, Jess G
2009-10-01
The glycosaminoglycan (GAG) dermatan sulfate and chondroitin sulfate side-chains of small leucine-rich proteoglycans have been increasingly posited to act as molecular cross links between adjacent collagen fibrils and to directly contribute to tendon elasticity. GAGs have also been implicated in tendon viscoelasticity, supposedly affecting frictional loss during elongation or fluid flow through the extra cellular matrix. The current study sought to systematically test these theories of tendon structure-function by investigating the mechanical repercussions of enzymatic depletion of GAG complexes by chondroitinase ABC in a reproducible tendon structure-function model (rat tail tendon fascicles). The extent of GAG removal (at least 93%) was verified by relevant spectrophotometric assays and transmission electron microscopy. Dynamic viscoelastic tensile tests on GAG depleted rat tail tendon fascicle were not mechanically different from controls in storage modulus (elastic behavior) over a wide range of strain-rates (0.05, 0.5, and 5% change in length per second) in either the linear or nonlinear regions of the material curve. Loss modulus (viscoelastic behavior) was only affected in the nonlinear region at the highest strain-rate, and even this effect was marginal (19% increased loss modulus, p=0.035). Thus glycosaminoglycan chains of small leucine-rich proteoglycans do not appear to mediate dynamic elastic behavior nor do they appear to regulate the dynamic viscoelastic properties in rat tail tendon fascicles.
Nonlinear Structure Formation with the Environmentally Dependent Dilaton
Brax, Phil; Davis, Anne-C; Li, Baojiu; Shaw, Douglas J
2011-01-01
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.
Linear Viscoelasticity, Reptation, Chain Stretching and Constraint Release
DEFF Research Database (Denmark)
Neergaard, Jesper; Schieber, Jay D.; Venerus, David C.
2000-01-01
A recently proposed self-consistent reptation model - alreadysuccessful at describing highly nonlinear shearing flows of manytypes using no adjustable parameters - is used here to interpretthe linear viscoelasticity of the same entangled polystyrenesolution. Using standard techniques, a relaxatio...
Dissipative nonlinear structures in tokamak plasmas
Directory of Open Access Journals (Sweden)
K. A. Razumova
2001-01-01
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.
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.)
2004-01-01
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.
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...
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....
Variable structure control of nonlinear systems through simplified uncertain models
Sira-Ramirez, Hebertt
1986-01-01
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.
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)
2014-07-15
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.
Instability analysis of cosmic viscoelastic gyro-gravitating clouds in the presence of dark matter
Karmakar, Pralay Kumar; Das, Papari
2017-08-01
A classical formalism for the weakly nonlinear instability analysis of a gravitating rotating viscoelastic gaseous cloud in the presence of gyratory dark matter is presented on the cosmic Jeans flat scales of space and time. The constituent neutral gaseous fluid (NGF) and dark matter fluid (DMF) are inter-coupled frictionally via mutual gravity alone. Application of standard nonlinear perturbation techniques over the complex gyro-gravitating clouds results in a unique conjugated pair of viscoelastic forced Burgers (VFB) equations. The VFB pair is conjointly twinned by correlational viscoelastic effects. There is no regular damping term here, unlike, in the conventional Burgers equation for the luminous (bright) matter solely. Instead, an interesting linear self-consistent derivative force-term naturalistically appears. A numerical illustrative platform is provided to reveal the micro-physical insights behind the weakly non-linear natural diffusive eigen-modes. It is fantastically seen that the perturbed NGF evolves as extended compressive solitons and compressive shock-like structures. In contrast, the perturbed DMF grows as rarefactive extended solitons and hybrid shocks. The latter is micro-physically composed of rarefactive solitons and compressive shocks. The consistency and reliability of the results are validated in the panoptic light of the existing reports based on the preeminent nonlinear advection-diffusion-based Burgers fabric. At the last, we highlight the main implications and non-trivial futuristic applications of the explored findings.
Nonlinear analysis and dynamic structure in the energy market
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
Fractal structures in nonlinear plasma physics.
Viana, R L; da Silva, E C; Kroetz, T; Caldas, I L; Roberto, M; Sanjuán, M A F
2011-01-28
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.
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...
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
2005-01-01
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.
Stable Solution of Nonlinear Age-structuredForest Evolution System
Institute of Scientific and Technical Information of China (English)
WANGDing-jiang; ZHAOTing-fang
2004-01-01
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.
Maximum Likelihood Estimation of Nonlinear Structural Equation Models.
Lee, Sik-Yum; Zhu, Hong-Tu
2002-01-01
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)
Case-Deletion Diagnostics for Nonlinear Structural Equation Models
Lee, Sik-Yum; Lu, Bin
2003-01-01
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…
Local Influence Analysis of Nonlinear Structural Equation Models
Lee, Sik-Yum; Tang, Nian-Sheng
2004-01-01
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…
Structure of Dirac matrices and invariants for nonlinear Dirac equations
2004-01-01
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.
Directory of Open Access Journals (Sweden)
V. Ovsianko
2012-01-01
Full Text Available The paper reveals a brand-new direction in simulation of frame and continual structures while calculating static and dynamic loads and stability. An electronic model has been synthesized for an investigated object and then it has been analyzed not with the help of specialized analog computing techniques but by means of high-performance software package for electronic circuit calculation using a personal computer.The given paper contains exact algebraic equations corresponding to differential equations for lateral bending calculation of frame structures without and with due account of viscoelastic material properties in compliance with the Kelvin model.The exact algebraic equation for a beam on elastic supports (or elastic Winkler foundation has been derived for quartic differential equation.The paper presents a number of exact algebraic equations which are equivalent to differential equations for transverse-longitudinal bending calculation of frame structures without and with due account of viscoelastic material properties when lateral and longitudinal loads are applied in the form of impulses with any periods of their duration and any interchangeability.
The Effect of Nonlinearities on Flexible Structures.
1987-04-30
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
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.)
2004-01-01
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.
Practical Soil-Shallow Foundation Model for Nonlinear Structural Analysis
Directory of Open Access Journals (Sweden)
Moussa Leblouba
2016-01-01
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.
A Nonlinear Theory for Smart Composite Structures
Chattopadhyay, Aditi
2002-01-01
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.
Do horizontal propulsive forces influence the nonlinear structure of locomotion?
Directory of Open Access Journals (Sweden)
Stergiou Nicholas
2007-08-01
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.
Lebon, Luc; Limat, Laurent; Gaillard, Antoine; Beaumont, Julien; Lhuissier, Henri; Laboratoire MSC Team
2015-11-01
We have investigated experimentally the properties and stability of viscoelastic curtains, falling from a long thin slot and maintained laterally by two highly wetting wires. We have observed several original facts, compared to the seminal work of Brown and Taylor on Newtonian curtains: (1) The stability with respect to breaking is considerably enhanced by the use of appropriate polymers. Even strange tree-like falling filament structures can be also stabilised, though less interesting for applications. (2) Specific instabilities can be observed, when the amount of polymers is excessive, with spatial and temporal modulations of the coating thickness. (3) Even the base state is modified, and does NOT reduce at large scale to a free fall, even slightly displaced vertically from the expected profile. We present this experimental exploration and also some attempts of analytical modeling based on Rheological theories of complex fluids.
Mathematical models for suspension bridges nonlinear structural instability
Gazzola, Filippo
2015-01-01
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.
Deformation and relaxation of an incompressible viscoelastic body with surface viscoelasticity
Liu, Liping; Yu, Miao; Lin, Hao; Foty, Ramsey
2017-01-01
Measuring mechanical properties of cells or cell aggregates has proven to be an involved process due to their geometrical and structural complexity. Past measurements are based on material models that completely neglect the elasticity of either the surface membrane or the interior bulk. In this work, we consider general material models to account for both surface and bulk viscoelasticity. The boundary value problems are formulated for deformations and relaxations of a closed viscoelastic surface coupled with viscoelastic media inside and outside of the surface. The linearized surface elasticity models are derived for the constant surface tension model and the Helfrich-Canham bending model for coupling with the bulk viscoelasticity. For quasi-spherical surfaces, explicit solutions are obtained for the deformation, stress-strain and relaxation behaviors under a variety of loading conditions. These solutions can be applied to extract the intrinsic surface and bulk viscoelastic properties of biological cells or cell aggregates in the indentation, electro-deformation and relaxation experiments.
Dynamic structural correlation via nonlinear programming techniques
Ting, T.; Ojalvo, I. U.
1988-01-01
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.
Dynamic response of a viscoelastic Timoshenko beam
Kalyanasundaram, S.; Allen, D. H.; Schapery, R. A.
1987-01-01
The analysis presented in this study deals with the vibratory response of viscoelastic Timoshenko (1955) beams under the assumption of small material loss tangents. The appropriate method of analysis employed here may be applied to more complex structures. This study compares the damping ratios obtained from the Timoshenko and Euler-Bernoulli theories for a given viscoelastic material system. From this study the effect of shear deformation and rotary inertia on damping ratios can be identified.
Nonlinear dynamic analysis of quasi-symmetric anisotropic structures
Noor, Ahmed K.; Peters, Jeanne M.
1987-01-01
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.
A nonlinear cointegration approach with applications to structural health monitoring
Shi, H.; Worden, K.; Cross, E. J.
2016-09-01
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.
Vibration isolation by exploring bio-inspired structural nonlinearity.
Wu, Zhijing; Jing, Xingjian; Bian, Jing; Li, Fengming; Allen, Robert
2015-10-08
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.
Bayesian Methods for Nonlinear System Identification of Civil Structures
Directory of Open Access Journals (Sweden)
Conte Joel P.
2015-01-01
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.
Institute of Scientific and Technical Information of China (English)
吕海炜; 李映辉; 李中华; 李亮
2013-01-01
Based on the Kelvin-Voigt constitutive law, the governing equations for the flutter vibration of the viscoelastic sandwich panel are established with consideration of the von-Karmen thin plate large deflection and the nonlinear piston theory. By using the method of the Galerkin truncation, the nonlinear dynamical characteristics of the viscoelastic sandwich panel under the supersonic flow and with the simple supports on four sides are analyzed. For the equation of the first-order Galerkin truncation, the equilibrium of the system and its stability are studied, the critical flow of the static bifurcation is obtained; for the equation of the second-order Galerkin truncation, the critical flow of the Hopf bifurcation is obtained by applying the Hopf bifurcation criterion, the dynamical behavior with the varying flow conditions is observed by employing the diagram of the response and phase portrait.%基于Kelvin-Voigt黏弹性本构模型、von-Karmen薄板大变形理论和三阶气动力活塞理论建立了三维黏弹性夹层壁板的气动弹性颤振方程.使用Galerkin截断方法,对超声速气流下,四边简支黏弹性夹层壁板颤振的非线性特性进行了研究.对于非线性一阶截断方程,研究了它的平衡点及稳定性随来流速度的变化情况,得到了系统发生静态分叉时的临界速度；对于非线性二阶截断方程,使用数值仿真分析方法,得到了系统发生Hopf分叉时的临界速度,并利用响应、相图等手段研究得到黏弹性夹层板随来流速度变化的动力学特性.
Ma, J.; Narayanan, H.; Garikipati, K.; Grosh, K.; Arruda, E. M.
The important mechanisms by which soft collagenous tissues such as ligament and tendon respond to mechanical deformation include non-linear elasticity, viscoelasticity and poroelasticity. These contributions to the mechanical response are modulated by the content and morphology of structural proteins such as type I collagen and elastin, other molecules such as glycosaminoglycans, and fluid. Our ligament and tendon constructs, engineered from either primary cells or bone marrow stromal cells and their autogenous matricies, exhibit histological and mechanical characteristics of native tissues of different levels of maturity. In order to establish whether the constructs have optimal mechanical function for implantation and utility for regenerative medicine, constitutive relationships for the constructs and native tissues at different developmental levels must be established. A micromechanical model incorporating viscoelastic collagen and non-linear elastic elastin is used to describe the non-linear viscoelastic response of our homogeneous engineered constructs in vitro. This model is incorporated within a finite element framework to examine the heterogeneity of the mechanical responses of native ligament and tendon.
Chiral Huygens metasurfaces for nonlinear structuring of linearly polarized light
Lesina, A Calà; Ramunno, L
2016-01-01
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...
Viscoelastic properties of cellular polypropylene ferroelectrets
Gaal, Mate; Bovtun, Viktor; Stark, Wolfgang; Erhard, Anton; Yakymenko, Yuriy; Kreutzbruck, Marc
2016-03-01
Viscoelastic properties of cellular polypropylene ferroelectrets (PP FEs) were studied at low frequencies (0.3-33 Hz) by dynamic mechanical analysis and at high frequencies (250 kHz) by laser Doppler vibrometry. Relaxation behavior of the in-plane Young's modulus ( Y11 ' ˜ 1500 MPa at room temperature) was observed and attributed to the viscoelastic response of polypropylene matrix. The out-of-plane Young's modulus is very small ( Y33 ' ≈ 0.1 MPa) at low frequencies, frequency- and stress-dependent, evidencing nonlinear viscoelastic response of PP FEs. The high-frequency mechanical response of PP FEs is shown to be linear viscoelastic with Y33 ' ≈ 0.8 MPa. It is described by thickness vibration mode and modeled as a damped harmonic oscillator with one degree of freedom. Frequency dependence of Y33 * in the large dynamic strain regime is described by the broad Cole-Cole relaxation with a mean frequency in kHz range attributed to the dynamics of the air flow between partially closed air-filled voids in PP FEs. Switching-off the relaxation contribution causes dynamic crossover from the nonlinear viscoelastic regime at low frequencies to the linear viscoelastic regime at high frequencies. In the small strain regime, contribution of the air flow seems to be insignificant and the power-law response, attributed to the mechanics of polypropylene cell walls and closed air voids, dominates in a broad frequency range. Mechanical relaxation caused by the air flow mechanism takes place in the sound and ultrasound frequency range (10 Hz-1 MHz) and, therefore, should be taken into account in ultrasonic applications of the PP FEs deal with strong exciting or receiving signals.
Understanding Viscoelasticity An Introduction to Rheology
Phan-Thien, Nhan
2013-01-01
This book presents an introduction to viscoelasticity; in particular, to the theories of dilute polymer solutions and dilute suspensions of rigid particles in viscous and incompressible fluids. These theories are important, not just because they apply to practical problems of industrial interest, but because they form a solid theoretical base upon which mathematical techniques can be built, from which more complex theories can be constructed, to better mimic material behaviour. The emphasis is not on the voluminous current topical research, but on the necessary tools to understand viscoelasticity at a first year graduate level. The main aim is to provide a still compact book, sufficient at the level of first year graduate course for those who wish to understand viscoelasticity and to embark in modeling of viscoelastic multiphase fluids. To this end, a new chapter on Dissipative Particle Dynamics (DPD) was introduced which is relevant to model complex-structured fluids. All the basic ideas in DPD are reviewed,...
Understanding viscoelasticity an introduction to rheology
Phan-Thien, Nhan
2017-01-01
This book presents an introduction to viscoelasticity, in particular, to the theories of dilute polymer solutions and dilute suspensions of rigid particles in viscous and incompressible fluids. These theories are important, not just because they apply to practical problems of industrial interest, but because they form a solid theoretical base upon which mathematical techniques can be built, from which more complex theories can be constructed, to better mimic material behaviour. The emphasis of this book is not on the voluminous current topical research, but on the necessary tools to understand viscoelasticity. This is a compact book for a first year graduate course in viscoelasticity and modelling of viscoelastic multiphase fluids. The Dissipative Particle Dynamics (DPD) is introduced as a particle-based method, relevant in modelling of complex-structured fluids. All the basic ideas in DPD are reviewed. The third edition has been updated and expanded with new results in the meso-scale modelling, links between...
Enhanced active swimming in viscoelastic fluids
Riley, Emily E
2014-01-01
Swimming microorganisms often self propel in fluids with complex rheology. While past theoretical work indicates that fluid viscoelasticity should hinder their locomotion, recent experiments on waving swimmers suggest a possible non-Newtonian enhancement of locomotion. We suggest a physical mechanism, based on fluid-structure interaction, leading to swimming in a viscoelastic fluid at a higher speed than in a Newtonian one. Using Taylor's two-dimensional swimming sheet model, we solve for the shape of an active swimmer as a balance between the external fluid stresses, the internal driving moments, and the passive elastic resistance. We show that this dynamic balance leads to a generic transition from hindered rigid swimming to enhanced flexible locomotion. The results are physically interpreted as due to a viscoelastic suction increasing the swimming amplitude in a non-Newtonian fluid and overcoming viscoelastic damping.
On the dimension of complex responses in nonlinear structural vibrations
Wiebe, R.; Spottswood, S. M.
2016-07-01
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
Structure-based control of complex networks with nonlinear dynamics
Zañudo, Jorge G T; Albert, Réka
2016-01-01
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...
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....
Nonlinear analysis of the forced response of structural elements
Nayfeh, A. H.; Mook, D. T.; Sridhar, S.
