Molecular Histopathology by Spectrally Reconstructed Nonlinear Interferometric Vibrational Imaging
Chowdary, Praveen D.; Jiang, Zhi; Chaney, Eric J.; Benalcazar, Wladimir A.; Marks, Daniel L.; Gruebele, Martin; Boppart, Stephen A.
2011-01-01
Sensitive assays for rapid quantitative analysis of histologic sections, resected tissue specimens, or in situ tissue are highly desired for early disease diagnosis. Stained histopathology is the gold standard but remains a subjective practice on processed tissue taking from hours to days. We describe a microscopy technique that obtains a sensitive and accurate color-coded image from intrinsic molecular markers. Spectrally reconstructed nonlinear interferometric vibrational imaging can differentiate cancer versus normal tissue sections with greater than 99% confidence interval in a preclinical rat breast cancer model and define cancer boundaries to ±100 μm with greater than 99% confidence interval, using fresh unstained tissue sections imaged in less than 5 minutes. By optimizing optical sources and beam delivery, this technique can potentially enable real-time point-of-care optical molecular imaging and diagnosis. PMID:21098699
Nonlinear Interferometric Vibrational Imaging (NIVI) with Novel Optical Sources
Boppart, Stephen A.; King, Matthew D.; Liu, Yuan; Tu, Haohua; Gruebele, Martin
Optical imaging is essential in medicine and in fundamental studies of biological systems. Although many existing imaging modalities can supply valuable information, not all are capable of label-free imaging with high-contrast and molecular specificity. The application of molecular or nanoparticle contrast agents may adversely influence the biological system under investigation. These substances also present ongoing concerns over toxicity or particle clearance, which must be properly addressed before their approval for in vivo human imaging. Hence there is an increasing appreciation for label-free imaging techniques. It is of primary importance to develop imaging techniques that can indiscriminately identify and quantify biochemical compositions to high degrees of sensitivity and specificity through only the intrinsic optical response of endogenous molecular species. The development and use of nonlinear interferometric vibrational imaging, which is based on the interferometric detection of optical signals from coherent anti-Stokes Raman scattering (CARS), along with novel optical sources, offers the potential for label-free molecular imaging.
Interferometric vibration sensor using phase-generated carrier method.
Li, Yang; Liu, Zhibo; Liu, Yan; Ma, Lin; Tan, Zhongwei; Jian, Shuisheng
2013-09-01
An interferometric fiber-optic vibration sensing system using the phase-generated carrier (PGC) method is proposed and experimentally demonstrated. The sensing section consists of a Sagnac interferometer combined with a Mach-Zehnder interferometer, a length of sensing fiber is shared between the two interferometers. The PGC demodulation scheme is used to demodulate the time-varying phase shifts induced by vibrations. Spatial information can be extracted from the demodulated results. A prototype sensing system with a 628 m long sensing fiber has been tested and a spatial resolution better than 12 m is successfully achieved.
Interferometric correlator for acoustic radiation and underlying structural vibration
Apostol, Adela; Kilpatrick, James; Markov, Vladimir; Bendiksen, Oddvar O.
2016-12-01
In this paper we discuss the background and principles of an optical non-contact sensor fusion concept, the Interferometric Correlator for Acoustic Radiation and Underlying Structural Vibration (ICARUSV) and give practical example of its capabilities, focusing on its ability to simultaneously capture, visualize and quantitatively characterize full-field non-stationary structural dynamics and unsteady radiated sound fields or transient flow fields around the structure of interest. The ICARUSV's multi-sensor design is based on a parallel architecture and therefore the data capture is fast and inherently support a wide variety of spatio-temporal or spatio-spectral analysis methods which characterize the structural or acoustic/flow field dynamics as it occurs in real time, including short-lived transient events. No other technology available today offers this level of multi-parameter multi-dimensional data1.
Interferometric and nonlinear-optical spectral-imaging techniques for outer space and live cells
Itoh, Kazuyoshi
2015-12-01
Multidimensional signals such as the spectral images allow us to have deeper insights into the natures of objects. In this paper the spectral imaging techniques that are based on optical interferometry and nonlinear optics are presented. The interferometric imaging technique is based on the unified theory of Van Cittert-Zernike and Wiener-Khintchine theorems and allows us to retrieve a spectral image of an object in the far zone from the 3D spatial coherence function. The retrieval principle is explained using a very simple object. The promising applications to space interferometers for astronomy that are currently in progress will also be briefly touched on. An interesting extension of interferometric spectral imaging is a 3D and spectral imaging technique that records 4D information of objects where the 3D and spectral information is retrieved from the cross-spectral density function of optical field. The 3D imaging is realized via the numerical inverse propagation of the cross-spectral density. A few techniques suggested recently are introduced. The nonlinear optical technique that utilizes stimulated Raman scattering (SRS) for spectral imaging of biomedical targets is presented lastly. The strong signals of SRS permit us to get vibrational information of molecules in the live cell or tissue in real time. The vibrational information of unstained or unlabeled molecules is crucial especially for medical applications. The 3D information due to the optical nonlinearity is also the attractive feature of SRS spectral microscopy.
The nonlinear piezoelectric tuned vibration absorber
Soltani, P.; Kerschen, G.
2015-07-01
This paper proposes a piezoelectric vibration absorber, termed the nonlinear piezoelectric tuned vibration absorber (NPTVA), for the mitigation of nonlinear resonances of mechanical systems. The new feature of the NPTVA is that its nonlinear restoring force is designed according to a principle of similarity, i.e., the NPTVA should be an electrical analog of the nonlinear host system. Analytical formulas for the NPTVA parameters are derived using the homotopy perturbation method. Doing so, a nonlinear generalization of Den Hartog’s equal-peak tuning rule is developed for piezoelectric vibration absorbers.
Design of a nonlinear torsional vibration absorber
Tahir, Ammaar Bin
Tuned mass dampers (TMD) utilizing linear spring mechanisms to mitigate destructive vibrations are commonly used in practice. A TMD is usually tuned for a specific resonant frequency or an operating frequency of a system. Recently, nonlinear vibration absorbers attracted attention of researchers due to some potential advantages they possess over the TMDs. The nonlinear vibration absorber, or the nonlinear energy sink (NES), has an advantage of being effective over a broad range of excitation frequencies, which makes it more suitable for systems with several resonant frequencies, or for a system with varying excitation frequency. Vibration dissipation mechanism in an NES is passive and ensures that there is no energy backflow to the primary system. In this study, an experimental setup of a rotational system has been designed for validation of the concept of nonlinear torsional vibration absorber with geometrically induced cubic stiffness nonlinearity. Dimensions of the primary system have been optimized so as to get the first natural frequency of the system to be fairly low. This was done in order to excite the dynamic system for torsional vibration response by the available motor. Experiments have been performed to obtain the modal parameters of the system. Based on the obtained modal parameters, the design optimization of the nonlinear torsional vibration absorber was carried out using an equivalent 2-DOF modal model. The optimality criterion was chosen to be maximization of energy dissipation in the nonlinear absorber attached to the equivalent 2-DOF system. The optimized design parameters of the nonlinear absorber were tested on the original 5-DOF system numerically. A comparison was made between the performance of linear and nonlinear absorbers using the numerical models. The comparison showed the superiority of the nonlinear absorber over its linear counterpart for the given set of primary system parameters as the vibration energy dissipation in the former is
Directory of Open Access Journals (Sweden)
E. L. Dmitrieva
2016-05-01
Full Text Available Basic peculiarities of nonlinear Kalman filtering algorithm applied to processing of interferometric signals are considered. Analytical estimates determining statistical characteristics of signal values prediction errors were obtained and analysis of errors histograms taking into account variations of different parameters of interferometric signal was carried out. Modeling of the signal prediction procedure with known fixed parameters and variable parameters of signal in the algorithm of nonlinear Kalman filtering was performed. Numerical estimates of prediction errors for interferometric signal values were obtained by formation and analysis of the errors histograms under the influence of additive noise and random variations of amplitude and frequency of interferometric signal. Nonlinear Kalman filter is shown to provide processing of signals with randomly variable parameters, however, it does not take into account directly the linearization error of harmonic function representing interferometric signal that is a filtering error source. The main drawback of the linear prediction consists in non-Gaussian statistics of prediction errors including cases of random deviations of signal amplitude and/or frequency. When implementing stochastic filtering of interferometric signals, it is reasonable to use prediction procedures based on local statistics of a signal and its parameters taken into account.
Modeling of the vibrating beam accelerometer nonlinearities
Romanowski, P. A.; Knop, R. C.
Successful modeling and processing of the output of a quartz Vibrating Beam Accelerometer (VBA), whose errors are inherently nonlinear with respect to input acceleration, are reported. The VBA output, with two signals that are frequencies of vibrating quartz beams, has inherent higher-order terms. In order to avoid vibration rectification errors, the signal output must be sampled at a rapid rate and the output must be reduced using a nonlinear model. The present model, with acceleration as a function of frequency, is derived by a least-squares process where the covariance matrix is obtained from simulated data. The system performance is found to be acceptable to strategic levels, and it is shown that a vibration rectification error of 400 micrograms/sq g can be reduced to 4 micrograms/sq g by using the processor electronics and a nonlinear model.
Dynamics and vibrations progress in nonlinear analysis
Kachapi, Seyed Habibollah Hashemi
2014-01-01
Dynamical and vibratory systems are basically an application of mathematics and applied sciences to the solution of real world problems. Before being able to solve real world problems, it is necessary to carefully study dynamical and vibratory systems and solve all available problems in case of linear and nonlinear equations using analytical and numerical methods. It is of great importance to study nonlinearity in dynamics and vibration; because almost all applied processes act nonlinearly, and on the other hand, nonlinear analysis of complex systems is one of the most important and complicated tasks, especially in engineering and applied sciences problems. There are probably a handful of books on nonlinear dynamics and vibrations analysis. Some of these books are written at a fundamental level that may not meet ambitious engineering program requirements. Others are specialized in certain fields of oscillatory systems, including modeling and simulations. In this book, we attempt to strike a balance between th...
Active vibration control of nonlinear benchmark buildings
Institute of Scientific and Technical Information of China (English)
ZHOU Xing-de; CHEN Dao-zheng
2007-01-01
The present nonlinear model reduction methods unfit the nonlinear benchmark buildings as their vibration equations belong to a non-affine system. Meanwhile,the controllers designed directly by the nonlinear control strategy have a high order, and they are difficult to be applied actually. Therefore, a new active vibration control way which fits the nonlinear buildings is proposed. The idea of the proposed way is based on the model identification and structural model linearization, and exerting the control force to the built model according to the force action principle. This proposed way has a better practicability as the built model can be reduced by the balance reduction method based on the empirical Grammian matrix. A three-story benchmark structure is presented and the simulation results illustrate that the proposed method is viable for the civil engineering structures.
Robust real-time self-mixing interferometric laser vibration sensor with embedded MEMS accelerometer
Zabit, Usman; Bernal, Olivier D.; Bosch, Thierry
2012-06-01
In this paper, we present a real-time implementation of a Self-Mixing (SM) interferometric laser diode (LD) based vibration sensor coupled with an embedded MEMS (microelectromechanical system) accelerometer. Such a sensor allows measuring correct target movements even when the LD based SM sensor is subject to extraneous movements. This results in a vibration sensing system that can be used for embedded applications as there is no more need of keeping the sensor stationary. Such an approach opens the way for the use of such laser sensors in conditions where the use of anti-vibration support is not available or possible. The proposed data fusion between a MEMS accelerometer and a LD based SM sensor results in a robust, compact and low-cost sensing system.
Laser interferometric vibration measurements of the middle ear in healthy humans
Jorge, J. Rodriguez; Hemmert, Werner; Burkhardt, Claus; Zenner, Hans-Peter; Gummer, Anthony W.