1974-01-01
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.
Global stabilization of nonlinear systems with uncertain structure
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
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.
Nonlinear Propagation of Light in One Dimensional Periodic Structures
Goodman, Roy H.; Weinstein, Michael I.; Philip J Holmes
2000-01-01
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...
Weakly nonlinear analysis and localised structures in nonlinear cavities with metamaterials
Slimani, N.; Makhoute, A.; Tlidi, M.
2016-04-01
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.
Energy Technology Data Exchange (ETDEWEB)
Cochrane, Alexander P. [Aerospace Engineering Department, University of Glasgow, University Avenue, Glasgow, Lanarkshire (United Kingdom); Merrett, Craig G. [Mechanical and Aerospace Engineering Department, Carleton Univ., 1125 Col. By Dr., Ottawa, ON (Canada); Hilton, Harry H. [Aerospace Engineering Department in the College of Engineering and Private Sector Program Division at the National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign, 104 South Wright Street, Urbana, IL 61801 (United States)
2014-12-10
The advent of new structural concepts employing composites in primary load carrying aerospace structures in UAVs, MAVs, Boeing 787s, Airbus A380s, etc., necessitates the inclusion of flexibility as well as viscoelasticity in static structural and aero-viscoelastic analyses. Differences and similarities between aeroelasticity and aero-viscoelasticity have been investigated in [2]. An investigation is undertaken as to the dependence and sensitivity of aerodynamic and stability derivatives to elastic and viscoelastic structural flexibility and as to time dependent flight and maneuver velocities. Longitudinal, lateral and directional stabilities are investigated. It has been a well established fact that elastic lifting surfaces are subject to loss of control effectiveness and control reversal at certain flight speeds, which depend on aerodynamic, structural and material properties [5]. Such elastic analyses are extended to linear viscoelastic materials under quasi-static, dynamic, and sudden and gradual loading conditions. In elastic wings one of the critical static parameters is the velocity at which control reversal takes place (V{sub REV}{sup E}). Since elastic formulations constitute viscoelastic initial conditions, viscoelastic reversal may occur at speeds V{sub REV<}{sup ≧}V{sub REV}{sup E}, but furthermore does so in time at 0 < t{sub REV} ≤ ∞. The influence of the twin effects of viscoelastic and elastic materials and of variable flight velocities on longitudinal, lateral, directional and spin stabilities are also investigated. It has been a well established fact that elastic lifting surfaces are subject to loss of control effectiveness and control reversal at certain flight speeds, which depend on aerodynamic, structural and material properties [5]. Such elastic analyses are here extended to linear viscoelastic materials under quasi-static, dynamic, and sudden and gradual loading conditions. In elastic wings the critical parameter is the velocity at
Evaluation of model fit in nonlinear multilevel structural equation modeling
Directory of Open Access Journals (Sweden)
Karin eSchermelleh-Engel
2014-03-01
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.
Evaluation of model fit in nonlinear multilevel structural equation modeling.
Schermelleh-Engel, Karin; Kerwer, Martin; Klein, Andreas G
2014-01-01
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.
Rahman, T.
2009-01-01
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
Protsenko, Iu L; Kobelev, A V; Lukin, O N; Balakin, A A; Smoliuk, L T
2009-07-01
Peculiarities of viscoelastic behavior of rabbit papillary muscle in passive state are studied by transversal versus longitudinal deformation curves, stress-strain and hysteresis curves, and stress relaxation curves under ramp stretching. The papillary muscle was chosen because of mostly longitudinal orientation of fibers and its elongated shape, which both make it as an appropriate model for uniaxial tests. The problem of evaluation of connective tissue protein structures and intracellular matrix contribution into the properties under consideration is solved by using the maceration method to remove intracellular structures. The different contribution of intracellular and extracellular protein features into total properties of a papillary muscle leads to nonlinearity of myocardial viscoelastic properties, such as the increase of differential elastic module and relaxation time with deformation.
Folding, stowage, and deployment of viscoelastic tape springs
DEFF Research Database (Denmark)
Kwok, Kawai; Pellegrino, Sergio
2013-01-01
This paper presents an experimental and numerical study of the folding, stowage, and deployment behavior of viscoelastic tape springs. Experiments show that during folding the relationship between load and displacement is nonlinear and varies with rate and temperature. In particular, the limit...... deployment and ends with a slow creep recovery. Unlike elastic tape springs, localized folds in viscoelastic tape springs do not move during deployment. Finite-element simulations based on a linear viscoelastic constitutive model with an experimentally determined relaxation modulus are shown to accurately...
The Behavior of Indonesian Stock Market: Structural Breaks and Nonlinearity
Directory of Open Access Journals (Sweden)
Rahmat Heru Setianto
2011-09-01
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.
Calculation of viscoelastic properties of edible films: application of three models
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CHANDRA Prabir K.
2000-01-01
Full Text Available The viscoelastic properties of edible films can provide information at the structural level of the biopolymers used. The objective of this work was to test three simple models of linear viscoelastic theory (Maxwell, Generalized Maxwell with two units in parallel, and Burgers using the results of stress relaxation tests in edible films of myofibrillar proteins of Nile Tilapia. The films were elaborated according to a casting technique and pre-conditioned at 58% relative humidity and 22ºC for 4 days. The testing sample (15mm x 118mm was submitted to tests of stress relaxation in an equipment of physical measurements, TA.XT2i. The deformation, imposed to the sample, was 1%, guaranteeing the permanency in the domain of the linear viscoelasticity. The models were fitted to experimental data (stress x time by nonlinear regression. The Generalized Maxwell model with two units in parallel and the Burgers model represented the relaxation curves of stress satisfactorily. The viscoelastic properties varied in a way that they were less dependent on the thickness of the films.
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)
1997-04-01
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.
Nonlinear dynamic behaviors of a floating structure in focused waves
Cao, Fei-feng; Zhao, Xi-zeng
2015-12-01
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.
Structural Health Monitoring under Nonlinear Environmental or Operational Influences
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Jyrki Kullaa
2014-01-01
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.
Structure and asymptotic theory for nonlinear models with GARCH errors
Directory of Open Access Journals (Sweden)
Felix Chan
2015-01-01
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.
Nonlinear Helicons ---an analytical solution elucidating multi-scale structure
Abdelhamid, Hamdi M
2016-01-01
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.
Fluid transport due to nonlinear fluid-structure interaction
Energy Technology Data Exchange (ETDEWEB)
Soendergaard Jensen, J.
1996-08-01
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.
Fluid transport due to nonlinear fluid-structure interaction
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard
1997-01-01
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...
Geometrically nonlinear creeping mathematic models of shells with variable thickness
Directory of Open Access Journals (Sweden)
V.M. Zhgoutov
2012-08-01
Full Text Available Calculations of strength, stability and vibration of shell structures play an important role in the design of modern devices machines and structures. However, the behavior of thin-walled structures of variable thickness during which geometric nonlinearity, lateral shifts, viscoelasticity (creep of the material, the variability of the profile take place and thermal deformation starts up is not studied enough.In this paper the mathematical deformation models of variable thickness shells (smoothly variable and ribbed shells, experiencing either mechanical load or permanent temperature field and taking into account the geometrical nonlinearity, creeping and transverse shear, were developed. The refined geometrical proportions for geometrically nonlinear and steadiness problems are given.
Mäkelä, J T A; Korhonen, R K
2016-06-14
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.
NONLINEAR BUCKLING CHARACTERISTIC OF GRADED MULTIWEB STRUCTURE OF HETEROGENEOUS MATERIALS
Institute of Scientific and Technical Information of China (English)
LI Yong; ZHANG Zhi-min
2005-01-01
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.
Optimization of nonlinear structural resonance using the incremental harmonic balance method
DEFF Research Database (Denmark)
Dou, Suguang; Jensen, Jakob Søndergaard
2015-01-01
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...
The mildly nonlinear imprint of structure on the CMB
Gebbie, T
1999-01-01
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...
Analysis of Nonlinear Structural Dynamics and Resonance in Trees
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H. Doumiri Ganji
2012-01-01
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.
Smart viscoelastic and self-healing characteristics of graphene nano-gels
Dhar, Purbarun; Katiyar, Ajay; Maganti, Lakshmi Sirisha
2016-12-01
Readily synthesizable nano-graphene and poly ethylene glycol based stable gels have been synthesized employing an easy refluxing method, and exhaustive rheological and viscoelastic characterizations have been performed to understand the nature of such complex gel systems. The gels exhibit shear thinning response with pronounced yield stress values which is indicative of a microstructure, where the graphene nanoflakes intercalate (possible due to the refluxing) with the polymer chains and form a pseudo spring damper network. Experimentations on the thixotropic behavior of the gels indicate that the presence of the G nanoflakes leads to immensely augmented structural stability capable of withstanding severe impact shears. Further information about the localized interactions of the G nanoflakes with the polymer chains is revealed from the amplitude and frequency sweep analyses in both linear and non-linear viscoelastic regimes. Massively enhanced cross over amplitude values are recorded and several smart effects such as enhanced elastic behavior at increasing forcing frequencies are registered. Structural resonance induced disruption of the elastic behavior is observed for the gels for a given range of frequency and the proposition of resonance has been justified mathematically. It is observed that, post this resonance bandwidth, the gels are able to self-heal and regain their original elastic behavior back without any external intervention. More detailed information on the viscoelastic nature of the gels has been obtained from creep and recovery compliance tests and justifications for the spring damper microstructure has been obtained. Smart features such as enhanced stress relaxation behavior with increasing strain have been observed and the same explained, based on the proposed microstructure. The viscoelastic response of the gels has been mathematically modeled and it has been revealed that such complex gels can be accommodated as modified Burger's viscoelastic
Nonlinear Aerodynamics-Structure Time Simulation for HALE Aircraft Design/Analysis Project
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...
Directory of Open Access Journals (Sweden)
Andrew S. Blasetti
2012-06-01
Full Text Available A key element in the seismic load resisting system of a wood framed structure is the shear wall which is typically sheathed on one side with plywood or oriented strand board (OSB and gypsum on the other. The shear capacity of gypsum sheathed shear walls is typically neglected in high seismic areas due to the susceptibility of conventional drywall screw connections to damage caused by earthquakes. The earthquake resistance of an innovative viscoelastic (VE gypsum shearwall is evaluated and compared to conventional structural and non-structural walls. Ten 8 ft × 8 ft wood framed wall specimens of three configurations [nailed-OSB, screw-gypsum, and VE polymer-gypsum] were subjected to a cyclic test protocol. The energy dissipation, stiffness, and damage characteristics of all shearwalls are reported herein. Testing results indicate the VE-gypsum walls can dissipate more energy than the OSB structural panels and 500% more energy that the conventional gypsum sheathed walls and contains a constant source of energy dissipation not seen in the structural and non-structural walls. The wall stiffness of the OSB wall degrades at a far greater rate that the VE gypsum wall and at continued cycling degrades below the VE wall stiffness. Unlike both of the conventional wall types, the VE wall showed no visible or audible signs of damage when subjected to shear displacements up to 1.
Nonlinear phononics and structural control of strongly correlated materials
Energy Technology Data Exchange (ETDEWEB)
Mankowsky, Roman
2016-01-20
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
Power-transfer effects in monomode optical nonlinear waveguiding structures.
Jakubczyk, Z; Jerominek, H; Patela, S; Tremblay, R; Delisle, C
1987-09-01
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.
Smart viscoelastic and self-healing characteristics of graphene nano-gels
Dhar, Purbarun; Maganti, Lakshmi Sirisha
2016-01-01
Readily synthesizable nano-graphene and poly ethylene glycol based stable gels have been synthesized employing an easy refluxing method and exhaustive rheological and viscoelastic characterizations have been performed to understand the nature of such complex gel systems. The gels exhibit shear thinning response with pronounced yield stress values which is indicative of a microstructure where the graphene nanoflakes intercalate with the polymer chains and form a pseudo spring damper network. Experimentations on the thixotropic behavior of the gels indicate that the presence of the G nanoflakes leads to immensely augmented structural stability capable of withstanding severe impact shears. Further information about the localized interactions of the G nanoflakes with the polymer chains is revealed from the amplitude and frequency sweep analyses in both linear and nonlinear viscoelastic regimes. Massively enhanced cross over amplitude values are recorded and several smart effects such as enhanced elastic behavior ...
Structural Optimization for Reliability Using Nonlinear Goal Programming
El-Sayed, Mohamed E.
1999-01-01
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.
Viscoelastic properties of laryngeal posturing muscles
Alipour, Fariborz; Hunter, Eric; Titze, Ingo
2003-10-01
Viscoelastic properties of canine laryngeal muscles were measured in a series of in vitro experiments. Laryngeal posturing that controls vocal fold length and adduction/abduction is an essential component of the voice production. The dynamics of posturing depends on the viscoelastic and physiological properties of the laryngeal muscles. The time-dependent and nonlinear behaviors of these tissues are also crucial in the voice production and pitch control theories. The lack of information on some of these muscles such as posterior cricoarytenoid muscle (PCA), lateral cricoarytenoid muscle (LCA), and intraarytenoid muscle (IA) was the major incentive for this study. Samples of PCA and LCA muscles were made from canine larynges and mounted on a dual-servo system (Ergometer) as described in our previous works. Two sets of experiments were conducted on each muscle, a 1-Hz stretch and release experiment that provides stress-strain data and a stress relaxation test. Data from these muscles were fitted to viscoelastic models and Young's modulus and viscoelastic constants are obtained for each muscle. Preliminary data indicates that elastics properties of these muscles are similar to those of thyroarytenoid and cricothyroid muscles. The relaxation response of these muscles also shows some similarity to other laryngeal muscles in terms of time constants.
Viscoelastic properties of the false vocal fold
Chan, Roger W.
2004-05-01
The biomechanical properties of vocal fold tissues have been the focus of many previous studies, as vocal fold viscoelasticity critically dictates the acoustics and biomechanics of phonation. However, not much is known about the viscoelastic response of the ventricular fold or false vocal fold. It has been shown both clinically and in computer simulations that the false vocal fold may contribute significantly to the aerodynamics and sound generation processes of human voice production, with or without flow-induced oscillation of the false fold. To better understand the potential role of the false fold in phonation, this paper reports some preliminary measurements on the linear and nonlinear viscoelastic behavior of false vocal fold tissues. Linear viscoelastic shear properties of human false fold tissue samples were measured by a high-frequency controlled-strain rheometer as a function of frequency, and passive uniaxial tensile stress-strain response of the tissue samples was measured by a muscle lever system as a function of strain and loading rate. Elastic moduli (Young's modulus and shear modulus) of the false fold tissues were calculated from the measured data. [Work supported by NIH.
Thioborates: potential nonlinear optical materials with rich structural chemistry.
Lian, Yu-Kun; Wu, Li-Ming; Chen, Ling
2017-03-27
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.
Current-mode analog nonlinear function synthesizer structures
Popa, Cosmin Radu
2013-01-01
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...
Role of nonlinear localized structures and turbulence in magnetized plasma
Pathak, Neha; Yadav, Nitin; Uma, R.; Sharma, R. P.
2016-09-01
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.
Nonlinear thermoelectric efficiency of superlattice-structured nanowires
Karbaschi, Hossein; Lovén, John; Courteaut, Klara; Wacker, Andreas; Leijnse, Martin
2016-09-01
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.
Structurally-Tailorable, Nonlinear, Snap-Through Spring
Starnes, James H., Jr.; Farley, Gary L.; Mantay, Wayne R.
1989-01-01
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
Topology optimization of viscoelastic rectifiers
DEFF Research Database (Denmark)
Jensen, Kristian Ejlebjærg; Szabo, Peter; Okkels, Fridolin
2012-01-01
An approach for the design of microfluidic viscoelastic rectifiers is presented based on a combination of a viscoelastic model and the method of topology optimization. This presumption free approach yields a material layout topologically different from experimentally realized rectifiers...
2009-10-14
explosion of cylindrical shells in order to arrive at the underpinnings of his model. He was guided by experimental results that indicated an...process of stretch-forming sheet metal. Int J Mech Sci 9:609-620. doi: 10.1016/0020-7403(67)90066-5 Mott NF (1947) Fragmentation of shell cases. Proc...surfaces of storage tanks, swimming pools, truck flat-beds, roofs , water and sewer pipes, bridges, boats and other marine struc- tures, and concrete
Stability of Couette flow past a viscoelastic solid
Hess, Andrew; Gao, Tong
2016-11-01
Soft materials such as polymer gels have been widely used in engineering applications such as microfluidics, micro-optics, and active surfaces. It is important to obtain fundamental understandings of the dynamics of various soft materials when interacting with fluid. Here we investigate the material behavior of a viscoelastic solid film immersed in a simple Newtonian Couette flow. An Eulerian formulation of the Zener model is used to model the solid phase with the surface tension effect. A linear stability analysis is first performed to predict the material instabilities induced by the shear flow field, and provide an analytical basis to the numerical results. The nonlinear fluid/elastic structure interactions are further explored by using the direct numerical simulations. Phase tracking is accomplished through the use of a generalized Cahn-Hilliard model for the surface tension between the gel-like material and the ambient fluid. The coupled Cahn-Hilliard/Navier-Stokes/Zener equations are then solved on a staggered grid through a finite difference method. The results are compared with previous studies for both the hyperelastic and viscoelastic materials.
An Enhanced Asymptotic Expansion for the Stability of Nonlinear Elastic Structures
DEFF Research Database (Denmark)
Christensen, Claus Dencker; Byskov, Esben
2010-01-01
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 ...
Energy Technology Data Exchange (ETDEWEB)
Nayfeh, A.H.; Burns, J.A.; Cliff, E.M.
1990-05-18
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.
3D Viscoelastic traction force microscopy.
Toyjanova, Jennet; Hannen, Erin; Bar-Kochba, Eyal; Darling, Eric M; Henann, David L; Franck, Christian
2014-10-28
Native cell-material interactions occur on materials differing in their structural composition, chemistry, and physical compliance. While the last two decades have shown the importance of traction forces during cell-material interactions, they have been almost exclusively presented on purely elastic in vitro materials. Yet, most bodily tissue materials exhibit some level of viscoelasticity, which could play an important role in how cells sense and transduce tractions. To expand the realm of cell traction measurements and to encompass all materials from elastic to viscoelastic, this paper presents a general, and comprehensive approach for quantifying 3D cell tractions in viscoelastic materials. This methodology includes the experimental characterization of the time-dependent material properties for any viscoelastic material with the subsequent mathematical implementation of the determined material model into a 3D traction force microscopy (3D TFM) framework. Utilizing this new 3D viscoelastic TFM (3D VTFM) approach, we quantify the influence of viscosity on the overall material traction calculations and quantify the error associated with omitting time-dependent material effects, as is the case for all other TFM formulations. We anticipate that the 3D VTFM technique will open up new avenues of cell-material investigations on even more physiologically relevant time-dependent materials including collagen and fibrin gels.
Institute of Scientific and Technical Information of China (English)
龚顺明; 周颖; 吕西林
2015-01-01
The numerical simulation of the shaking table test on a 3-story steel frame structure added with viscoelastic (VE) dampers using OpenSees is conducted in order to verify the mechanical model and analytical method of VE dampers.Firstly,the shaking table test is described,and the dissipation characteristics and control effect of VE dampers are summarized.Then the mechanical property of a VE damper is simulated by Bouc-Wen model,and the shaking table test is simulated through the nonlinear dynamic time-history analysis using OpenSees.Finally,the dynamic properties and structural responses in the simulation and those in the test are compared.The comparative result indicates that they agree with each other well,which means the selection and identification of Bouc-Wen model and the nonlinear analysis method are reasonable.%该文利用OpenSees对一座三层带黏弹性阻尼器钢框架结构进行振动台试验的数值模拟,以此验证黏弹性阻尼器力学模型及分析方法的正确性.首先介绍了振动台试验,总结了黏弹性阻尼器耗能特征及减震效果;然后利用Bouc-Wen模型模拟黏弹性阻尼器的力学性能,在OpenSees中进行非线性动力时程分析模拟振动台试验;最后将数值模拟结果和试验结果进行对比分析.结果表明,模拟结果和试验结果在结构动力特征和结构响应上均吻合良好,因此验证了黏弹性阻尼器力学模型及分析方法的正确性.
Equilibrium circulation and stress distribution in viscoelastic creeping flow
Biello, Joseph A
2015-01-01
An analytic, asymptotic approximation of the nonlinear steady-state equations for viscoelastic creeping flow, modeled by the Oldroyd-B equations with polymer stress diffusion, is derived. Near the extensional stagnation point the flow stretches and aligns polymers along the outgoing streamlines of the stagnation point resulting in a stress-island, or birefringent strand. The polymer stress diffusion coefficient is used, both, as an asymptotic parameter and a regularization parameter. The structure of the singular part of polymer stress tensor is a Gaussian aligned with the incoming streamline of the stagnation point; a smoothed $\\delta$-distribution whose width is proportional to the square-root of the diffusion coefficient. The amplitude of the stress island scales with the Wiessenberg number and, although singular in the limit of vanishing diffusion, it is integrable in the cross stream direction due to its vanishing width; this yields a convergent secondary flow. The leading order velocity response to this...
Nonlinear structure formation in the Cubic Galileon gravity model
Barreira, Alexandre; Hellwing, Wojciech A; Baugh, Carlton M; Pascoli, Silvia
2013-01-01
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...
Finsler geometry of nonlinear elastic solids with internal structure
Clayton, J. D.
2017-02-01
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
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
2007-01-01
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.
Nonlinear Electrodynamics Analysis Of The Fine Structure Constant
Mbelek, Jean Paul
2010-10-01
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.
Dynamics of a reinforced viscoelastic plate
Directory of Open Access Journals (Sweden)
Igor V. Andrianov
2006-01-01
Full Text Available Oscillations and static bending deformation of a viscoelastic reinforced plate are considered. Analytical solutions are derived. An asymptotic technique, based on the homogenization method, is used for this purpose. In addition, a special perturbation approach is employed. An example is given for the purpose of illustration. The approximate analytical expressions are shown to adequately meet the requirements of optimal structural design.
Energy Technology Data Exchange (ETDEWEB)
Bhaumik, Lopamudra, E-mail: lbhaumi2@illinois.edu [University of Illinois at Urbana-Champaign (United States); Raychowdhury, Prishati, E-mail: prishati@iitk.ac.in [Indian Institute of Technology Kanpur (India)
2013-12-15
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.
PCI-SS: MISO dynamic nonlinear protein secondary structure prediction
Directory of Open Access Journals (Sweden)
Aboul-Magd Mohammed O
2009-07-01
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 http://bioinf.sce.carleton.ca/PCISS. 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
Bednarcyk, Brett A.; Arnold, Steven M.
2012-01-01
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.
Wang, Zuo-Cai; Xin, Yu; Ren, Wei-Xin
2016-08-01
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.
Viscoelastic properties of oat ß-glucan-rich aqueous dispersions
C-trim is a healthy food product containing the dietary of soluble fiber ß-glucan. The suspension of C-trim in water is a hydrocolloid biopolymer. The linear and non-linear rheological properties for suspensions of C-trim biopolymers were investigated. The linear viscoelastic behaviors for C-trim...
A COMPUTER PROGRAMME FOR THE NON-LINEAR ANALYSIS OF COMPLETE STRUCTURES
Directory of Open Access Journals (Sweden)
Turgay ÇOŞGUN
2003-02-01
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.
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
2005-01-01
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.
Predictive Dynamic Stimulation of Structures with Non-Smooth Nonlinearities
2005-06-30
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
Extreme value distribution and reliability of nonlinear stochastic structures
Institute of Scientific and Technical Information of China (English)
Chen Jianbing; Li Jie
2005-01-01
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.
Time-domain seismic reliability of nonlinear structures
Indian Academy of Sciences (India)
Achintya Haldar; Jungwon Huh; Ali Mehrabian
2006-08-01
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.
Composite structures for the enhancement of nonlinear optical materials.
Neeves, A E; Birnboim, M H
1988-12-01
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.
Astroza, Rodrigo; Ebrahimian, Hamed; Li, Yong; Conte, Joel P.
2017-09-01
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.
DEFF Research Database (Denmark)
Tuz, Vladimir R.; Novitsky, Denis V.; Prosvirnin, Sergey L.
2014-01-01
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...
DEFF Research Database (Denmark)
Lindgaard, Esben; Lund, Erik
2012-01-01
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...
Maximum Likelihood Analysis of Nonlinear Structural Equation Models with Dichotomous Variables
Song, Xin-Yuan; Lee, Sik-Yum
2005-01-01
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…
Estimating Nonlinear Structural Models: EMM and the Kenny-Judd Model
Lyhagen, Johan
2007-01-01
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…
Nonlinear Control Structure of Grid Connected Modular Multilevel Converters
DEFF Research Database (Denmark)
Hajizadeh, Amin; Norum, Lars; Ahadpour Shal, Alireza
2017-01-01
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...
Nonlinear Control Structure of Grid Connected Modular Multilevel Converters
DEFF Research Database (Denmark)
Hajizadeh, Amin; Norum, Lars; Ahadpour Shal, Alireza
2017-01-01
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...
Nonlinear evolution of large-scale structure in the universe
Energy Technology Data Exchange (ETDEWEB)
Frenk, C.S.; White, S.D.M.; Davis, M.
1983-08-15
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.
Nonlinear density fluctuation field theory for large scale structure
Institute of Scientific and Technical Information of China (English)
Yang Zhang; Hai-Xing Miao
2009-01-01
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.
Structure-preserving integrators in nonlinear structural dynamics and flexible multibody dynamics
2016-01-01
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...
[Viscoelastic properties of relaxed papillary muscle at physiological hypertrophy].
Smoliuk, L T; Lisin, R V; Kuznetsov, D A; Protsenko, Iu L
2012-01-01
Viscoelastic properties of relaxed rat papillary muscles at physiological hypertrophy (intensive swimming for 5 weeks) have been obtained. It has been ascertained that viscoelastic properties of hypertrophied muscles are not significantly distinguished from those of control papillary muscles. A three-dimensional model of myocardial fascicle has been verified in compliance with experimental data of biomechanical tests of hypertrophied muscles. Elastic and viscous parameters of structural elements of the model negligibly differ from the parameters of the model of a control muscle. It is shown that physiological hypertrophy has a slight influence on viscoelastic properties of papillary muscles.
A Modal Model to Simulate Typical Structural Dynamic Nonlinearity [PowerPoint
Energy Technology Data Exchange (ETDEWEB)
Mayes, Randall L.; Pacini, Benjamin Robert; Roettgen, Dan
2016-01-01
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.
The emergence of a coherent structure for coherent structures: localized states in nonlinear systems
Dawes, Jonathan
2010-01-01
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. ...
Nonlinear Kalman Filtering in Affine Term Structure Models
DEFF Research Database (Denmark)
Christoffersen, Peter; Dorion, Christian; Jacobs, Kris;
2014-01-01
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...
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)
2015-09-01
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.
Structural Identification of Nonlinear Static System on Basis of Analysis Sector Sets
Directory of Open Access Journals (Sweden)
Nikolay Karabutov
2013-12-01
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.
Optimization Formulations for the Maximum Nonlinear Buckling Load of Composite Structures
DEFF Research Database (Denmark)
Lindgaard, Esben; Lund, Erik
2011-01-01
, 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....
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)
2010-03-01
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.
Analysis of Dynamic Model of a Structure with Nonlinear Damped Behavior
Directory of Open Access Journals (Sweden)
G. Domairry
2010-04-01
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.
Damage detection in structures through nonlinear excitation and system identification
Hajj, Muhammad R.; Bordonaro, Giancarlo G.; Nayfeh, Ali H.; Duke, John C., Jr.
2008-03-01
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.
Indications of nonlinear structures in brain electrical activity
Gautama, Temujin; Mandic, Danilo P.; van Hulle, Marc M.
2003-04-01
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.
Nonlinear characterization of a bolted, industrial structure using a modal framework
Roettgen, Daniel R.; Allen, Matthew S.
2017-02-01
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.
Chortis, Dimitris I
2013-01-01
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...
Viscoelastic behavior of stock indices
Gündüz, Güngör; Gündüz, Yalin
2010-12-01
The scattering diagram of a stock index results in a complex network structure, which can be used to analyze the viscoelastic properties of the index. The change along x- or y-direction of the diagram corresponds to purely elastic (or spring like) movement whereas the diagonal change at an angle of 45° corresponds to purely viscous (or dashpot like) movement. The viscous component pushes the price from its current value to any other value, while the elastic component acts like a restoring force. Four indices, namely, DJI, S&P-500, NASDAQ-100, and NASDAQ-composite were studied for the period of 2001-2009. NASDAQ-composite displayed very high elasticity while NASDAQ-100 displayed the highest fluidity in the time period considered. The fluidity of DJI and S&P-500 came out to be close to each other, and they are almost the same in the second half of the period.
DEFF Research Database (Denmark)
Kragh, Knud Abildgaard; Thomsen, Jon Juel; Tcherniak, Dmitri
2010-01-01
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...
Nonlinear Super Integrable Couplings of Super Dirac Hierarchy and Its Super Hamiltonian Structures
Institute of Scientific and Technical Information of China (English)
尤福财
2012-01-01
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.
The influence of and the identification of nonlinearity in flexible structures
Zavodney, Lawrence D.
1988-01-01
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.
Optimization of hardening/softening behavior of plane frame structures using nonlinear normal modes
DEFF Research Database (Denmark)
Dou, Suguang; Jensen, Jakob Søndergaard
2016-01-01
/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...
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...
Nonlinear system identification in structural dynamics: 10 more years of progress
Noël, J. P.; Kerschen, G.
2017-01-01
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.
Structure property relationships for the nonlinear optical response of fullerenes
Rustagi, Kailash C.; Ramaniah, Lavanya M.; Nair, Selvakumar V.
1994-11-01
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.
A NUMERICAL METHOD FOR SIMULATING NONLINEAR FLUID-RIGID STRUCTURE INTERACTION PROBLEMS
Institute of Scientific and Technical Information of China (English)
XingJ.T; PriceW.G; ChenY.G
2005-01-01
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.
Generalized Dromion Structures of New (2 + 1)-Dimensional Nonlinear EvolutionEquation
Institute of Scientific and Technical Information of China (English)
ZHANG Jie-Fang
2001-01-01
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.
PATH INTEGRAL SOLUTION OF NONLINEAR DYNAMIC BEHAVIOR OF STRUCTURE UNDER WIND EXCITATION
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
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.
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
2009-01-01
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.
Yang, Zhijian; Liu, Zhiming
2017-03-01
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}-\
Walker, Christoph
2010-01-01
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.
Long term structural dynamics of mechanical systems with local nonlinearities
Fey, R.H.B.; Campen, D.H. van; Kraker, A. de
1996-01-01
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
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)
2006-10-15
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.
Note About Hamiltonian Structure of Non-Linear Massive Gravity
Kluson, J
2011-01-01
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.
Structure and Asymptotic theory for Nonlinear Models with GARCH Errors
F. Chan (Felix); M.J. McAleer (Michael); M.C. Medeiros (Marcelo)
2011-01-01
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
Nonlinear analysis of a structure loaded by a stochastic excitation
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
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.
Koyuncu, A.; Cigeroglu, E.; Özgüven, H. N.
2017-10-01
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.
High-order finite difference solution for 3D nonlinear wave-structure interaction
DEFF Research Database (Denmark)
Ducrozet, Guillaume; Bingham, Harry B.; Engsig-Karup, Allan Peter;
2010-01-01
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...
Investigation of planar barrier discharges for coherent nonlinear structures
Uzun-Kaymak, I. U.
2017-02-01
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.
Numerical Analysis of the Dynamics of Nonlinear Solids and Structures
2008-08-01
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
Travelling and standing envelope solitons in discrete non-linear cyclic structures
Grolet, Aurelien; Hoffmann, Norbert; Thouverez, Fabrice; Schwingshackl, Christoph
2016-12-01
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.
A Taylor-Galerkin finite element algorithm for transient nonlinear thermal-structural analysis
Thornton, E. A.; Dechaumphai, P.
1986-01-01
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.
Unsteady Boundary-Layer Flow over Jerked Plate Moving in a Free Stream of Viscoelastic Fluid
Directory of Open Access Journals (Sweden)
Sufian Munawar
2014-01-01
Full Text Available This study aims to investigate the unsteady boundary-layer flow of a viscoelastic non-Newtonian fluid over a flat surface. The plate is suddenly jerked to move with uniform velocity in a uniform stream of non-Newtonian fluid. Purely analytic solution to governing nonlinear equation is obtained. The solution is highly accurate and valid for all values of the dimensionless time 0≤τ<∞. Flow properties of the viscoelastic fluid are discussed through graphs.
Micro-mechanisms of residual oil mobilization by viscoelastic fluids
Institute of Scientific and Technical Information of China (English)
Zhang Lijuan; Yue Xiang'an; Guo Fenqiao
2008-01-01
Four typical types of residual oil, residual oil trapped in dead ends, oil ganglia in pore throats,oil at pore comers and oil film adhered to pore walls, were studied. According to main pore structure characteristics and the fundamental morphological features of residual oil, four displacement models for residual oil were proposed, in which pore-scale flow behavior of viscoelastic fluid was analyzed by a numerical method and micro-mechanisms for mobilization of residual oil were discussed. Calculated results indicate that the viscoelastic effect enhances micro displacement efficiency and increases swept volume. For residual oil trapped in dead ends, the flow field of viscoelastic fluid is developed in dead ends more deeply, resulting in more contact with oil by the displacing fluid, and consequently increasing swept volume. In addition, intense viscoelastic vortex has great stress, under which residual oil becomes small oil ganglia, and finally be carried into main channels. For residual oil at pore throats, its displacement mechanisms are similar to the oil trapped in dead ends. Vortices are developed in the depths of the throats and oil ganglia become smaller. Besides, viscoelastic fluid causes higher pressure drop on oil ganglia, as a driving force, which can overcome capillary force, consequently, flow direction can be changed and the displacing fluid enter smaller throats. For oil at pore comers, viscoelastic fluid can enhance displacement efficiency as a result of greater velocity and stress near the comers. For residual oil adhered to pore wall,viscoelastic fluid can provide a greater displacing force on the interface between viscoelastic fluid and oil,thus, making it easier to exceed the minimum interfacial tension for mobilizing the oil film.