1996-01-01
The use of spontaneous and evoked otacoustic emissions is now a standard clinical tool for diagnosis of the function of the inner ear. However, it is not possible to extract this information over the entire, functionally relevant frequency range because of imperfect coupling of: (1) stapedial to ear-drum vibrations through the ossicular chain of the middle ear and (2) ear-drum vibrations to air in the external auditory meatus. The problem could be circumvented if it were possible to measure the vibration of the stapes and ear drum. The ear drum can be visualized non-invasively, whereas the stapes is only accessible intra-operatively. Therefore, we designed a laser-interferometric system to non-invasively measure the vibration of the human ear drum. Vibrations were measured with a laser Doppler velocimeter (Polytec OFV-302) coupled into the side arm of an operating microscope (Zeiss OPMI MDM). The wavelength was 633 nm and emitted power was less than 1 mW. Direct coupling through the optics of the operating microscope, instead of through glass fibers, enabled a larger signal-to- noise ratio (20 - 30 dB) due to collection of more reflected light. This coupling scheme avoids the problems associated with having to place a reflecting material on the ear drum. The developed vibration measurement system allows non-invasive, fast and reproducible characterization of the dynamics of the human ear drum and as such can be used for clinical diagnostics.
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 vibrating system identification via Hilbert decomposition
Feldman, Michael; Braun, Simon
2017-02-01
This paper deals with the identification of nonlinear vibration systems, based on measured signals for free and forced vibration regimes. Two categories of time domain signal are analyzed, one of a fast inter-modulation signal and a second as composed of several mono-components. To some extent, this attempts to imitate analytic studies of such systems, with its two major analysis groups - the perturbation and the harmonic balance methods. Two appropriate signal processing methods are then investigated, one based on demodulation and the other on signal decomposition. The Hilbert Transform (HT) has been shown to enable effective and simple methods of analysis. We show that precise identification of the nonlinear parameters can be obtained, contrary to other average HT based methods where only approximation parameters are obtained. The effectiveness of the proposed methods is demonstrated for the precise nonlinear system identification, using both the signal demodulation and the signal decomposition methods. Following the exposition of the tools used, both the signal demodulation as well as decomposition are applied to classical examples of nonlinear systems. Cases of nonlinear stiffness and damping forces are analyzed. These include, among other, an asymmetric Helmholtz oscillator, a backlash with nonlinear turbulent square friction, and a Duffing oscillator with dry friction.
A hybrid nonlinear vibration energy harvester
Yang, Wei; Towfighian, Shahrzad
2017-06-01
Vibration energy harvesting converts mechanical energy from ambient sources to electricity to power remote sensors. Compared to linear resonators that have poor performance away from their natural frequency, nonlinear vibration energy harvesters perform better because they use vibration energy over a broader spectrum. We present a hybrid nonlinear energy harvester that combines bi-stability with internal resonance to increase the frequency bandwidth. A two-fold increase in the frequency bandwidth can be obtained compared to a bi-stable system with fixed magnets. The harvester consists of a piezoelectric cantilever beam carrying a movable magnet facing a fixed magnet. A spring allows the magnet to move along the beam and it provides an extra stored energy to further increase the amplitude of vibration acting as a mechanical amplifier. An electromechanically coupled mathematical model of the system is presented to obtain the dynamic response of the cantilever beam, the movable magnet and the output voltage. The perturbation method of multiple scales is applied to solve these equations and obtain approximate analytical solutions. The effects of various system parameters on the frequency responses are investigated. The numerical approaches of the long time integration (Runge-Kutta method) and the shooting technique are used to verify the analytical results. The results of this study can be used to improve efficiency in converting wasted mechanical vibration to useful electrical energy by broadening the frequency bandwidth.
Nonlinear dynamic vibration absorbers with a saturation
Febbo, M.; Machado, S. P.
2013-03-01
The behavior of a new type of nonlinear dynamic vibration absorber is studied. A distinctive characteristic of the proposed absorber is the impossibility to extend the system to infinity. The mathematical formulation is based on a finite extensibility nonlinear elastic potential to model the saturable nonlinearity. The absorber is attached to a single degree-of-freedom linear/nonlinear oscillator subjected to a periodic external excitation. In order to solve the equations of motion and to analyze the frequency-response curves, the method of averaging is used. The performance of the FENE absorber is evaluated considering a variation of the nonlinearity of the primary system, the damping and the linearized frequency of the absorber and the mass ratio. The numerical results show that the proposed absorber has a very good efficiency when the nonlinearity of the primary system increases. When compared with a cubic nonlinear absorber, for a large nonlinearity of the primary system, the FENE absorber shows a better effectiveness for the whole studied frequency range. A complete absence of quasi-periodic oscillations is also found for an appropriate selection of the parameters of the absorber. Finally, direct integrations of the equations of motion are performed to verify the accuracy of the proposed method.
Linear and nonlinear piezoelectric shunting strategies for vibration mitigation
Directory of Open Access Journals (Sweden)
Soltani P.
2014-01-01
Full Text Available This paper studies linear and nonlinear piezoelectric vibration absorbers that are designed based on the equal-peak method. A comparison between the performance of linear mechanical and electrical tuned vibration absorbers coupled to a linear oscillator is first performed. Nonlinearity is then introduced in the primary oscillator to which a new nonlinear electrical tuned vibration absorber is attached. Despite the frequency-energy dependence of nonlinear oscillations, we show that the nonlinear absorber is capable of effectively mitigating the vibrations of the nonlinear primary system in a large range of forcing amplitudes.
Nonlinear characteristics of an autoparametric vibration system
Yan, Zhimiao; Taha, Haithem E.; Tan, Ting
2017-03-01
The nonlinear characteristics of an autoparametric vibration system are investigated. This system consists of a base structure and a cantilever beam with a tip mass. The dynamic equations for the system are derived using the extended Hamilton's principle. The method of multiple scales (MMS) is used to determine an approximate analytical solution of the nonlinear governing equations and, hence, analyze the stability and bifurcation of the system. Compared with the numerical simulation, the first-order MMS is not sufficient. A Lagrangian-based approach is proposed to perform a second-order analysis, which is applicable to a large class of nonlinear systems. The effects of the amplitude and frequency of the external force, damping and frequency of the attached cantilever beam, and the tip mass on the nonlinear responses of the autoparametric vibration system are determined. The results show that this system exhibits many interesting nonlinear phenomena including saturation, jumps, hysteresis and different kinds of bifurcations, such as saddle-node, supercritical pitchfork and subcritical pitchfork bifurcations. Power spectra, phase portraits and Poincare maps are employed to analyze the unstable behavior and the associated Hopf bifurcation and chaos. Depending on the application of such a system, its dynamical behaviors could be exploited or avoided.
Vibrational mechanics nonlinear dynamic effects, general approach, applications
Blekhman, Iliya I
2000-01-01
This important book deals with vibrational mechanics - the new, intensively developing section of nonlinear dynamics and the theory of nonlinear oscillations. It offers a general approach to the study of the effect of vibration on nonlinear mechanical systems.The book presents the mathematical apparatus of vibrational mechanics which is used to describe such nonlinear effects as the disappearance and appearance under vibration of stable positions of equilibrium and motions (i.e. attractors), the change of the rheological properties of the media, self-synchronization, self-balancing, the vibrat
Practical design of a nonlinear tuned vibration absorber
DEFF Research Database (Denmark)
Grappasonni, C.; Habib, G.; Detroux, T.
2014-01-01
The aim of the paper is to develop a new nonlinear tuned vibration absorber (NLTVA) capable of mitigating the vibrations of nonlinear systems which are known to exhibit frequency-energy-dependent oscillations. A nonlinear generalization of Den Hartog's equal-peak method is proposed to ensure equal...
Nonlinear auto-adjusting iterative reconstruction technique for interferometric tomography
Song, Yizhong; Sun, Tao; Qu, Peishu
2013-07-01
A new algebraic reconstruction technique (ART), nonlinear auto-adjusting iterative reconstruction technique (NAIRT), is proposed and applied to reconstruct a section of an actual thermal air flow field. With numerical simulation, NAIRT was tested to reconstruct a complicated field to demonstrate its superior reconstructive capability. In contrast, three typical ARTs, the basic ART, simultaneous ART (SART), and a modified SART (MSART), were simulated to demonstrate the reconstructive capability improvement attained through the use of the proposed NAIRT. The calculated results were discussed with mean square error (MSE) and peak error (PE). A thermal air flow field was produced with an alcohol burner and was detected by a laser beam. With laser beam projections, a cross-section of the field was reconstructed by NAIRT. As a result, the reconstructive capability was improved much by NAIRT. The MSE decreased by 95.5%, and PE by 97.2% from that of the basic ART. Only NAIRT converged without filters while its reconstructive accuracy improved. By increasing the projections from 42 to 84, the accuracy of NAIRT without filters was improved significantly. NAIRT could effectively reconstruct the section of the thermal field. The proposed NAIRT needed no filter for its convergence and it had the highest reconstructive accuracy and simplest iterative expression of those analyzed.
Uniform Stability of Damped Nonlinear Vibrations of an Elastic String
Indian Academy of Sciences (India)
Ganesh C Gorain; Sujit K Bose
2003-11-01
Here we are concerned about uniform stability of damped nonlinear transverse vibrations of an elastic string fixed at its two ends. The vibrations governed by nonlinear integro-differential equation of Kirchoff type, is shown to possess energy uniformly bounded by exponentially decaying function of time. The result is achieved by considering an energy-like Lyapunov functional for the system.
Analytical Evaluation of the Nonlinear Vibration of Coupled Oscillator Systems
DEFF Research Database (Denmark)
Bayat, M.; Shahidi, M.; Barari, Amin
2011-01-01
We consider periodic solutions for nonlinear free vibration of conservative, coupled mass-spring systems with linear and nonlinear stiffnesses. Two practical cases of these systems are explained and introduced. An analytical technique called energy balance method (EBM) was applied to calculate ap...... accuracy which is valid for a wide range of vibration amplitudes as indicated in the presented examples.......We consider periodic solutions for nonlinear free vibration of conservative, coupled mass-spring systems with linear and nonlinear stiffnesses. Two practical cases of these systems are explained and introduced. An analytical technique called energy balance method (EBM) was applied to calculate...
A principle of similarity for nonlinear vibration absorbers
Habib, G.; Kerschen, G.
2016-10-01
This paper develops a principle of similarity for the design of a nonlinear absorber, the nonlinear tuned vibration absorber (NLTVA), attached to a nonlinear primary system. Specifically, for effective vibration mitigation, we show that the NLTVA should feature a nonlinearity possessing the same mathematical form as that of the primary system. A compact analytical formula for the nonlinear coefficient of the absorber is then derived. The formula, valid for any polynomial nonlinearity in the primary system, is found to depend only on the mass ratio and on the nonlinear coefficient of the primary system. When the primary system comprises several polynomial nonlinearities, we demonstrate that the NLTVA obeys a principle of additivity, i.e., each nonlinear coefficient can be calculated independently of the other nonlinear coefficients using the proposed formula.
Identification of the nonlinear vibration system of power transformers
Jing, Zheng; Hai, Huang; Pan, Jie; Yanni, Zhang
2017-01-01
This paper focuses on the identification of the nonlinear vibration system of power transformers. A Hammerstein model is used to identify the system with electrical inputs and the vibration of the transformer tank as the output. The nonlinear property of the system is modelled using a Fourier neural network consisting of a nonlinear element and a linear dynamic block. The order and weights of the network are determined based on the Lipschitz criterion and the back-propagation algorithm. This system identification method is tested on several power transformers. Promising results for predicting the transformer vibration and extracting system parameters are presented and discussed.
Practical design of a nonlinear tuned vibration absorber
DEFF Research Database (Denmark)
Grappasonni, C.; Habib, G.; Detroux, T.
2014-01-01
The aim of the paper is to develop a new nonlinear tuned vibration absorber (NLTVA) capable of mitigating the vibrations of nonlinear systems which are known to exhibit frequency-energy-dependent oscillations. A nonlinear generalization of Den Hartog's equal-peak method is proposed to ensure equal...... peaks in the nonlinear frequency response for a large range of forcing amplitudes. An analytical tuning procedure is developed and provides the load-deflection characteristic of the NLTVA. Based on this prescribed relation, the NLTVA design is performed by two different approaches, namely thanks to (i...
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 ...
Nonlinear vibrations and stability of aerostatic bearing
Directory of Open Access Journals (Sweden)
Kozánek J.