Dynamic Behaviors of Axially Moving Viscoelastic Plate with Varying Thicknessn
Institute of Scientific and Technical Information of China (English)
ZHOU Yinfeng; WANG Zhongmin
2009-01-01
Structural components of varying thickness draw increasing attention these days due to economy and light-weight considerations. In view of the absence of research in vibration analysis of viscoelastic plate with varying thickness, this study devotes to investigate the dynamic behaviors of axially moving viscoelastic plate with varying thickness. Based on the thin plate theory and the two-dimensional viscoelastic differential constitutive relation, the differential equation of motion of the axially moving viscoelastic rectangular plate is derived, the plate constituted by Kelvin-Voigt model has linearly varying thickness in the y-direction. The dimensionless complex frequencies of axially moving viscoelastic plate with four edges simply supported are calculated by the differential quadrature method, curves of real parts and imaginary parts of the first three-order dimensionless complex frequencies versus dimensionless moving speed are obtained, the effects of the aspect ratio, thickness ratio, the dimensionless moving speed and delay time on the dynamic behaviors of the axially moving viscoelastic rectangular plate with varying thickness are analyzed. When other parameters keep constant, with the decrease of thickness ratio, the real parts of the first three-order natural frequencies decrease, and the critical divergence speeds of various modes decrease too, moreover, whether the delay time is large or small, the frequencies are all complex numbers.
A numerical-perturbation method for the nonlinear analysis of structural vibrations
Nayfeh, A. H.; Mook, D. T.; Lobitz, D. W.
1974-01-01
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.
Guerin, Heather Lynch; Elliott, Dawn M
2007-04-01
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.
Wei, Jingsong; Wang, Rui; Yan, Hui; Fan, Yongtao
2014-04-07
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.
Tamma, Kumar K.; Railkar, Sudhir B.
1987-01-01
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.
DEFF Research Database (Denmark)
Thomsen, Jon Juel; Blekhman, Iliya I.
2007-01-01
, 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...
Nonlinear Structured Illumination Using a Fluorescent Protein Activating at the Readout Wavelength
Hou, Wenya; Kielhorn, Martin; Arai, Yoshiyuki; Nagai, Takeharu; Kessels, Michael M.; Qualmann, Britta; Heintzmann, Rainer
2016-01-01
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
Nonlinear dynamics of phase space zonal structures and energetic particle physics in fusion plasmas
Zonca, Fulvio; Briguglio, Sergio; Fogaccia, Giuliana; Vlad, Gregorio; Wang, Xin
2014-01-01
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.
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
1995-07-01
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.
Geometric Structure-Preserving Discretization Schemes for Nonlinear Elasticity
2015-08-13
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
Thermal rectification in non-linear structures with bulk losses
Schmidt, Martin; Kottos, Tsampikos
2013-03-01
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
Fluid transport due to nonlinear fluid-structure interaction
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard
1997-01-01
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...
Microscopic structures from reduction of continuum nonlinear problems
Lovison, Alberto
2011-01-01
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.
2010-03-31
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
Theory of viscoelasticity an introduction
Christensen, R
1982-01-01
Theory of Viscoelasticity: An Introduction, Second Edition discusses the integral form of stress strain constitutive relations. The book presents the formulation of the boundary value problem and demonstrates the separation of variables condition.The text describes the mathematical framework to predict material behavior. It discusses the problems to which integral transform methods do not apply. Another topic of interest is the thermoviscoelastic stress analysis. The section that follows describes the heat conduction, glass transition criterion, viscoelastic Rayleigh waves, optimal str
Viscoelastic behavior of concrete pile
Institute of Scientific and Technical Information of China (English)
丁科; 唐小弟
2008-01-01
Based on constitutive theory of viscoelasticity,the viscoelastic behaviour of concrete pile was investigated.The influence of viscosity coefficient on the stress,displacement and velocity response was discussed.With the increase of viscosity coefficient,the amplitude of stress wave decreases,and the maximum value of the stress wave shifts to deeper position of the pile.In other words,the viscosity coefficient behaves as lag effect to stress wave.
Adhesive nonlinearity in Lamb-wave-based structural health monitoring systems
Shan, Shengbo; Cheng, Li; Li, Peng
2017-02-01
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
Characterizing the structure of nonlinear systems using gradual wavelet reconstruction
Directory of Open Access Journals (Sweden)
C. J. Keylock
2010-11-01
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.
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)
1995-12-31
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.
Lee, Pilhwa; Wolgemuth, Charles W.
2016-01-01
The swimming of microorganisms typically involves the undulation or rotation of thin, filamentary objects in a fluid or other medium. Swimming in Newtonian fluids has been examined extensively, and only recently have investigations into microorganism swimming through non-Newtonian fluids and gels been explored. The equations that govern these more complex media are often nonlinear and require computational algorithms to study moderate to large amplitude motions of the swimmer. Here, we develop an immersed boundary method for handling fluid-structure interactions in a general two-phase medium, where one phase is a Newtonian fluid and the other phase is viscoelastic (e.g., a polymer melt or network). We use this algorithm to investigate the swimming of an undulating, filamentary swimmer in 2D (i.e., a sheet). A novel aspect of our method is that it allows one to specify how forces produced by the swimmer are distributed between the two phases of the fluid. The algorithm is validated by comparing theoretical predictions for small amplitude swimming in gels and viscoelastic fluids. We show how the swimming velocity depends on material parameters of the fluid and the interaction between the fluid and swimmer. In addition, we simulate the swimming of Caenorhabditis elegans in viscoelastic fluids and find good agreement between the swimming speeds and fluid flows in our simulations and previous experimental measurements. These results suggest that our methodology provides an accurate means for exploring the physics of swimming through non-Newtonian fluids and gels.
Lee, Pilhwa; Wolgemuth, Charles
2016-11-01
While swimming in Newtonian fluids has been examined extensively, only recently have investigations into microorganism swimming through non-Newtonian fluids and gels been explored. The equations that govern these more complex media are often nonlinear and require computational algorithms to study moderate to large amplitude motions of the swimmer. Here we develop an immersed boundary method for handling fluid-structure interactions in a general two-phase medium, where one phase is a Newtonian fluid and the other phase is viscoelastic. We use this algorithm to investigate the swimming of an undulating, filamentary swimmer in 2D. A novel aspect of our method is that it allows one to specify how forces produced by the swimmer are distributed between the two phases of the fluid. The algorithm is validated by comparison to theoretical predictions for small amplitude swimming in gels and viscoelastic fluids. We show how the swimming velocity depends on material parameters of the fluid and the interaction between the fluid and swimmer. In addition, we simulate the swimming of Caenorhabditis elegans in viscoelastic fluids and find good agreement between the swimming speeds and fluid flows in our simulations and previous experimental measurements. NIH R01 GM072004, NIH P50GM094503.
Nonlinear wave structures as exact solutions of Vlasov-Maxwell equations.
Dasgupta, B.; Tsurutani, B. T.; Janaki, M. S.; Sharma, A. S.
2001-12-01
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.
Ebrahimian, Hamed
2015-01-01
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 ...
GEOMETRICALLY NONLINEAR FE FORMULATIONS FOR THE MACRO-ELEMENT UNIPLET OF FOLDABLE STRUCTURES
Institute of Scientific and Technical Information of China (English)
陈务军; 付功义; 何艳丽; 董石麟
2002-01-01
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.
Lousse, V; Vigneron, J P
2001-02-01
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.
Tene, Yair; Tene, Noam; Tene, G.
1993-08-01
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.
Creep and recovery behavior analysis of space mesh structures
Tang, Yaqiong; Li, Tuanjie; Ma, Xiaofei
2016-11-01
The Schapery's nonlinear viscoelastic theory and nonlinear force-density method have been investigated to analyze the creep and recovery behaviors of space deployable mesh reflectors in this paper. Based on Schapery's nonlinear viscoelastic theory, we establish the creep and recovery constitutive model for cables whose pretensions were applied stepwise in time. This constitutive model has been further used for adjustment of cables' elongation rigidity. In addition, the time-dependent tangent stiffness matrix is calculated by the partial differentiation of the corresponding load vector with respect to the nodal coordinate vector obtained by the nonlinear force-density method. An incremental-iterative solution based on the Newton-Raphson method is adopted for solving the time-dependent nonlinear statics equations. Finally, a hoop truss reflector antenna is presented as a numerical example to illustrate the efficiency of the proposed method for the creep and recovery behavior analysis of space deployable mesh structures.
Energy Technology Data Exchange (ETDEWEB)
Liu, J.C. [College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058 (China); Zhang, Y.Q., E-mail: cyqzhang@zju.edu.cn [College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058 (China); State Key Laboratory of Mechanical Structural Strength and Vibration, Xi' an Jiaotong University, Xi' an 710049 (China); Fan, L.F. [College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100084 (China)
2017-04-11
The general equation for transverse vibration of double-viscoelastic-FGM-nanoplate system with viscoelastic Pasternak medium in between and each nanoplate subjected to in-plane edge loads is formulated on the basis of the Eringen's nonlocal elastic theory and the Kelvin model. The factors of the structural damping, medium damping, small size effect, loading ratio, and Winkler modulus and shear modulus of the medium are incorporated in the formulation. Based on the Navier's method, the analytical solutions for vibrational frequency and buckling load of the system with simply supported boundary conditions are obtained. The influences of these factors on vibrational frequency and buckling load of the system are discussed. It is demonstrated that the vibrational frequency of the system for the out-of-phase vibration is dependent upon the structural damping, small size effect and viscoelastic Pasternak medium, whereas the vibrational frequency for the in-phase vibration is independent of the viscoelastic Pasternak medium. While the buckling load of the system for the in-phase buckling case has nothing to do with the viscoelastic Pasternak medium, the buckling load for the out-of-phase case is related to the small size effect, loading ratio and Pasternak medium. - Highlights: • Vibration of double-viscoelastic-FGM-nanoplate system under in-plane edge loads is investigated. • Biaxial buckling of the system with simply supported boundary conditions is analyzed. • Explicit expression for the vibrational frequency and buckling load is obtained. • Impacts of viscoelastic Pasternak medium on vibrational frequency and buckling load are discussed. • Influences of structural damping, small size effect and loading ratio are also considered.
Przekop, Adam; Wu, Hsi-Yung T.; Shaw, Peter
2014-01-01
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
DEFF Research Database (Denmark)
Yu, Yi; Chen, Yaohui; Hu, Hao;
2015-01-01
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...
Indian Academy of Sciences (India)
Sabapathi Gokulnath; Tavarekere K Chandrashekar
2008-01-01
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.
Ultrasonic nonlinear guided wave inspection of microscopic damage in a composite structure
Zhang, Li; Borigo, Cody; Owens, Steven; Lissenden, Clifford; Rose, Joseph; Hakoda, Chris
2017-02-01
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.
Maximum Likelihood Analysis of a Two-Level Nonlinear Structural Equation Model with Fixed Covariates
Lee, Sik-Yum; Song, Xin-Yuan
2005-01-01
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…
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)
2012-06-15
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.
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))
1990-05-01
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.
Axisymmetric Nonlinear Waves And Structures in Hall Plasmas
Islam, Tanim
2011-01-01
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.
Nonlinear interface optical switch structure for dual mode switching revisited
Bussjager, Rebecca J.; Osman, Joseph M.; Chaiken, Joseph
1998-07-01
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.
Nonlinear dynamics of breathers in the spiral structures of magnets
Energy Technology Data Exchange (ETDEWEB)
Kiselev, V. V., E-mail: kiselev@imp.uran.ru; Raskovalov, A. A. [Russian Academy of Sciences, Mikheev Institute of Metal Physics, Ural Branch (Russian Federation)
2016-06-15
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.
Generalized Fractional Derivative Anisotropic Viscoelastic Characterization
Directory of Open Access Journals (Sweden)
Harry H. Hilton
2012-01-01
Full Text Available Isotropic linear and nonlinear fractional derivative constitutive relations are formulated and examined in terms of many parameter generalized Kelvin models and are analytically extended to cover general anisotropic homogeneous or non-homogeneous as well as functionally graded viscoelastic material behavior. Equivalent integral constitutive relations, which are computationally more powerful, are derived from fractional differential ones and the associated anisotropic temperature-moisture-degree-of-cure shift functions and reduced times are established. Approximate Fourier transform inversions for fractional derivative relations are formulated and their accuracy is evaluated. The efficacy of integer and fractional derivative constitutive relations is compared and the preferential use of either characterization in analyzing isotropic and anisotropic real materials must be examined on a case-by-case basis. Approximate protocols for curve fitting analytical fractional derivative results to experimental data are formulated and evaluated.
Shi, Zhong-Ke; Wu, Fang-Xiang
2013-06-01
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.
Ko, William L.; Fleischer, Van Tran; Lung, Shun-Fat
2017-01-01
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.
LINEAR AND NONLINEAR AERODYNAMIC THEORY OF INTERACTION BETWEEN FLEXIBLE LONG STRUCTURE AND WIND
Institute of Scientific and Technical Information of China (English)
徐旭; 曹志远
2001-01-01
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.
Estimations of non-linearities in structural vibrations of string musical instruments
Ege, Kerem; Boutillon, Xavier
2012-01-01
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.
Molecular structure-property correlations from optical nonlinearity and thermal-relaxation dynamics.
Bhattacharyya, Indrajit; Priyadarshi, Shekhar; Goswami, Debabrata
2009-02-01
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.
Kukreja, Sunil L.; Brenner, martin J.
2006-01-01
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
Cosmology emerging as the gauge structure of a nonlinear quantum system
Kam, Chon-Fai
2016-01-01
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...
Output-only identification of civil structures using nonlinear finite element model updating
Ebrahimian, Hamed; Astroza, Rodrigo; Conte, Joel P.
2015-03-01
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.
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
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.
Energy Technology Data Exchange (ETDEWEB)
Zawadzka, A., E-mail: azawa@fizyka.umk.pl [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)
2013-10-31
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.
Dynamic Stability of Viscoelastic Plates with Finite Deformation and Shear Effects
Institute of Scientific and Technical Information of China (English)
李晶晶; 程昌钧; 等
2002-01-01
Based on Reddy's theory of plates with higher-order shear deformations and the Boltzmann superposition principles,the governing equations were established for dynamic stability of viscoelastic plates with finite deformations taking account of shear effects,The Galerkin method was applied to simplify the set of equations.The numerical methods in nonlinear dynamics were used to solve the simplified system.It could e seen that there are plenty of dynamic properties for this kind of viscoelastic plates under transverse harmonic loads.The influences of the transverse shear deformations and material parameter on the dynamic behavior of nonlinear viscoelatic plates were investigated.
Liu, J. C.; Zhang, Y. Q.; Fan, L. F.
2017-04-01
The general equation for transverse vibration of double-viscoelastic-FGM-nanoplate system with viscoelastic Pasternak medium in between and each nanoplate subjected to in-plane edge loads is formulated on the basis of the Eringen's nonlocal elastic theory and the Kelvin model. The factors of the structural damping, medium damping, small size effect, loading ratio, and Winkler modulus and shear modulus of the medium are incorporated in the formulation. Based on the Navier's method, the analytical solutions for vibrational frequency and buckling load of the system with simply supported boundary conditions are obtained. The influences of these factors on vibrational frequency and buckling load of the system are discussed. It is demonstrated that the vibrational frequency of the system for the out-of-phase vibration is dependent upon the structural damping, small size effect and viscoelastic Pasternak medium, whereas the vibrational frequency for the in-phase vibration is independent of the viscoelastic Pasternak medium. While the buckling load of the system for the in-phase buckling case has nothing to do with the viscoelastic Pasternak medium, the buckling load for the out-of-phase case is related to the small size effect, loading ratio and Pasternak medium.
DEFF Research Database (Denmark)
Sedaghatizadeh, N.; Atefi, G.; Fardad, A. A.
2011-01-01
In this investigation, semiempirical and numerical studies of blood flow in a viscoelastic artery were performed using the Cosserat continuum model. The large-amplitude oscillatory shear deformation model was used to quantify the nonlinear viscoelastic response of blood flow. The finite differenc...
Electron vortex magnetic holes: a nonlinear coherent plasma structure
Haynes, Christopher T; Camporeale, Enrico; Sundberg, Torbjorn
2014-01-01
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 ...
Simulating Nonlinear Dynamics of Deployable Space Structures Project
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...
Institute of Scientific and Technical Information of China (English)
彭凡; 顾勇军; 马庆镇
2012-01-01
Based on classical correspondence principle, Mori-Tanaka and other micromechanical approaches are extended to treat the case of linear viscoelasticity in the constant thermal environment. The relaxation modulus and coefficient of thermal expansion of linearly viscoelastic FGMs are given directly in Laplace phase space, and multi-dimensional viscoelastic constitutive relation coupling thermal strain is constructed through considering the weak time-dependent feature of Poisson＇s ratio. Following the above work, the problem of axial symmetrical bending of viscoelastic functionally graded circular cylindrical thin shells is solved. The steady temperature field is determined taking into account of the temperature dependence of thermal and mechanical parameters. The analytic solution is derived in phase space and the creep deflection is obtained by means of Laplace numerical inversion. It is shown that the thermal effect is obvious at initial creep stage, but abates with the increase of time due to the relaxation of the thermal stresses, and the constraint effect for hinged ends is more prominent than that of clamped ends on the deflection near ends when circular cylindrical thin shell is subjected to axial compression. It is expected to give the general approach to analyze the creep deformation of viscoelastic functionally graded structures with arbitrary distribution of volume content under thermal and mechanical loading by solving above problem of axial symmetrical bending.%基于经典的对应原理，将Mori-Tanaka方法等细观力学结果推广于定常温度环境下的黏弹性情形．根据泊松比与时间呈弱相关的特点，给出Laplace象空间中功能梯度材料的松弛模最和热膨胀系数，并直接建立耦合热应变的多维黏弹性本构关系．在此基础上，求解黏弹性功能梯度网柱薄壳在热环境中的轴对称弯曲蠕变变形问题．考虑材料热物参数的温度相关性，首
Probabilistic Nonlinear Analysis of Reinforced Concrete Bubbler Tower Structure Failure
Directory of Open Access Journals (Sweden)
Králik Juraj
2014-06-01
Full Text Available This paper describes the reliability analysis of concrete bubbler tower structure of nuclear power plant with the reactor WWER 440 under high internal overpressure. There is showed summary of calculation models and calculation methods for the probability analysis of the structural integrity considering degradation effects and high internal overpressure. The uncertainties of the resistance and the calculation model were taking in the account in the RSM method.
Electron vortex magnetic holes: A nonlinear coherent plasma structure
Haynes, Christopher T.; Burgess, David; Camporeale, Enrico; Sundberg, Torbjorn
2015-01-01
We report the properties of a novel type of sub-proton scale magnetic hole found in two dimensional particle-in-cell 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 some initial perpendicular temperature anisotropy at the structure location. The properties of these structures (scale size, trapped population, etc.) are able to explain the observed properties of magnetic holes in the terrestrial plasma sheet. EVMHs may also contribute to turbulence properties, such as intermittency, at short scale lengths in other astrophysical plasmas.
Electron vortex magnetic holes: A nonlinear coherent plasma structure
Energy Technology Data Exchange (ETDEWEB)
Haynes, Christopher T., E-mail: c.t.haynes@qmul.ac.uk; Burgess, David; Sundberg, Torbjorn [School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS (United Kingdom); Camporeale, Enrico [Multiscale Dynamics, Centrum Wiskunde and Informatica (CWI), Amsterdam (Netherlands)
2015-01-15
We report the properties of a novel type of sub-proton scale magnetic hole found in two dimensional particle-in-cell 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 some initial perpendicular temperature anisotropy at the structure location. The properties of these structures (scale size, trapped population, etc.) are able to explain the observed properties of magnetic holes in the terrestrial plasma sheet. EVMHs may also contribute to turbulence properties, such as intermittency, at short scale lengths in other astrophysical plasmas.
A hybrid-stress solid-shell element for non-linear analysis of piezoelectric structures
Institute of Scientific and Technical Information of China (English)
SZE; K; Y
2009-01-01
This paper presents eight-node solid-shell elements for geometric non-linear analyze of piezoelectric structures. To subdue shear, trapezoidal and thickness locking, the assumed natural strain method and an ad hoc modified generalized laminate stiffness matrix are employed. With the generalized stresses arising from the modified generalized laminate stiffness matrix assumed to be independent from the ones obtained from the displacement, an extended Hellinger-Reissner functional can be derived. By choosing the assumed generalized stresses similar to the assumed stresses of a previous solid ele- ment, a hybrid-stress solid-shell element is formulated. The presented finite shell element is able to model arbitrary curved shell structures. Non-linear numerical examples demonstrate the ability of the proposed model to analyze nonlinear piezoelectric devices.
Min, Changjun; Wang, Pei; Chen, Chunchong; Deng, Yan; Lu, Yonghua; Ming, Hai; Ning, Tingyin; Zhou, Yueliang; Yang, Guozhen
2008-04-15
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.
Material and Geometric Nonlinear Analysis of Functionally Graded Plate-Shell Type Structures
Moita, J. S.; Araújo, A. L.; Mota Soares, C. M.; Mota Soares, C. A.; Herskovits, J.
2016-08-01
A nonlinear formulation for general Functionally Graded Material plate-shell type structures is presented. The formulation accounts for geometric and material nonlinear behaviour of these structures. Using the Newton-Raphson incremental-iterative method, the incremental equilibrium path is obtained, and in case of snap-through occurrence the automatic arc-length method is used. This simple and fast element model is a non-conforming triangular flat plate/shell element with 24 degrees of freedom for the generalized displacements. It is benchmarked in the solution of some illustrative plate- shell examples and the results are presented and discussed with numerical alternative models. Benchmark tests with material and geometrically nonlinear behaviour are also proposed.
NONLINEAR FLUID DAMPING IN STRUCTURE-WAKE OSCILLATORS IN MODELING VORTEX-INDUCED VIBRATIONS
Institute of Scientific and Technical Information of China (English)
LIN Li-ming; LING Guo-can; WU Ying-xiang; ZENG Xiao-hui
2009-01-01
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.
Seismic Behavior of Posttensioned Concrete Bridge Piers with External Viscoelastic Dampers
Directory of Open Access Journals (Sweden)
Anxin Guo
2016-01-01
Full Text Available This paper investigates the seismic performance of posttensioned concrete piers with external viscoelastic dampers to improve the energy dissipation capacity of this type of structure. An installation scheme for viscoelastic dampers on bridge piers is proposed, and the mechanical models of the damper are analyzed according to the installation scheme. By attaching the viscoelastic dampers to the posttensioned bridge piers, the analytical model of the hybrid system is established using the OpenSees finite element analysis package. Cyclic behavior and time history analyses are conducted on a posttensioned bridge with and without viscoelastic dampers using the established finite element model. The analysis results indicate that the viscoelastic dampers can effectively improve the seismic performance of the bridge structures with posttensioned piers.
Vibration Analysis of Cylindrical Sandwich Aluminum Shell with Viscoelastic Damping Treatment
Directory of Open Access Journals (Sweden)
Tai-Hong Cheng
2013-01-01
Full Text Available This paper has applied the constrained viscoelastic layer damping treatments to a cylindrical aluminum shell using layerwise displacement theory. The transverse shear, the normal strains, and the curved geometry are exactly taken into account in the present layerwise shell model, which can depict the zig-zag in-plane and out-of-plane displacements. The damped natural frequencies, modal loss factors, and frequency response functions of cylindrical viscoelastic aluminum shells are compared with those of the base thick aluminum panel without a viscoelastic layer. The thickness and damping ratio of the viscoelastic damping layer, the curvature of proposed cylindrical aluminum structure, and placement of damping layer of the aluminum panel were investigated using frequency response function. The presented results show that the sandwiched viscoelastic damping layer can effectively suppress vibration of cylindrical aluminum structure.
Directory of Open Access Journals (Sweden)
Xiongqi Peng
2012-01-01
Full Text Available This paper presents a phenomenological thermal-mechanical viscoelastic constitutive modeling for polypropylene wood composites. Polypropylene (PP wood composite specimens are compressed at strain rates from 10−4 to 10−2 s−1 and at temperature of , , and , respectively. The mechanical responses are shown to be sensitive both to strain rate and to temperature. Based on the Maxwell viscoelastic model, a nonlinear thermal-mechanical viscoelastic constitutive model is developed for the PP wood composite by decoupling the effect of temperature with that of the strain rate. Corresponding viscoelastic parameters are obtained through curve fitting with experimental data. Then the model is used to simulate thermal compression of the PP wood composite. The predicted theoretical results coincide quite well with experimental data. The proposed constitutive model is then applied to the thermoforming simulation of an automobile interior part with the PP wood composites.
Viscoelastic Phase Separation of Protein Solutions
Tanaka, Hajime; Nishikawa, Yuya
2005-08-01
In addition to the known behavior of normal phase separation and gelation, we report novel phase-separation behavior of protein solutions as their intermediate case. A network structure of the protein-rich phase may be formed even if it is the minority phase, contrary to the conventional wisdom. This behavior is characteristic of viscoelastic phase separation found in polymer solutions. This kinetic pathway may play crucial roles in the complex phase ordering of protein solutions, in particular, protein network formation in biological systems and foods.
Lubrication of soft viscoelastic solids
Pandey, Anupam; Venner, Kees; Snoeijer, Jacco
2015-01-01
Lubrication flows appear in many applications in engineering, biophysics, and in nature. Separation of surfaces and minimisation of friction and wear is achieved when the lubrication fluid builds up a lift force. In this paper we analyse soft lubricated contacts by treating the solid walls as viscoelastic: soft materials are typically not purely elastic, but dissipate energy under dynamical loading conditions. We present a method for viscoelastic lubrication and focus on three canonical examples, namely Kelvin-Voigt-, Standard Linear-, and Power Law-rheology. It is shown how the solid viscoelasticity affects the lubrication process when the timescale of loading becomes comparable to the rheological timescale. We derive asymptotic relations between lift force and sliding velocity, which give scaling laws that inherit a signature of the rheology. In all cases the lift is found to decrease with respect to purely elastic systems.
Two-phase viscoelastic jetting
Energy Technology Data Exchange (ETDEWEB)
Yu, J-D; Sakai, S.; Sethian, J.A.
2008-12-10
A coupled finite difference algorithm on rectangular grids is developed for viscoelastic ink ejection simulations. The ink is modeled by the Oldroyd-B viscoelastic fluid model. The coupled algorithm seamlessly incorporates several things: (1) a coupled level set-projection method for incompressible immiscible two-phase fluid flows; (2) a higher-order Godunov type algorithm for the convection terms in the momentum and level set equations; (3) a simple first-order upwind algorithm for the convection term in the viscoelastic stress equations; (4) central difference approximations for viscosity, surface tension, and upper-convected derivative terms; and (5) an equivalent circuit model to calculate the inflow pressure (or flow rate) from dynamic voltage.
Spatial properties of entangled photon pairs generated in nonlinear layered structures
Perina, Jan
2011-01-01
A spatial quantum model of spontaneous parametric down-conversion in nonlinear layered structures is developed expanding the interacting vectorial fields into monochromatic plane waves. A two-photon spectral amplitude depending on the signal- and idler-field frequencies and propagation directions is used to derive transverse profiles of the emitted fields as well as their spatial correlations. Intensity spatial profiles and their spatial correlations are mainly determined by the positions of transmission peaks formed in these structures with photonic bands. A method for geometry optimization of the structures with respect to efficiency of the nonlinear process is suggested. Several structures composed of GaN/AlN layers are analyzed as typical examples. They allow the generation of photon pairs correlated in several emission directions. Photon-pair generation rates increasing better than the second power of the number of layers can be reached. Also structures efficiently generated photon pairs showing anti-bun...
Miyata, Shogo; Tateishi, Tetsuya; Furukawa, Katsuko; Ushida, Takashi
Recently, many types of methodologies have been developed to regenerate articular cartilage. It is important to assess whether the reconstructed cartilaginous tissue has the appropriate mechanical functions to qualify as hyaline (articular) cartilage. In some cases, the reconstructed tissue may become fibrocartilage and not hyaline cartilage. In this study, we determined the dynamic viscoelastic properties of these two types of cartilage by using compression and shear tests, respectively. Hyaline cartilage specimens were harvested from the articular surface of bovine knee joints and fibrocartilage specimens were harvested from the meniscus tissue of the same. The results of this study revealed that the compressive energy dissipation of hyaline cartilage showed a strong dependence on testing frequency at low frequencies, while that of fibrocartilage did not. Therefore, the compressive energy dissipation that is indicated by the loss tangent could become the criterion for the in vitro assessment of the mechanical function of regenerated cartilage.
Directory of Open Access Journals (Sweden)
Hyung Jin Lim
2017-02-01
Full Text Available It has been shown that nonlinear ultrasonics can be more sensitive to local incipient defects, such as a fatigue crack, than conventional linear ultrasonics. Therefore, there is an increasing interest in utilizing nonlinear ultrasonics for structural health monitoring and nondestructive testing applications. While the conditions, which are the necessary conditions that should be satisfied for the generation of nonlinear harmonic components, are extensively studied for distributed material nonlinearity, little work has been done to understand the necessary conditions at the presence of a localized nonlinear source such as a fatigue crack. In this paper, the necessary conditions of nonlinear ultrasonic modulation generation in a plate-like structure are formulated specifically for a localized nonlinear source. Then, the correctness of the formulated necessary conditions is experimentally verified using ultrasounds obtained from aluminum plates.
空间桁架结构采用黏弹性阻尼的振动控制技术%Passive Vibration Control of Space Truss Structure with Viscoelastic Dampers
Institute of Scientific and Technical Information of China (English)
李东旭; 刘望; 蒋建平
2011-01-01
For the special physical environment of the space, the vibration control of space truss structure (STS) of spacecrafts is an important problem in aerospace technology. Passive damping control technology provides a good way for solving this vibration control problem. In this paper, a double layer cylindrical viscoelastic damper (VED) is designed on the base of theoretical analysis of the damping mechanism of viscoelastic material (VEM). Then the optimal placement of the viscoelastic damping rod is determined, and the dynamic equation of STS is derived. Furthermore, the dynamic quality of the truss structure is analyzed with the consideration of the damping characteristics of VEM. Taking a truss with a straight configuration as an example, the control effect of VED passive damping control is simulated. Numerical result shows that the amplitude of vibration in the resonance region is attenuated by 35 %, and this VED has a good control effect.%航天器空间桁架结构在太空特殊物理环境下的振动控制问题是航天技术中的一大难题,为探讨阻尼被动控制技术的有效程度.首先从理论上分析黏弹性材料(VEM)的阻尼作用机理,由此设计一种双夹层圆柱式黏弹性阻尼器(VED),研究VED阻尼杆在桁架中的最佳位置配置问题,并推导阻尼桁架结构的动力学方程,结合VEM的阻尼特性分析结构的动态品质.最后以一字型桁架为例,对VED阻尼被动控制效果进行仿真分析,结果显示在共振区内桁架的振幅衰减达35％,可取得良好的控制效果.
Coherent structures and the saturation of a nonlinear dynamo
Rempel, Erico L; Brandenburg, Axel; Muñoz, Pablo R
2012-01-01
Eulerian and Lagrangian tools are used to detect coherent structures in the velocity and magnetic fields of a mean--field dynamo, produced by direct numerical simulations of the three--dimensional compressible magnetohydrodynamic equations with an isotropic helical forcing and moderate Reynolds number. Two distinct stages of the dynamo are studied, the kinematic stage, where a seed magnetic field undergoes exponential growth, and the saturated regime. It is shown that the Lagrangian analysis detects structures with greater detail, besides providing information on the chaotic mixing properties of the flow and the magnetic fields. The traditional way of detecting Lagrangian coherent structures using finite--time Lyapunov exponents is compared with a recently developed method called function M. The latter is shown to produce clearer pictures which readily permit the identification of hyperbolic regions in the magnetic field, where chaotic transport/dispersion of magnetic field lines is highly enhanced.
Tailoring Hydrogel Viscoelasticity with Physical and Chemical Crosslinking
Directory of Open Access Journals (Sweden)
Michal Bartnikowski
2015-12-01
Full Text Available Biological tissues are viscoelastic, demonstrating a mixture of fluid and solid responses to mechanical strain. Whilst viscoelasticity is critical for native tissue function, it is rarely used as a design criterion in biomaterials science or tissue engineering. We propose that viscoelasticity may be tailored to specific levels through manipulation of the hydrogel type, or more specifically the proportion of physical and chemical crosslinks present in a construct. This theory was assessed by comparing the mechanical properties of various hydrogel blends, comprising elastic, equilibrium, storage and loss moduli, as well as the loss tangent. These properties were also assessed in human articular cartilage explants. It was found that whilst very low in elastic modulus, the physical crosslinks found in gellan gum-only provided the closest approximation of loss tangent levels found in cartilage. Blends of physical and chemical crosslinks (gelatin methacrylamide (GelMA combined with gellan gum gave highest values for elastic response. However, a greater proportion of gellan gum to GelMA than investigated may be required to achieve native cartilage viscoelasticity in this case. Human articular chondrocytes encapsulated in hydrogels remained viable over one week of culture. Overall, it was shown that viscoelasticity may be tailored similarly to other mechanical properties and may prove a new criterion to be included in the design of biomaterial structures for tissue engineering.