2008-12-01
Full Text Available Bearings based on aerostatic principle belong to the new machine elements advantageous for low- and high-speed applications, but their dynamic and stability properties are not yet sufficiently known. This paper presents a new elaborated method and gained results of theoretical investigation of dynamic properties of aerostatic bearing in general dimensionless form. It is aimed also as a supporting tool for diagnostic and identification methods used at developing of new bearings proposed by TECHLAB, Prague for industrial applications. Mathematical model expresses nonlinear and evolutive properties in the entire area of bearing clearance, contains sufficient number of free parameters in functions of restoring and damping forces and can therefore describe all types of motions occurring in gas bearings as periodic, quasi-periodic, including beats and instability, which can leads to chaotic and self-excited vibrations. The influence of non-diagonal elements of stiffness and damping matrices of linearized model on the spectral properties and the stability of system is investigated, too.
Nonlinear Vibrations of Timoshenko Beams with Various Boundary Conditions
Institute of Scientific and Technical Information of China (English)
郭强; 刘曦; 钟宏志
2004-01-01
This paper is concerned with the effects of boundary conditions on the large-amplitude free vibrations of Timoshenko beams. The effects of nonlinear terms on the frequency of Timoshenko beams with simply supported ends (supported-supported, SS), clamped ends (clamped-clamped, CC) and one end simply supported and the other end clamped (clamped-supported, CS) are discussed in detail. Given a specific vibration amplitude, the change of nonlinear frequency according to the effects of boundary conditions is always in the following descending order: SS, CS, and CC. It is found that the slenderness ratio has a significant influence on the nonlinear frequency. For slender beams, the nonlinear effects of bending curvature and shear strain are negligible regardless of the boundary conditions. For short beams and especially for those of large amplitude vibrations, however, the nonlinear effects of bending curvature and shear strain become noticeable in the following ascending order: SS, CS, and CC.
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.
Liquid viscosity sensing using nonlinear vibration of a fiberoptic sensor.
Wang, Wei-Chih; Liu, Chao-Shih
2013-07-01
This paper investigates the nonlinear dynamic motion of a vibrating optical fiber viscosity sensor through representative cases of primary and super-harmonic resonance. The results show that a nonlinear effect drastically improves the sensitivity of the viscosity measurement by nearly an order of magnitude from the previously developed linear systems. Experimental results and several applications of the viscosity sensor are also presented.
Nonlinear vibration absorption for a flexible arm via a virtual vibration absorber
Bian, Yushu; Gao, Zhihui
2017-07-01
A semi-active vibration absorption method is put forward to attenuate nonlinear vibration of a flexible arm based on the internal resonance. To maintain the 2:1 internal resonance condition and the desirable damping characteristic, a virtual vibration absorber is suggested. It is mathematically equivalent to a vibration absorber but its frequency and damping coefficients can be readily adjusted by simple control algorithms, thereby replacing those hard-to-implement mechanical designs. Through theoretical analyses and numerical simulations, it is proven that the internal resonance can be successfully established for the flexible arm, and the vibrational energy of flexible arm can be transferred to and dissipated by the virtual vibration absorber. Finally, experimental results are presented to validate the theoretical predictions. Since the proposed method absorbs rather than suppresses vibrational energy of the primary system, it is more convenient to reduce strong vibration than conventional active vibration suppression methods based on smart material actuators with limited energy output. Furthermore, since it aims to establish an internal vibrational energy transfer channel from the primary system to the vibration absorber rather than directly respond to external excitations, it is especially applicable for attenuating nonlinear vibration excited by unpredictable excitations.
Free-vibration acoustic resonance of a nonlinear elastic bar
Tarumi, Ryuichi; Oshita, Yoshihito
2011-02-01
Free-vibration acoustic resonance of a one-dimensional nonlinear elastic bar was investigated by direct analysis in the calculus of variations. The Lagrangian density of the bar includes a cubic term of the deformation gradient, which is responsible for both geometric and constitutive nonlinearities. By expanding the deformation function into a complex Fourier series, we derived the action integral in an analytic form and evaluated its stationary conditions numerically with the Ritz method for the first three resonant vibration modes. This revealed that the bar shows the following prominent nonlinear features: (i) amplitude dependence of the resonance frequency; (ii) symmetry breaking in the vibration pattern; and (iii) excitation of the high-frequency mode around nodal-like points. Stability of the resonant vibrations was also addressed in terms of a convex condition on the strain energy density.
Nonlinear vibration behaviors of casing pipe in the deep water
Tang, You-Gang; Zhang, Su-Xia; Yi, Cong
2006-10-01
The vortex-induced nonlinear vibration of casing pipes in the deep water was investigated considering the loads of current and combined wave-current. The vortex-induced vibration equation of a casing pipe was set up with considering the beam mode and Morison's nonlinear fluid loads as well as the vortex-excited loads. The approach of calculating vortex-excited nonlinear vibration by Galerkin's method was proposed. The natural vibration frequencies and modes were obtained, and the response including primary resonance induced by current and the composite resonance under combined wave-current for the 170 m long casing pipe in the 160 m depth of water were investigated. The results show that the dynamics response of casing pipe obviously increases, and the complicated response behaviors of casing pipe are described under combined wave-current.
Vibration Analysis of Timoshenko Beams on a Nonlinear Elastic Foundation
Institute of Scientific and Technical Information of China (English)
MO Yihua; OU Li; ZHONG Hongzhi
2009-01-01
The vibrations of beams on a nonlinear elastic foundation were analyzed considering the effects of transverse shear deformation and the rotational inertia of beams. A weak form quadrature element method (QEM) is used for the vibration analysis. The fundamental frequencies of beams are presented for various slenderness ratios and nonlinear foundation parameters for both slender and short beams. The results for slender beams compare well with finite element results. The analysis shows that the transverse shear de-formation and the nonlinear foundation parameter significantly affect the fundamental frequency of the beams.
Background-Free Nonlinear Microspectroscopy with Vibrational Molecular Interferometry
Garbacik, Erik T.; Korterik, Jeroen P.; Otto, Cees; Mukamel, Shaul; Herek, Jennifer L.; Offerhaus, Herman L.