Viscoelastic Properties of Organic Hybrid of Chlorinated Polythylene and Small Molecule
Institute of Scientific and Technical Information of China (English)
Chifei Wu
2000-01-01
Viscoelastic properties of an organic hybrid of chlorinated polyethylene (CPE) and N,Ndicyclohexyl-benzthiazyl-2-sulfenaamid (DZ) are investigated. All CPE/DZ hybrids show a single loss tangent (Fan δ ) peak. Its position shift linearly to higher temperature and its maximum value increases nonlinearly with increasing DZ content. The energy absorptinity (EA, a ratio of loss modulus to complex modulus) is used to characterize these hybrids. The DZ content dependence of EA changes at a critical value. The existence of a bending point in the DZ content dependence of glass transition temperature and energy absorptinity is due to the microseparation and the crystallization of DZ molecules in CPE/DZ hybrids with high DZ content. The molecular structural model can successfully explain the influence of dispersion state of DZ molecules in the matrix polymer CPE on the maximum value and the position of Tan δ of CPE/DZ hybrids.
Institute of Scientific and Technical Information of China (English)
YANG Ning; WU Zhigang; YANG Chao
2011-01-01
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.
Sun, Limin; Chen, Lin
2017-10-01
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.
Institute of Scientific and Technical Information of China (English)
俞英娜
2011-01-01
以轻型门式钢架结构为研究对象，分析了黏弹性阻尼器的动力特性，建立了计算模型，采用目前通用的大型有限元分析软件ANSYS，建立了有吊车荷载作用的单层单跨门式钢架结构和消能减震结构两种不同的结构模型，并选取Elcentro地震波，在不同柱距下对两种结构模型进行了罕遇地震下的非线性时程分析，通过对计算结果的分析最终得出一些有益的结论。%Introduction of the mechanics performances and calculation model with viscoelastic dampers and energy dissipation braced Is put forward. Portal frame with crane、eccentrically and energy dissipation braced Portal frame with crane were analyzed by using the finite element analytical software ANSYS. At the effects of seismic waves Elcentro, the nonlinear time-history analysis at the scarce earthquake. The results are obtained after these analysis and comparison.
Monitoring Technical Conditions of Engineering Structures Using the Non-Linear Approach
Volkova, V. E.
2015-11-01
Conventional methods of monitoring technical condition are based on detection of damage in the structures of buildings or facilities during the entire period of their operation. In spite of considerable interest displayed to this issue and a significant number of publications, there is no unity of opinions. These methods differ from each other in the sets of values fixed for investigations, the techniques of their recording, transfer and further processing. Today's rules and regulations for structural designs expand the scope of application of the structures operating in the elastic-plastic stage. These damage-free structures originally display the nonlinear properties and can be adequately described only by the non-linear models. This paper presents a method for determining the type and level of non-linearity from the structural oscillations data for monitoring the change in the health of structures. It is shown that a plot of acceleration against the magnitude of the displacement represents the restoring force of a structure. If the structure is damaged during a new striking motion, the phase trajectories in plane “acceleration-displacement” will deviate from its healthy signature.
Advances in the analysis and prediction of turbulent viscoelastic flows
Gatski, T. B.; Thais, L.; Mompean, G.
2014-08-01
It has been well-known for over six decades that the addition of minute amounts of long polymer chains to organic solvents, or water, can lead to significant turbulent drag reduction. This discovery has had many practical applications such as in pipeline fluid transport, oil well operations, vehicle design and submersible vehicle projectiles, and more recently arteriosclerosis treatment. However, it has only been the last twenty-five years that the full utilization of direct numerical simulation of such turbulent viscoelastic flows has been achieved. The unique characteristics of viscoelastic fluid flow are dictated by the nonlinear differential relationship between the flow strain rate field and the extra-stress induced by the additive polymer. A primary motivation for the analysis of these turbulent fluid flows is the understanding of the effect on the dynamic transfer of energy in the turbulent flow due to the presence of the extra-stress field induced by the presence of the viscoelastic polymer chain. Such analyses now utilize direct numerical simulation data of fully developed channel flow for the FENE-P (Finite Extendable Nonlinear Elastic - Peterlin) fluid model. Such multi-scale dynamics suggests an analysis of the transfer of energy between the various component motions that include the turbulent kinetic energy, and the mean polymeric and elastic potential energies. It is shown that the primary effect of the interaction between the turbulent and polymeric fields is to transfer energy from the turbulence to the polymer.
Electron vortex magnetic holes: A nonlinear coherent plasma structure
Haynes, C.T.; Burgess, D.; Camporeale, E.; Sundberg, T.
2015-01-01
We report the properties of a novel type of sub-proton scale magnetic hole found in two dimensional particle-in-cell 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
The explicit structure of the nonlinear Schrödinger prolongation algebra
Eck, van H.N.; Gragert, P.K.H.; Martini, R.
1983-01-01
The structure of the nonlinear Schrödinger prolongation algebra, introduced by Estabrook and Wahlquist, is explicitly determined. It is proved that this Lie algebra is isomorphic with the direct product H× (A1 C[t]), where H is a three-dimensional commutative Lie algebra.
Nonlinear structure of the wakefield generated by relativistic intense ion bunch
Koshelev, A. A.; Andreev, N. E.
2016-11-01
The resonant excitation of the nonlinear wakefield by a single proton bunch is investigated with the parameters characteristic of the AWAKE experiment. It is shown that obtained structure of the wakefield at a distance more than twenty periods behind the driver proton bunch can be suitable for the side injection and further acceleration of the witness electron bunch in the wakefield.
Institute of Scientific and Technical Information of China (English)
LI Wei-hua; LUO En; HUANG Wei-jiang
2007-01-01
According to the basic idea of classical yin-yang complementarity and modem dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for geometrically nonlinear elastodynamics of orthogonal cable-net structures are established systematically, which can fully characterize the initial-boundary-value problem of this kind of dynamics. An important integral relation is made, which can be considered as the generalized principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures in mechanics. Based on such relationship, it is possible not only to obtain the principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures, but also to derive systematically the complementary functionals for five-field, four-field, three-field and two-field unconventional Hamilton-type variational principles, and the functional for the unconventional Hamilton-type variational principle in phase space and the potential energy functional for one-field unconventional Hamilton-type variational principle for geometrically nonlinear elastodynamics of orthogonal cable-net structures by the generalized Legendre transformation given in this paper. Furthermore, the intrinsic relationship among various principles can be explained clearly with this approach.
On global controllability of affine nonlinear systems with a triangular-like structure
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, we investigate a class of affine nonlinear systems with a triangular-like structure and present its necessary and sufficient condition for global controllability,by using the techniques developed by Sun Yimin and Guo Lei recently.Furthermore,we will give two examples to illustrate its application.
Dijkstra, T.K.; Henseler, J.
2011-01-01
The recent advent of nonlinear structural equation models with indices poses a new challenge to the measurement of scientific constructs. We discuss, exemplify and add to a family of statistical methods aimed at creating linear indices, and compare their suitability in a complex path model with line
Lee, Sik-Yum; Song, Xin-Yuan; Cai, Jing-Heng
2010-01-01
Analysis of ordered binary and unordered binary data has received considerable attention in social and psychological research. This article introduces a Bayesian approach, which has several nice features in practical applications, for analyzing nonlinear structural equation models with dichotomous data. We demonstrate how to use the software…
Manisera, M.; Kooij, A.J. van der; Dusseldorp, E.
2010-01-01
The component structure of 14 Likert-type items measuring different aspects of job satisfaction was investigated using nonlinear Principal Components Analysis (NLPCA). NLPCA allows for analyzing these items at an ordinal or interval level. The participants were 2066 workers from five types of social
Maximum Likelihood Estimation of Nonlinear Structural Equation Models with Ignorable Missing Data
Lee, Sik-Yum; Song, Xin-Yuan; Lee, John C. K.
2003-01-01
The existing maximum likelihood theory and its computer software in structural equation modeling are established on the basis of linear relationships among latent variables with fully observed data. However, in social and behavioral sciences, nonlinear relationships among the latent variables are important for establishing more meaningful models…
Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data
Lee, Sik-Yum
2006-01-01
A Bayesian approach is developed for analyzing nonlinear structural equation models with nonignorable missing data. The nonignorable missingness mechanism is specified by a logistic regression model. A hybrid algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm is used to produce the joint Bayesian estimates of…
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)
2015-09-01
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
Nonlinear ultrasonic stimulated thermography for damage assessment in isotropic fatigued structures
Fierro, Gian Piero Malfense; Calla', Danielle; Ginzburg, Dmitri; Ciampa, Francesco; Meo, Michele
2017-09-01
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.
Practical Soil-Shallow Foundation Model for Nonlinear Structural Analysis
Moussa Leblouba; Salah Al Toubat; Muhammad Ekhlasur Rahman; Omer Mugheida
2016-01-01
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...
NONLINEAR OPTICS: Coherent laser spectroscopy of matter utilizing waveguide structures
Chaus, A. I.; Yashkir, Yu N.
1990-07-01
Some features of CARS spectroscopy in waveguide structures are investigated theoretically taking into account stimulated Raman amplification of a weak pump wave in the field of a strong wave and allowing for the phase matching. A four-photon intermode coupling which occurs under amplification conditions results in energy diffusion between different modes. General expressions for the intensities of the pump waves undergoing stimulated amplification and for the anti-Stokes signal are derived and analyzed.
Micromechanics Models for Viscoelastic Plain-Weave Composite Tape Springs
DEFF Research Database (Denmark)
Kwok, Kawai; Pellegrino, Sergio
2017-01-01
The viscoelastic behavior of polymer composites decreases the deployment force and the postdeployment shape accuracy of composite deployable space structures. This paper presents a viscoelastic model for single-ply cylindrical shells (tape springs) that are deployed after being held folded...... for a given period of time. The model is derived from a representative unit cell of the composite material, based on the microstructure geometry. Key ingredients are the fiber volume density in the composite tows and the constitutive behavior of the fibers (assumed to be linear elastic and transversely...
Viscoelastic struts for vibration mitigation of FORTE
Maly, Joseph R.; Butler, Thomas A.
1996-05-01
FORTE is a small satellite being developed by Los Alamos National Laboratory (LANL) and Sandia National Laboratories Albuquerque (SNLA). It will be placed into orbit via a Pegasus launch in 1996. Testing a full-scale engineering model of the structure using the proto- qualification, system-level vibration spectrum indicated that acceleration levels caused by structural resonances exceed component levels to which certain sensitive components had previously been qualified. Viscoelastic struts were designed to reduce response levels associated with these resonances by increasing the level of damping in key structural modes of the spacecraft. Four identical shear-lap struts were fabricated and installed between the two primary equipment decks. The struts were designed using a system finite element model (FEM) of the spacecraft, a component FEM of the strut, and measured viscoelastic properties. Direct complex stiffness testing was performed to characterize the frequency-dependent behavior of the struts, and these measured properties (shear modulus and loss factor) were used to represent the struts in the spacecraft model. System-level tests were repeated with the struts installed and the response power spectral densities at critical component locations were reduced by as much as 10 dB in the frequency range of interest.
Zhu, Chengjie; Huang, Guoxiang
2011-11-07
We study linear and nonlinear propagations of probe and signal pulses in a multiple quantum-well structure with a four-level, double Λ-type configuration. We show that slow, mutually matched group velocities and giant Kerr nonlinearity of the probe and the signal pulses may be achieved with nearly vanishing optical absorption. Based on these properties we demonstrate that two-qubit quantum polarization phase gates can be constructed and highly entangled photon pairs may be produced. In addition, we show that coupled slow-light soliton pairs with very low generation power can be realized in the system.
Heteroclinic structure of parametric resonance in the nonlinear Schr\\"odinger equation
Conforti, M; Kudlinski, A; Rota-Nodari, S; Dujardin, G; De Bievre, S; Armaroli, A; Trillo, S
2016-01-01
We show that the nonlinear stage of modulational instability induced by parametric driving in the {\\em defocusing} nonlinear Schr\\"odinger equation can be accurately described by combining mode truncation and averaging methods, valid in the strong driving regime. The resulting integrable oscillator reveals a complex hidden heteroclinic structure of the instability. A remarkable consequence, validated by the numerical integration of the original model, is the existence of breather solutions separating different Fermi-Pasta-Ulam recurrent regimes. Our theory also shows that optimal parametric amplification unexpectedly occurs outside the bandwidth of the resonance (or Arnold tongues) arising from the linearised Floquet analysis.
Robust Passivity and Feedback Design for Nonlinear Stochastic Systems with Structural Uncertainty
Directory of Open Access Journals (Sweden)
Zhongwei Lin
2013-01-01
Full Text Available This paper discusses the robust passivity and global stabilization problems for a class of uncertain nonlinear stochastic systems with structural uncertainties. A robust version of stochastic Kalman-Yakubovitch-Popov (KYP lemma is established, which sustains the robust passivity of the system. Moreover, a robust strongly minimum phase system is defined, based on which the uncertain nonlinear stochastic system can be feedback equivalent to a robust passive system. Following with the robust passivity theory, a global stabilizing control is designed, which guarantees that the closed-loop system is globally asymptotically stable in probability (GASP. A numerical example is presented to illustrate the effectiveness of our results.
Energy Technology Data Exchange (ETDEWEB)
Gul-e-Ali,; Mirza, Arshad M. [Theoretical Plasma Physics Group, Physics Department, Quaid-i-Azam University, Islamabad 45320 (Pakistan); Masood, W. [COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad 44000 (Pakistan); National Centre for Physics, Shahdara Valley Road, Islamabad (Pakistan)
2016-02-15
Coupling of drift vortex and the ion acoustic modes in the linear and nonlinear regimes are investigated with sheared ion flow perpendicular to the ambient magnetic field in a plasma comprising of hot ions and nonthermal population of electrons. In this regard, generation of nonlinear vortex structures in the presence of kappa, Cairns, and q-nonextensive electron distributions are investigated in detail, and comparison with the Maxwellian distribution is also made. The appositeness of the present investigation in the matter of auroral F-region is also pointed out.
New variable structure control for MIMO nonlinear system based on I/O linearization
Institute of Scientific and Technical Information of China (English)
许春山; 孙兴进; 曹广益
2004-01-01
A novel variable structure control (VSC) with new rapid-smooth reaching law (RSRL) and new rapid-convergent sliding mode (FCSM) is proposed, which is based on analysis of normal VSC system. When it is used for an MIMO nonlinear system, we combine the method of Input/Output linearizing (I/O L) with VSC. After analyzing the robustness of the MIMO nonlinear system, we use this novel controller for Precision One Robot position control system. Simulation provides a quite satisfactory performance with uncertainties and external disturbances.
Padovan, J.; Lackney, J.
1986-01-01
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.
Institute of Scientific and Technical Information of China (English)
张天莉; 严继民
2001-01-01
Quantum-chemical AM1 calculations were performed to study the geometries,the electronic structures and the second nonlinear optical properties of phthalocyanine and some asymmetrically substituted phthalocyanines,which include tert-butyl,amino,dimethylamino,nitro,fluoro,chloro,bromo iodo and nitrile substituents. The relationships of the second nonlinear optical coefficients β with dipole moment μ, and β with the energy-gap differences of frontier orbitals ΔEDA were discussed. Two relationships are regular and all ΔEDA-μ show very good linear relationship.
Energy Technology Data Exchange (ETDEWEB)
Stalin, S. [Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620024, Tamil Nadu (India); Senthilvelan, M., E-mail: velan@cnld.bdu.ac.in [Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620024, Tamil Nadu (India)
2011-10-17
In this Letter, we formulate an exterior differential system for the newly discovered cubically nonlinear integrable Camassa-Holm type equation. From the exterior differential system we establish the integrability of this equation. We then study Cartan prolongation structure of this equation. We also discuss the method of identifying conservation laws and Baecklund transformation for this equation from the identified exterior differential system. -- Highlights: → An exterior differential system for a cubic nonlinear integrable equation is given. → The conservation laws from the exterior differential system is derived. → The Baecklund transformation from the Cartan-Ehresmann connection is obtained.