2013-01-01
We demonstrate a method for performing nonlinear microspectroscopy that provides an intuitive and unified description of the various signal contributions, and allows the direct extraction of the vibrational response. Three optical fields create a pair of Stokes Raman pathways that interfere in the same vibrational state. Frequency modulating one of the fields leads to amplitude modulations on all of the fields. This vibrational molecular interferometry technique allows imaging at high speed free of nonresonant background, and is able to distinguish between electronic and vibrational contributions to the total signal. PMID:22243075
Nonlinear vibration of corrugated shallow shells under Uniform load
Institute of Scientific and Technical Information of China (English)
YUAN Hong; LIU Ren-huai
2007-01-01
Based on the large deflection dynamic equations of axisymmetric shallow shells of revolution,the nonlinear forced vibration of a corrugated shallow shell under uniform load is investigated.The nonlinear partial differential equations of shallow shell are reduced to the nonlinear integral-differential equations by the method of Green's function. To solve the integral-differential equations,expansion method is used to obtain Green's function.Then the integral-differential equations are reduced to the form with degenerate core by expanding Green's function as series of characteristic function.Therefore,the integral-differential equations become nonlinear ordinary differential equations with regard to time. The amplitude-frequency response under harmonic for is obtained by considering single mode vibration.As a numerical example,forced vibration phenomena of shallow spherical shells with sinusoidal corrugation are studied.The obtained solutions are available for reference to design of corrugated shells
Parameter Identification of Weakly Nonlinear Vibration System in Frequency Domain
Directory of Open Access Journals (Sweden)
Jiehua Peng
2004-01-01
Full Text Available A new method of identifying parameters of nonlinearly vibrating system in frequency domain is presented in this paper. The problems of parameter identification of the nonlinear dynamic system with nonlinear elastic force or nonlinear damping force are discussed. In the method, the mathematic model of parameter identification is frequency response function. Firstly, by means of perturbation method the frequency response function of weakly nonlinear vibration system is derived. Next, a parameter transformation is made and the frequency response function becomes a linear function of the new parameters. Then, based on this function and with the least square method, physical parameters of the system are identified. Finally, the applicability of the proposed technique is confirmed by numerical simulation.
Vibration measurement with nonlinear converter in the presence of noise
Mozuras, Almantas
2017-10-01
Conventional vibration measurement methods use the linear properties of physical converters. These methods are strongly influenced by nonlinear distortions, because ideal linear converters are not available. Practically, any converter can be considered as a linear one, when an output signal is very small. However, the influence of noise increases significantly and signal-to-noise ratio decreases at lower signals. When the output signal is increasing, the nonlinear distortions are also augmenting. If the wide spectrum vibration is measured, conventional methods face a harmonic distortion as well as intermodulation effects. Purpose of this research is to develop a measurement method of wide spectrum vibration by using a converter described by a nonlinear function of type f(x), where x =x(t) denotes the dependence of coordinate x on time t due to the vibration. Parameter x(t) describing the vibration is expressed as Fourier series. The spectral components of the converter output f(x(t)) are determined by using Fourier transform. The obtained system of nonlinear equations is solved using the least squares technique that permits to find x(t) in the presence of noise. This method allows one to carry out the absolute or relative vibration measurements. High resistance to noise is typical for the absolute vibration measurement, but it is necessary to know the Taylor expansion coefficients of the function f(x). If the Taylor expansion is not known, the relative measurement of vibration parameters is also possible, but with lower resistance to noise. This method allows one to eliminate the influence of nonlinear distortions to the measurement results, and consequently to eliminate harmonic distortion and intermodulation effects. The use of nonlinear properties of the converter for measurement gives some advantages related to an increased frequency range of the output signal (consequently increasing the number of equations) that allows one to decrease the noise influence on
Nonlinear Vibration of Oscillation Systems using Frequency-Amplitude Formulation
Directory of Open Access Journals (Sweden)
A. Fereidoon
2012-01-01
Full Text Available In this paper we study the periodic solutions of free vibration of mechanical systems with third and fifth-order nonlinearity for two examples using He's Frequency-Amplitude Formulation (HFAF.The effectiveness and convenience of the method is illustrated in these examples. It will be shown that the solutions obtained with current method have a fabulous conformity with those achieved from time marching solution. HFAF is easy with powerful concepts and the high accuracy, so it can be found widely applicable in vibrations, especially strong nonlinearity oscillatory problems.
Confinement of Vibrations in Variable-Geometry Nonlinear Flexible Beam
Directory of Open Access Journals (Sweden)
W. Gafsi
2014-01-01
Full Text Available In this paper, we propose a novel strategy for controlling a flexible nonlinear beam with the confinement of vibrations. We focus principally on design issues related to the passive control of the beam by proper selection of its geometrical and physical parameters. Due to large deflections within the regions where the vibrations are to be confined, we admit a nonlinear model that describes with precision the beam dynamics. In order to design a set of physical and geometrical parameters of the beam, we first formulate an inverse eigenvalue problem. To this end, we linearize the beam model and determine the linearly assumed modes that guarantee vibration confinement in selected spatial zones and satisfy the boundary conditions of the beam to be controlled. The approximation of the physical and geometrical parameters is based on the orthogonality of the assumed linear mode shapes. To validate the strategy, we input the resulting parameters into the nonlinear integral-partial differential equation that describes the beam dynamics. The nonlinear frequency response curves of the beam are approximated using the differential quadrature method and the finite difference method. We confirm that using the linear model, the strategy of vibration confinement remains valid for the nonlinear beam.
Approximate Series Solutions for Nonlinear Free Vibration of Suspended Cables
Directory of Open Access Journals (Sweden)
Yaobing Zhao
2014-01-01
Full Text Available This paper presents approximate series solutions for nonlinear free vibration of suspended cables via the Lindstedt-Poincare method and homotopy analysis method, respectively. Firstly, taking into account the geometric nonlinearity of the suspended cable as well as the quasi-static assumption, a mathematical model is presented. Secondly, two analytical methods are introduced to obtain the approximate series solutions in the case of nonlinear free vibration. Moreover, small and large sag-to-span ratios and initial conditions are chosen to study the nonlinear dynamic responses by these two analytical methods. The numerical results indicate that frequency amplitude relationships obtained with different analytical approaches exhibit some quantitative and qualitative differences in the cases of motions, mode shapes, and particular sag-to-span ratios. Finally, a detailed comparison of the differences in the displacement fields and cable axial total tensions is made.
Lindner, D. K.; Zvonar, G. A.; Baumann, W. T.; Delos, P. L.
1993-01-01
Recently, a modal domain optical fiber sensor has been demonstrated as a sensor in a control system for vibration suppression of a flexible cantilevered beam. This sensor responds to strain through a mechanical attachment to the structure. Because this sensor is of the interferometric type, the output of the sensor has a sinusoidal nonlinearity. For small levels of strain, the sensor can be operated in its linear region. For large levels of strain, the detection electronics can be configured to count fringes. In both of these configurations, the sensor nonlinearity imposes some restrictions on the performance of the control system. In this paper we investigate the effects of these sensor nonlinearities on the control system, and identify the region of linear operation in terms of the optical fiber sensor parameters.
Non-Linear Vibration of Euler-Bernoulli Beams
DEFF Research Database (Denmark)
Barari, Amin; Kaliji, H. D.; Domairry, G.
2011-01-01
In this paper, variational iteration (VIM) and parametrized perturbation (PPM)methods have been used to investigate non-linear vibration of Euler-Bernoulli beams subjected to the axial loads. The proposed methods do not require small parameter in the equation which is difficult to be found for no...... for nonlinear problems. Comparison of VIM and PPM with Runge-Kutta 4th leads to highly accurate solutions....
NONLINEARLY VIBRATIONAL ENERGY-SPECTRA OF MOLECULAR CRYSTALS
Institute of Scientific and Technical Information of China (English)
PANG XIAO-FENG; CHEN XIANG-RONG
2000-01-01
The nonlinear quantum vibrational energy spectra of amide-I in the molecular crystals acetanilide are calculatedby using the discrete nonlinear Schrodinger equation appropriate to this kind of crystals. The numerical results obtainedby this method are in good agreement with the experimental values. Meanwhile, the energy levels at high excited stateshave also been obtained for the acetanilide, which is helpful in researching the Raman scattering and infrared absorptionproperties of the this kind of crystals.
Non-Linear Vibration of Euler-Bernoulli Beams
DEFF Research Database (Denmark)
Barari, Amin; Kaliji, H. D.; Domairry, G.
2011-01-01
In this paper, variational iteration (VIM) and parametrized perturbation (PPM)methods have been used to investigate non-linear vibration of Euler-Bernoulli beams subjected to the axial loads. The proposed methods do not require small parameter in the equation which is difficult to be found...
Background-free nonlinear microspectroscopy with vibrational molecular interferometry
Garbacik, E.T.; Korterik, Jeroen P.; Otto, Cornelis; Mukamel, S.; Herek, Jennifer Lynn; Offerhaus, Herman L.; Periasamy, A.; König, K.; So, P.T.C.
2012-01-01
We demonstrate a method for performing nonlinear microspectroscopy that provides an intuitive and unified description of the various signal contributions, and allows the direct extraction of the vibrational response. Three optical fields create a pair of Stokes Raman pathways that interfere in the
Background-Free Nonlinear Microspectroscopy with Vibrational Molecular Interferometry
Garbacik, Erik T.; Korterik, Jeroen P.; Otto, Cees; Mukamel, Shaul; Herek, Jennifer L.; Offerhaus, Herman L.
2011-01-01
We demonstrate a method for performing nonlinear microspectroscopy that provides an intuitive and unified description of the various signal contributions, and allows the direct extraction of the vibrational response. Three optical fields create a pair of Stokes Raman pathways that interfere in the s
Dynamic Analysis of Vibrating Systems with Nonlinearities
M. Kalami, Yazdi; Ahmadian, H.; Mirzabeigy, A.; Yildirim, A.
2012-02-01
The max-min approach is applied to mathematical models of some nonlinear oscillations. The models are regarding to three different forms that are governed by nonlinear ordinary differential equations. In this context, the strongly nonlinear Duffing oscillator with third, fifth, and seventh powers of the amplitude, the pendulum attached to a rotating rigid frame and the cubic Duffing oscillator with discontinuity are taken into consideration. The obtained results via the approach are compared with ones achieved utilizing other techniques. The results indicate that the approach has a good agreement with other well-known methods. He's max-min approach is a promising technique and can be successfully exerted to a lot of practical engineering and physical problems.
Periodic solutions of nonlinear vibrating beams
Directory of Open Access Journals (Sweden)
J. Berkovits
2003-01-01
Full Text Available The aim of this paper is to prove new existence and multiplicity results for periodic semilinear beam equation with a nonlinear time-independent perturbation in case the period is not prescribed. Since the spectrum of the linear part varies with the period, the solvability of the equation depends crucially on the period which can be chosen as a free parameter. Since the period of the external forcing is generally unknown a priori, we consider the following natural problem. For a given time-independent nonlinearity, find periods T for which the equation is solvable for any T-periodic forcing. We will also deal with the existence of multiple solutions when the nonlinearity interacts with the spectrum of the linear part. We show that under certain conditions multiple solutions do exist for any small forcing term with suitable period T. The results are obtained via generalized Leray-Schauder degree and reductions to invariant subspaces.
NONLINEAR VIBRATION OF CIRCULAR SANDWICH PLATES UNDER CIRCUMJACENT LOAD
Institute of Scientific and Technical Information of China (English)
DU Guo-jun; MA Jian-qing
2006-01-01
Based on yon Karman plate theory, the issue about nonlinear vibration for circular sandwich plates under circumjacent load with the loosely clamped boundary condition was researched. Nonlinear differential eigenvalue equations and boundary conditions of the problem were formulated by variational method and then their exact static solution can be got. The solution was derived by modified iteration method, so the anslytic relations between amplitude and nonlinear oscillating frequency for circular sandwich plates were obtained. When circumjacent load makes the lowest natural frequency zero,critical load is obtained.
NONLINEAR DYNAMICAL CHARACTERISTICS OF PILES UNDER HORIZONTAL VIBRATION
Institute of Scientific and Technical Information of China (English)
HU Yu-jia; CHENG Chang-jun; YANG Xiao
2005-01-01
The pile-soil system is regarded as a visco-elastic half-space embedded pile. Based on the method of continuum mechanics, a nonlinear mathematical model of pilesoil interaction was established-a coupling nonlinear boundary value problem. Under the case of horizontal vibration, the nonlinearly dynamical characteristics of pile applying the axis force were studied in horizontal direction in frequency domain. The effects of parameters, especially the axis force on the stiffness were studied in detail. The numerical results suggest that it is possible that the pile applying an axis force will lose its stability. So, the effect of the axis force on the pile is considered.
Nonlinear random vibration experimental results and research needs
Ibrahim, R. A.