New nonlinear structures in a degenerate one-dimensional electron gas
Ghosh, S; Haas, F
2014-01-01
The collective dynamics of nonlinear electron waves in an one-dimensional degenerate electron gas is treated using the Lagrangian fluid approach. A new class of solutions with a nontrivial space and time dependence is derived. Both analytical and numerical results demonstrate the formation of stable, breather-like modes, provided certain conditions are meet. For large amplitude of the initial density perturbation, a catastrophic collapse of the plasma density is predicted, even in the presence of the quantum statistical pressure and quantum diffraction dispersive effects. The results are useful for the understanding of the properties of general nonlinear structures in dense plasmas.
Time-dependent viscoelastic behavior of an LDPE melt
Institute of Scientific and Technical Information of China (English)
Shuxin Huang; Chuanjing Lu; Yurun Fan
2006-01-01
Two differential constitutive equations,i.e.Giesekus model and Johnson-Segalman model were employed here to predict the time-dependent viscoelastic behavior of an LDPE melt in thixotropy-loop experiments and step shear rate experiment. Multiple relaxation modes were adopted, and the parameters used to describe the nonlinear viscoelasticity in the two models were obtained by fitting the shear-thinning viscosity. The predictions on those transient shear characteristics by the two models are found in qualitative agreement with our previous experiments. Johnson-Segalman model predicts oscillation behavior in the thixotropy-loop and step shear rate experiments, whereas Giesekus model does not. Both models predict higher shear stresses than the experimental data in the case of long time shearing, implying that both models are not able to completely characterize the time-dependent shear stress of the-melt at high shear rate.
Analytical and Experimental Random Vibration of Nonlinear Aeroelastic Structures.
1987-01-28
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
Identification and determination of solitary wave structures in nonlinear wave propagation
Energy Technology Data Exchange (ETDEWEB)
Newman, W.I.; Campbell, D.K.; Hyman, J.M.
1991-01-01
Nonlinear wave phenomena are characterized by the appearance of solitary wave coherent structures'' traveling at speeds determined by their amplitudes and morphologies. Assuming that these structures are briefly noninteracting, we propose a method for the identification of the number of independent features and their respective speeds. Using data generated from an exact two-soliton solution to the Korteweg-de-Vries equation, we test the method and discuss its strengths and limitations. 41 refs., 2 figs.
Analytical solitary wave solutions of the nonlinear Kronig-Penney model in photonic structures.
Kominis, Y
2006-06-01
A phase space method is employed for the construction of analytical solitary wave solutions of the nonlinear Kronig-Penney model in a photonic structure. This class of solutions is obtained under quite generic conditions, while the method is applicable to a large variety of systems. The location of the solutions on the spectral band gap structure as well as on the low dimensional space of system's conserved quantities is studied, and robust solitary wave propagation is shown.
Directory of Open Access Journals (Sweden)
Yonghwan Kim
2011-03-01
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.
Large amplitude nonlinear structures in the nighttime polar mesosphere
Maharaj, Shimul K.; Bharuthram, Ramashwar; Singh Lakhina, Gurbax; Muralikrishna, Polinaya; Singh, Satyavir
2016-07-01
The existence of large amplitude potential structures will be investigated for a plasma composed of negative ions, positive ions, electrons and an additional fourth component of charged (usually positive) nano-sized ions in an attempt to model the plasma composition in the nighttime polar mesosphere (˜80 - 90 km altitude) [1]. The fourth ionic component becomes positively charged if there is a high enough concentration of negative ions which are sufficiently heavy. The positive charge on the fourth component can be explained by the capture of currents, and is not a result of photo-emission and secondary electron emission processes. Consequently, if the negative ions are much lighter, then the fourth ion component will become negatively charged. The charged ion species will be treated as inertial species which are cold or adiabatic, whilst the electrons will be considered to be Boltzmann-distributed (isothermal). Taking into consideration not only the dynamics of the heaviest species (dust-acoustic) but also the lighter ions (ion-acoustic), the theoretical study will use the Sagdeev pseudo-potential formalism to explore the existence of arbitrary amplitude solitons and double layer potential structures. [1] Observations of positively charged nanoparticles in the nighttime polar mesosphere, M. Rapp, J. Hedin, I. Strelnikova, M. Friederich, J. Gumbel, and F.˜J. Lübken, Geophys. Res. Letters. 32, L23821, doi:10.1029/2005GL024676 (2005).
Probing the Structure of Quantum Mechanics : Nonlinearity, Nonlocality, Computation and Axiomatics
Durt, Thomas; Czachor, Marek
2002-01-01
During the last decade, scientists working in quantum theory have been engaging in promising new fields such as quantum computation and quantum information processing, and have also been reflecting on the possibilities of nonlinear behavior on the quantum level. These are challenging undertakings because (1) they will result in new solutions to important technical and practical problems that were unsolvable by the classical approaches (for example, quantum computers can calculate problems that are intractable if one uses classical computers); and (2) they open up new 'hard' problems of a fundamental nature that touch the foundation of quantum theory itself (for example, the contradiction between locality and nonlinearity and the interpretation of quantum computing as a universal process). In this book, one can distinguish two main streams of research to approach the just-mentioned problem field: (1) a theoretical structural part, which concentrates on the elaboration of a nonlinear quantum mechanics and the ...
Attractor of Beam Equation with Structural Damping under Nonlinear Boundary Conditions
Directory of Open Access Journals (Sweden)
Danxia Wang
2015-01-01
Full Text Available Simultaneously, considering the viscous effect of material, damping of medium, and rotational inertia, we study a kind of more general Kirchhoff-type extensible beam equation utt-uxxtt+uxxxx-σ(∫0l(ux2dxuxx-ϕ(∫0l(ux2dxuxxt=q(x, in [0,L]×R+ with the structural damping and the rotational inertia term. Little attention is paid to the longtime behavior of the beam equation under nonlinear boundary conditions. In this paper, under nonlinear boundary conditions, we prove not only the existence and uniqueness of global solutions by prior estimates combined with some inequality skills, but also the existence of a global attractor by the existence of an absorbing set and asymptotic compactness of corresponding solution semigroup. In addition, the same results also can be proved under the other nonlinear boundary conditions.
Identification of nonlinear vibrating structures by polynomial expansion in the z-domain
Fasana, Alessandro; Garibaldi, Luigi; Marchesiello, Stefano
2017-02-01
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.
Directory of Open Access Journals (Sweden)
Bonić Zoran
2010-01-01
Full Text Available The paper presents application of nonlinear material models in the software package Ansys. The development of the model theory is presented in the paper of the mathematical modeling of material nonlinear problems in structural analysis (part I - theoretical foundations, and here is described incremental-iterative procedure for solving problems of nonlinear material used by this package and an example of modeling of spread footing by using Bilinear-kinematics and Drucker-Prager mode was given. A comparative analysis of the results obtained by these modeling and experimental research of the author was made. Occurrence of the load level that corresponds to plastic deformation was noted, development of deformations with increasing load, as well as the distribution of dilatation in the footing was observed. Comparison of calculated and measured values of reinforcement dilatation shows their very good agreement.
S-polarized nonlinear surface and guided waves in an asymmetric layered structure
Energy Technology Data Exchange (ETDEWEB)
Mihalache, D.; Totia, H.
1983-08-01
An exact solution of Maxwell's equations is found, corresponding to s-polarized nonlinear surface and guided waves in an asymmetric layered structure. The system under consideration consists of a film with dielectric constant epsilon/sub 2/ bounded at the negative-z side by a linear medium with dielectric constant epsilon/sub 1/ and at the positive -z side by a nonlinear substrate characterized by the diagonal dielectric tensor epsilon/sub 11/ = epsilon/sub 22/ = epsilon/sub 33/ = epsilon/sub 0/ + ..cap alpha.. absolute value of E-vector/sup 2/, ..cap alpha.. > 0 (a selffocussing medium). We predict bistable states of s-polarized nonlinear surface and guided waves provided that the power flow in the wave is the control parameter.
Directory of Open Access Journals (Sweden)
Jurado-Piña, R.
2014-12-01
Full Text Available When designing a tension structure the shape is not known at the beginning of the process. Form-finding methods allow the designer to obtain an initial shape from given boundary conditions. Several form-finding methods for tension structures are already available in the technical literature; all of them posses certain limitations and drawbacks and no single method is optimal for all problems. The engineer may select the proper combination of methods best suited to the designer’s needs. In this paper it is proposed a combined method to achieve satisfactory equilibrium configurations for fabric tension structures. The force density method (FDM implemented with topological mapping (TM is used as a search engine for the preliminary design, and a procedure that employs nonlinear structural analysis is proposed for final refinement of the initial equilibrium configuration hence allowing the use of the same analysis tool for both refinement of the solution and analysis under loading.Al diseñar una estructura tensada la forma inicial es normalmente desconocida. Los métodos de búsqueda de forma permiten al ingeniero obtener una geometría inicial dadas unas condiciones de contorno. Existen diferentes métodos de búsqueda de formas de equilibrio, pero todos tienen limitaciones y no existe uno único óptimo para cualquier tipo de problema. El ingeniero debe elegir la combinación de métodos que mejor se adapte a sus necesidades. En este artículo se propone un método combinado para generar configuraciones de equilibrio satisfactorias en estructuras tensadas. Como motor de búsqueda para el diseño preliminar se emplea el método de las densidades de fuerza (FDM implementado con mallado en topología (TM, y se propone un procedimiento basado en análisis no lineal de estructuras para el refinamiento de la configuración inicial de equilibrio, permitiéndose así el empleo de las mismas herramientas tanto para el refinamiento de la solución inicial
Simulations of flow induced ordering in viscoelastic fluids
Santos de Oliveira, I.S.
2012-01-01
In this thesis we report on simulations of colloidal ordering phenomena in shearthinning viscoelastic fluids under shear flow. Depending on the characteristics of the fluid, the colloids are observed to align in the direction of the flow. These string-like structures remain stable as long as the she
Viscoelastic behavior of rubbery materials
Roland, C M
2011-01-01
The gigantic size of polymer molecules makes them viscoelastic - their behavior changes depending on how fast and for how long the material is used. This book looks at the latest discoveries in the field from a fundamental molecular perspective, in order to guide the development of better and new applications for soft materials.
Simulation of Transient Viscoelastic Flow
DEFF Research Database (Denmark)
Rasmussen, Henrik Koblitz; Hassager, Ole
1993-01-01
The Lagrangian kinematic description is used to develop a numerical method for simulation of time-dependent flow of viscoelastic fluids described by integral models. The method is shown to converge to first order in the time step and at least second order in the spatial discretization. The method...
Simulation of Transient Viscoelastic Flow
DEFF Research Database (Denmark)
Rasmussen, Henrik Koblitz; Hassager, Ole
1993-01-01
The Lagrangian kinematic description is used to develop a numerical method for simulation of time-dependent flow of viscoelastic fluids described by integral models. The method is shown to converge to first order in the time step and at least second order in the spatial discretization. The method...
A time stepping method in analysis of nonlinear structural dynamics
Directory of Open Access Journals (Sweden)
Gholampour A. A.
2011-12-01
Full Text Available In this paper a new method is proposed for the direct time integration method for structural dynamics problems. The proposed method assumes second order variations of the acceleration at each time step. Therefore more terms in the Taylor series expansion were used compared to other methods. Because of the increase in order of variations of acceleration, this method has higher accuracy than classical methods. The displacement function is a polynomial with five constants and they are calculated using: two equations for initial conditions (from the end of previous time step, two equations for satisfying the equilibrium at both ends of the time step, and one equation for the weighted residual integration. Proposed method has higher stability and order of accuracy than the other methods.
Directory of Open Access Journals (Sweden)
M.R. Mofakhami
2008-01-01
Full Text Available In this paper sound transmission through the multilayered viscoelastic air filled cylinders subjected to the incident acoustic wave is studied using the technique of separation of variables on the basis of linear three dimensional theory of elasticity. The effect of interior acoustic medium on the mode maps (frequency vs geometry and noise reduction is investigated. The effects of internal absorption and external moving medium on noise reduction are also evaluated. The dynamic viscoelastic properties of the structure are rigorously taken into account with a power law technique that models the viscoelastic damping of the cylinder. A parametric study is also performed for the two layered infinite cylinders to obtain the effect of viscoelastic layer characteristics such as thickness, material type and frequency dependency of viscoelastic properties on the noise reduction. It is shown that using constant and frequency dependent viscoelastic material with high loss factor leads to the uniform noise reduction in the frequency domain. It is also shown that the noise reduction obtained for constant viscoelastic material property is subjected to some errors in the low frequency range with respect to those obtained for the frequency dependent viscoelastic material.
Energy Technology Data Exchange (ETDEWEB)
Driessen, W. [Technischer Ueberwachungs-Verein Nord e.V., Hamburg (Germany)
2000-07-01
Because of modifications to a feed-water line of a power plant structural calculations of the pipework were performed. As a result of a linear (modal) analysis very high restraint forces on the supports were calculated. In order to reduce conservatisms in the calculation the model was optimized with regard to the support stiffnesses and nonlinear behavior of slide bearings, guides and shock absorbers were taken into account. The main result of the non-linear analysis, which was performed by methods of direct-integration, was that nonlinearity yields evident differences in structural frequencies and in energy dissipation (damping) in comparison to the linear analysis. The high restraint forces on the supports became smaller for most of the supports but at some points the forces of the non-linear analysis were even higher. So the conservatism of the linear analysis is not fully valid for the whole structure. The relevance of the non-linear effects in dynamic piping calculations is shown by comparing the calculation result with measurements which were performed on structures in the plant. (orig.) [German] Im Rahmen der Aenderung der Speisewasserleitung einer Kraftwerksanlage wurde die Struktur neu berechnet. Die Analysen mit einem linearen Modell (modal), das ueblicherweise verwendet wird, ergaben hohe Lasten an Halterungen. Zum Abbau von Konservativitaeten wurde eine realistischere Modellierung durch die Beruecksichtigung des nichtlinearen Verhaltens der in der Anlage befindlichen Gleitlager, Fuehrungen und Stossbremsen in der Berechnung vorgenommen. Die Untersuchungen haben ergeben, dass durch die Nichtlinearitaet das Frequenzverhalten der Struktur und die Dissipation von Energie durch Reibvorgaenge wesentlich beeinflusst werden. Des Weiteren ist festzustellen, dass aus linearen Analysen nicht uneingeschraenkt konservative Ergebnisse gewonnen werden. Die Relevanz der Beruecksichtigung des nichtlinearen Lagerverhaltens bei einer dynamischen Strukturberechnung wird
Polymer engineering science and viscoelasticity an introduction
Brinson, Hal F
2015-01-01
This book provides a unified mechanics and materials perspective on polymers: both the mathematics of viscoelasticity theory as well as the physical mechanisms behind polymer deformation processes. Introductory material on fundamental mechanics is included to provide a continuous baseline for readers from all disciplines. Introductory material on the chemical and molecular basis of polymers is also included, which is essential to the understanding of the thermomechanical response. This self-contained text covers the viscoelastic characterization of polymers including constitutive modeling, experimental methods, thermal response, and stress and failure analysis. Example problems are provided within the text as well as at the end of each chapter. New to this edition: · One new chapter on the use of nano-material inclusions for structural polymer applications and applications such as fiber-reinforced polymers and adhesively bonded structures · Brings up-to-date polymer pro...
van de Walle, Axel; Rouleau, Lucie; Deckers, Elke; Desmet, Wim
2015-01-01
In many engineering applications, viscoelastic treatments are used to suppress vibrations of lightly damped structures. Computational methods provide powerful tools for the design and analysis of these structures. The most commonly used method to model the dynamics of complex structures is the finite element method. Its use, however, often results in very large and computationally demanding models, especially when viscoelastic material behaviour has to be taken into account. To alleviate this...
Energy Technology Data Exchange (ETDEWEB)
Ito, M. [Nagoya Institute of Technology, Nagoya (Japan). Faculty of Engineering; Moroi, T. [Toyoda Automatic Loom Works, Ltd., Aichi (Japan); Toda, H. [Toray Industries, Inc., Tokyo (Japan)
1998-05-25
Numerical simulations by a finite-difference method have been made for a viscoelastic flow due to a rotating disc enclosed in a cylindrical casing with large axial clearance. The Giesekus model with a single relaxation time was applied as a constitutive equation. We could simulate some typical secondary flow patterns for viscoelastic fluids which were different from Newtonian fluids; e.g., a secondary flow of which circulation direction at very low Reynolds number is reversed compared with that for a Newtonian fluid and a double-cell flow structure which Escudier et. all observed at relatively high Reynolds number. We show that the double-cell flow structure relates to nonlinear terms of the constitutive equation. The secondary flow patterns are characterized by the elasticity number (=Weissenberg number/Reynolds number) from low to high Reynolds numbers. 16 refs., 14 figs., 1 tab.
Energy Technology Data Exchange (ETDEWEB)
Zaytsev, Kirill I., E-mail: kirzay@gmail.com; Katyba, Gleb M.; Yakovlev, Egor V.; Yurchenko, Stanislav O., E-mail: st.yurchenko@mail.ru [Bauman Moscow State Technical University, 2nd Baumanskaya str. 5, Moscow 105005 (Russian Federation); Gorelik, Vladimir S. [P. N. Lebedev Physics Institute of the Russian Academy of Sciences, Leninskiy Prospekt 53, Moscow 119991 (Russian Federation)
2014-06-07
A novel approach for the enhancement of nonlinear optical effects inside globular photonic crystals (PCs) is proposed and systematically studied via numerical simulations. The enhanced optical harmonic generation is associated with two- and three-dimensional PC pumping with the wavelength corresponding to different PC band-gaps. The interactions between light and the PC are numerically simulated using the finite-difference time-domain technique for solving the Maxwell's equations. Both empty and infiltrated two-dimensional PC structures are considered. A significant enhancement of harmonic generation is predicted owing to the highly efficient PC pumping based on the structural light focusing effect inside the PC structure. It is shown that a highly efficient harmonic generation could be attained for both the empty and infiltrated two- and three-dimensional PCs. We are demonstrating the ability for two times enhancement of the parametric decay efficiency, one order enhancement of the second harmonic generation, and two order enhancement of the third harmonic generation in PC structures in comparison to the nonlinear generations in appropriate homogenous media. Obviously, the nonlinear processes should be allowed by the molecular symmetry. The criteria of the nonlinear process efficiency are specified and calculated as a function of pumping wavelength position towards the PC globule diameter. Obtained criterion curves exhibit oscillating characteristics, which indicates that the highly efficient generation corresponds to the various PC band-gap pumping. The highest efficiency of nonlinear conversions could be reached for PC pumping with femtosecond optical pulses; thus, the local peak intensity would be maximized. Possible applications of the observed phenomenon are also discussed.
Institute of Scientific and Technical Information of China (English)
Panos C. Tsopelas; Panayiotis C. Roussis; Michael C. Constantinou
2009-01-01
The complexity of modern seismically isolated structures requires the analysis of the structural system and the isolation system in its entirety and the ability to capture potential discontinuous phenomena such as isolator uplift and their effects on the superstructures and the isolation hardware. In this paper, an analytical model is developed and a computational algorithm is formulated to analyze complex seismically isolated superstructures even when undergoing highly-nonlinear phenomena such as uplift. The computational model has the capability of modeling various types of isolation devices with strong nonlinearities, analyzing multiple superstructures (up to five separate superstructures) on multiple bases (up to five bases), and capturing the effects of lateral loads on bearing axial forces, including bearing uplift. The model developed herein has been utilized to form the software platform 3D-BASIS-ME-MB, which provides the practicing engineering community with a versatile tool for analysis and design of complex structures with modem isolation systems.
Energy Technology Data Exchange (ETDEWEB)
Manson, G; Worden, K, E-mail: graeme.manson@sheffield.ac.u, E-mail: k.worden@sheffield.ac.u [Dynamics Research Group, Department of Mechanical Engineering, University of Sheffield, Mappin St, Sheffield S1 3JD (United Kingdom)
2009-08-01
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.
Geometry effect on energy transfer rate in a coupled-quantum-well structure: nonlinear regime
Salavati-fard, T.; Vazifehshenas, T.
2014-12-01
We study theoretically the effect of geometry on the energy transfer rate at nonlinear regime in a coupled-quantum-well system using the balance equation approach. To investigate comparatively the effect of both symmetric and asymmetric geometry, different structures are considered. The random phase approximation dynamic dielectric function is employed to include the contributions from both quasiparticle and plasmon excitations. Also, the short-range exchange interaction is taken into account through the Hubbard approximation. Our numerical results show that the energy transfer rate increases by increasing the well thicknesses in symmetric structures. Furthermore, by increasing spatial asymmetry, the energy transfer rate decreases for the electron temperature range of interest. From numerical calculations, it is obtained that the nonlinear energy transfer rate is proportional to the square of electron drift velocity in all structures and also, found that the influence of Hubbard local field correction on the energy transfer rate gets weaker by increasing the strength of applied electric field.
An analytical study on performance of a diagrid structure using nonlinear static pushover analysis
Directory of Open Access Journals (Sweden)
Kiran Kamath
2016-09-01
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.
A Kernel Time Structure Independent Component Analysis Method for Nonlinear Process Monitoring☆
Institute of Scientific and Technical Information of China (English)
Lianfang Cai; Xuemin Tian; Ni Zhang
2014-01-01
Kernel independent component analysis (KICA) is a newly emerging nonlinear process monitoring method, which can extract mutually independent latent variables cal ed independent components (ICs) from process var-iables. However, when more than one IC have Gaussian distribution, it cannot extract the IC feature effectively and thus its monitoring performance will be degraded drastical y. To solve such a problem, a kernel time struc-ture independent component analysis (KTSICA) method is proposed for monitoring nonlinear process in this paper. The original process data are mapped into a feature space nonlinearly and then the whitened data are calculated in the feature space by the kernel trick. Subsequently, a time structure independent component analysis algorithm, which has no requirement for the distribution of ICs, is proposed to extract the IC feature. Finally, two monitoring statistics are built to detect process faults. When some fault is detected, a nonlinear fault identification method is developed to identify fault variables based on sensitivity analysis. The proposed monitoring method is applied in the Tennessee Eastman benchmark process. Applications demonstrate the superiority of KTSICA over KICA.
Non-linear structural dynamics characterization using a scanning laser vibrometer
Pai, P. F.; Lee, S.-Y.
2003-07-01
This paper presents the use of a scanning laser vibrometer and a signal decomposition method to characterize non-linear dynamics of highly flexible structures. A Polytec PI PSV-200 scanning laser vibrometer is used to measure transverse velocities of points on a structure subjected to a harmonic excitation. Velocity profiles at different times are constructed using the measured velocities, and then each velocity profile is decomposed using the first four linear mode shapes and a least-squares curve-fitting method. From the variations of the obtained modal velocities with time we search for possible non-linear phenomena. A cantilevered titanium alloy beam subjected to harmonic base-excitations around the second, third, and fourth natural frequencies are examined in detail. Influences of the fixture mass, gravity, mass centers of mode shapes, and non-linearities are evaluated. Geometrically exact equations governing the planar, harmonic large-amplitude vibrations of beams are solved for operational deflection shapes using the multiple shooting method. Experimental results show the existence of 1:3 and 1:2:3 external and internal resonances, energy transfer from high-frequency modes to the first mode, and amplitude- and phase-modulation among several modes. Moreover, the existence of non-linear normal modes is found to be questionable.
Shen, Yanfeng
2017-04-01
This paper presents a numerical investigation of the nonlinear interactions between multimodal guided waves and delamination in composite structures. The elastodynamic wave equations for anisotropic composite laminate were formulated using an explicit Local Interaction Simulation Approach (LISA). The contact dynamics was modeled using the penalty method. In order to capture the stick-slip contact motion, a Coulomb friction law was integrated into the computation procedure. A random gap function was defined for the contact pairs to model distributed initial closures or openings to approximate the nature of rough delamination interfaces. The LISA procedure was coded using the Compute Unified Device Architecture (CUDA), which enables the highly parallelized computation on powerful graphic cards. Several guided wave modes centered at various frequencies were investigated as the incident wave. Numerical case studies of different delamination locations across the thickness were carried out. The capability of different wave modes at various frequencies to trigger the Contact Acoustic Nonlinearity (CAN) was studied. The correlation between the delamination size and the signal nonlinearity was also investigated. Furthermore, the influence from the roughness of the delamination interfaces was discussed as well. The numerical investigation shows that the nonlinear features of wave delamination interactions can enhance the evaluation capability of guided wave Structural Health Monitoring (SHM) system. This paper finishes with discussion, concluding remarks, and suggestions for future work.
Cisek, Richard
Physical and functional properties of advanced nano-composite materials and biological structures are determined by self-organized atoms and molecules into nanostructures and in turn by microscopic organization of the nanostructures into assemblies of higher structural complexity. Therefore, microscopes are indispensable tools for structural investigations at various levels of organization. In this work, novel nonlinear optical microscopy methods were developed to non-invasively study structural organization at the nanoscopic and microscopic levels. Atomic organization of semiconductor nanowires, molecular organization of amylose biocrystallites in starch granules, and microscopic organization of several photosynthetic organisms was elucidated. The structure of ZnSe nanowires, key components in many modern nanodevices, was investigated using polarization harmonic generation microscopy. Based on nonlinear optical properties of the different crystal lattices, zinc blende and wurtzite nanowires were differentiated, and the three-dimensional orientation of the zinc blende nanowires could be found. The structure of starch granules, a model biocrystal, important in food as well as health sciences, was also investigated using polarization harmonic microscopy. The study was combined with ab initio calculations using the crystal structures of amylose A and B, revealing that second harmonic signals originate from the hydroxide and hydrogen bonds in the starch granules. Visualization of several photosynthetic organisms including the green algae, Chlamydomonas reinhardtii, two species of cyanobacteria, Leptolyngbya sp. and Anabaena sp., aggregates of light-harvesting pigment-protein complexes as well as chloroplasts from green plants were also explored, revealing that future nonlinear microscopy applications could include structural studies of cell walls, the Chlamydomonas eyespot, and photosynthetic membranes. In this study, several nonlinear optical microscopy modalities
Energy Technology Data Exchange (ETDEWEB)
Solberg, Jerome M., E-mail: solberg2@llnl.gov [Methods Development Group, Lawrence Livermore Nat’l Lab, P.O. Box 808, Mailstop L-125, Livermore, CA 94550 (United States); Hossain, Quazi, E-mail: hossain1@llnl.gov [Structural and Applied Mechanics Group, Lawrence Livermore Nat’l Lab, P.O. Box 808, Mailstop L-129, Livermore, CA 94550 (United States); Mseis, George, E-mail: george.mseis@gmail.com [Structural and Applied Mechanics Group, Lawrence Livermore Nat’l Lab, P.O. Box 808, Mailstop L-129, Livermore, CA 94550 (United States)
2016-08-01
Highlights: • Derived modified version of Bielak’s SSI method for nonlinear time-domain analysis. • Utilized a Ramberg–Osgood material with parameters that can be fit to EPRI data. • Matched vertically propagating shear wave results from CARES. • Applied this technique to a representative SMR, compared well with SASSI. • The technique is extensible to other material models and nonlinear effects. - Abstract: A generalized time-domain method for soil–structure interaction analysis is developed, based upon an extension of the work of the domain reduction method of Bielak et al. The methodology is combined with the use of a simple hysteretic soil model based upon the Ramberg–Osgood formulation and applied to a notional Small Modular Reactor. These benchmark results compare well (with some caveats) with those obtained by using the industry-standard frequency-domain code SASSI. The methodology provides a path forward for investigation of other sources of nonlinearity, including those associated with the use of more physically-realistic material models incorporating pore-pressure effects, gap opening/closing, the effect of nonlinear structural elements, and 3D seismic inputs.
Nonlinear wave structures in collisional plasma of auroral E-region ionosphere
Directory of Open Access Journals (Sweden)
A. V. Volosevich
Full Text Available Studies of the auroral plasma with small-scale inhomogenieties producing the VHF-radar reflections (radar aurora when observed in conditions of the saturated Farley-Buneman instability within the auroral E region, show strong nonlinear interactions and density fluctuations of 5–15%. Such nonlinearity and high fluctation amplitudes are inconsistent with the limitations of the weak turbulence theory, and thus a theory for arbitrary amplitudes is needed. To this end, a nonlinear theory is described for electrostatic MHD moving plasma structures of arbitrary amplitude for conditions throughout the altitude range of the collisional auroral E region. The equations are derived, from electron and ion motion self-consistent with the electric field, for the general case of the one-dimensional problem. They take into account nonlinearity, electron and ion inertia, diffusion, deviation from quasi-neutrality, and dynamical ion viscosity. The importance of the ion viscosity for dispersion is stressed, while deviation from the quasi-neutrality can be important only at rather low plasma densities, not typical for the auroral E region. In a small amplitude limit these equations have classical nonlinear solutions of the type of "electrostatic shock wave" or of knoidal waves. In a particular case these knoidal waves degrade to a dissipative soliton. A two-dimensional case of a quasi-neutral plasma is considered in the plane perpendicular to the magnetic field by way of the Poisson brackets, but neglecting the nonlinearity and ion inertia. It is shown that in these conditions an effective saturation can be achieved at the stationary turbulence level of order of 10%.
ALE Fractional Step Finite Element Method for Fluid-Structure Nonlinear Interaction Problem
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A computational procedure is developed to solve the problems of coupled motion of a structure and a viscous incompressible fluid. In order to incorporate the effect of the moving surface of the structure as well as the free surface motion, the arbitrary Lagrangian-Eulerian formulation is employed as the basis of the finite element spatial discretization. For numerical integration in time, the fraction step method is used. This method is useful because one can use the same linear interpolation function for both velocity and pressure. The method is applied to the nonlinear interaction of a structure and a tuned liquid damper. All computations are performed with a personal computer.
Ding, Hang
2014-01-01
Structures in recurrence plots (RPs), preserving the rich information of nonlinear invariants and trajectory characteristics, have been increasingly analyzed in dynamic discrimination studies. The conventional analysis of RPs is mainly focused on quantifying the overall diagonal and vertical line structures through a method, called recurrence quantification analysis (RQA). This study extensively explores the information in RPs by quantifying local complex RP structures. To do this, an approach was developed to analyze the combination of three major RQA variables: determinism, laminarity, and recurrence rate (DLR) in a metawindow moving over a RP. It was then evaluated in two experiments discriminating (1) ideal nonlinear dynamic series emulated from the Lorenz system with different control parameters and (2) data sets of human heart rate regulations with normal sinus rhythms (n = 18) and congestive heart failure (n = 29). Finally, the DLR was compared with seven major RQA variables in terms of discriminatory power, measured by standardized mean difference (DSMD). In the two experiments, DLR resulted in the highest discriminatory power with DSMD = 2.53 and 0.98, respectively, which were 7.41 and 2.09 times the best performance from RQA. The study also revealed that the optimal RP structures for the discriminations were neither typical diagonal structures nor vertical structures. These findings indicate that local complex RP structures contain some rich information unexploited by RQA. Therefore, future research to extensively analyze complex RP structures would potentially improve the effectiveness of the RP analysis in dynamic discrimination studies.
Ding, Hang
2014-01-01
Structures in recurrence plots (RPs), preserving the rich information of nonlinear invariants and trajectory characteristics, have been increasingly analyzed in dynamic discrimination studies. The conventional analysis of RPs is mainly focused on quantifying the overall diagonal and vertical line structures through a method, called recurrence quantification analysis (RQA). This study extensively explores the information in RPs by quantifying local complex RP structures. To do this, an approach was developed to analyze the combination of three major RQA variables: determinism, laminarity, and recurrence rate (DLR) in a metawindow moving over a RP. It was then evaluated in two experiments discriminating (1) ideal nonlinear dynamic series emulated from the Lorenz system with different control parameters and (2) data sets of human heart rate regulations with normal sinus rhythms (n = 18) and congestive heart failure (n = 29). Finally, the DLR was compared with seven major RQA variables in terms of discriminatory power, measured by standardized mean difference (DSMD). In the two experiments, DLR resulted in the highest discriminatory power with DSMD = 2.53 and 0.98, respectively, which were 7.41 and 2.09 times the best performance from RQA. The study also revealed that the optimal RP structures for the discriminations were neither typical diagonal structures nor vertical structures. These findings indicate that local complex RP structures contain some rich information unexploited by RQA. Therefore, future research to extensively analyze complex RP structures would potentially improve the effectiveness of the RP analysis in dynamic discrimination studies.
Viscoelastic properties of actin-coated membranes
Helfer, E.; Harlepp, S.; Bourdieu, L.; Robert, J.; Mackintosh, F. C.; Chatenay, D.
2001-02-01
In living cells, cytoskeletal filaments interact with the plasma membrane to form structures that play a key role in cell shape and mechanical properties. To study the interaction between these basic components, we designed an in vitro self-assembled network of actin filaments attached to the outer surface of giant unilamellar vesicles. Optical tweezers and single-particle tracking experiments are used to study the rich dynamics of these actin-coated membranes (ACM). We show that microrheology studies can be carried out on such an individual microscopic object. The principle of the experiment consists in measuring the thermally excited position fluctuations of a probe bead attached biochemically to the membrane. We propose a model that relates the power spectrum of these thermal fluctuations to the viscoelastic properties of the membrane. The presence of the actin network modifies strongly the membrane dynamics with respect to a fluid, lipid bilayer one. It induces first a finite (ω=0) two-dimensional (2D) shear modulus G02D~0.5 to 5 μN/m in the membrane plane. Moreover, the frequency dependence at high frequency of the shear modulus [G'2D(f )~f0.85+/-0.07] and of the bending modulus (κACM(f)~f0.55+/-0.21) demonstrate the viscoelastic behavior of the composite membrane. These results are consistent with a common exponent of 0.75 for both moduli as expected from our model and from prior measurements on actin solutions.