Experimental investigations of random excitation of dynamic systems are valuable but scarce. They are particularly important for nonlinear random vibration, since different approaches can lead to different results for the same problem. They are also useful in providing physical insight into a number of complex dynamic phenomena. The scarcity of random vibration testing is mainly due to a number of difficulties and errors encountered in generating the correct random excitation, and data acquisition. The purpose of this review article is to assess the recent experimental results reported in the literature by the author and others. An attempt will be made to correlate the experimental measurements qualitatively with those predicted analytically. In most cases, no quantitative comparisons have been made. New research directions based on recent analytical and experimental developments in the theory of nonlinear random vibration will also be outlined.
Cigeroglu, Ender; Samandari, Hamed
2014-11-01
Nonlinear free vibration analysis of curved double-walled carbon nanotubes (DWNTs) embedded in an elastic medium is studied in this study. Nonlinearities considered are due to large deflection of carbon nanotubes (geometric nonlinearity) and nonlinear interlayer van der Waals forces between inner and outer tubes. The differential quadrature method (DQM) is utilized to discretize the partial differential equations of motion in spatial domain, which resulted in a nonlinear set of algebraic equations of motion. The effect of nonlinearities, different end conditions, initial curvature, and stiffness of the surrounding elastic medium, and vibrational modes on the nonlinear free vibration of DWCNTs is studied. Results show that it is possible to detect different vibration modes occurring at a single vibration frequency when CNTs vibrate in the out-of-phase vibration mode. Moreover, it is observed that boundary conditions have significant effect on the nonlinear natural frequencies of the DWCNT including multiple solutions.
Slegrová, Zuzana; Bálek, Rudolf
2005-03-01
This paper deals with the analysis of ultrasonic fields inside waveguides generated by ultrasonic waves of high amplitude. These waves behave nonlinearly, so it is not possible to use standard linear equations to describe their behaviour. Therefore, we started with an experimental determination of the acoustic pressure of air in glass tubes. We chose two methods of measurement--by a microphone and by an optical interferometric probe. The conventional method by a microphone creates numerous problems, which can be avoided by using an optical method, a heterodyne laser interferometer.
Nonlinear Forced Vibration Analysis for Thin Rectangular Plate on Nonlinear Elastic Foundation
Directory of Open Access Journals (Sweden)
Zhong Zhengqiang
2013-02-01
Full Text Available Nonlinear forced vibration is analyzed for thin rectangular plate with four free edges on nonlinear elastic foundation. Based on Hamilton variation principle, equations of nonlinear vibration motion for thin rectangular plate under harmonic loads on nonlinear elastic foundation are established. In the case of four free edges, viable expressions of trial functions for this specification are proposed, satisfying all boundary conditions. Then, equations are transformed to a system of nonlinear algebraic equations by using Galerkin method and are solved by using harmonic balance method. In the analysis of numerical computations, the effect on the amplitude-frequency characteristic curve due to change of the structural parameters of plate, parameters of foundation and parameters of excitation force are discussed.
Vibration suppression of speed-controlled robots with nonlinear control
Boscariol, Paolo; Gasparetto, Alessandro
2016-06-01
In this paper, a simple nonlinear control strategy for the simultaneous position tracking and vibration damping of robots is presented. The control is developed for devices actuated by speed-controlled servo drives. The conditions for the asymptotic stability of the closed-loop system are derived by ensuring its passivity. The capability of achieving improved trajectory tracking and vibration suppression is shown through experimental tests conducted on a three-axis Cartesian robot. The control is aimed to be compatible with most industrial applications given the simplicity of implementation, the reduced computational requirements, and the use of joint position as the only measured signal.
A Nonlinear Vortex Induced Vibration Model of Marine Risers
Institute of Scientific and Technical Information of China (English)
LIU Juan; HUANG Weiping
2013-01-01
With the exploitation of oil and gas in deep water,the traditional vortex induced vibration (VIV) theory is challenged by the unprecedented flexibility of risers.A nonlinear time-dependent VIV model is developed in this paper based on a VIV lift force model and the Morison equation.Both the inline vibration induced by the flow due to vortex shedding and the fluid-structure interaction in the transverse direction are included in the model.One of the characteristics of the model is the response-dependent lift force with nonlinear damping,which is different from other VIV models.The calculations show that the model can well describe the VIV of deepwater risers with the results agreeing with those calculated by other models.
Chaotic vibrations of tubes with nonlinear supports in crossflow
Energy Technology Data Exchange (ETDEWEB)
Cai, Y.; Chen, S.S.
1992-12-01
By means of the unsteady flow theory and a bilinear mathematical model, a theoretical study is presented for chaotic vibrations associated with the fluidelastic instability of nonlinearly supported tubes in a crossflow. A series of effective tools, including phase portraits, power spectral density, Poincar`e maps, Lyapunov exponent, fractal dimension, and bifurcation diagrams, are utilized to distinguish periodic and chaotic motions when the tubes vibrate in the instability region. Results show periodic and chaotic motions in the region corresponding to the fluid damping controlled instability. Nonlinear supports, with symmetric or asymmetric gaps, significantly affect the distributions of periodic, quasiperiodic and chaotic motions of the tube with various flow velocity in the instability region of the TSP(tube-support-plate)-inactive mode.
Chaotic vibrations of tubes with nonlinear supports in crossflow
Energy Technology Data Exchange (ETDEWEB)
Cai, Y.; Chen, S.S.
1992-01-01
By means of the unsteady flow theory and a bilinear mathematical model, a theoretical study is presented for chaotic vibrations associated with the fluidelastic instability of nonlinearly supported tubes in a crossflow. A series of effective tools, including phase portraits, power spectral density, Poincar'e maps, Lyapunov exponent, fractal dimension, and bifurcation diagrams, are utilized to distinguish periodic and chaotic motions when the tubes vibrate in the instability region. Results show periodic and chaotic motions in the region corresponding to the fluid damping controlled instability. Nonlinear supports, with symmetric or asymmetric gaps, significantly affect the distributions of periodic, quasiperiodic and chaotic motions of the tube with various flow velocity in the instability region of the TSP(tube-support-plate)-inactive mode.
Chaotic vibrations of nonlinearly supported tubes in crossflow
Energy Technology Data Exchange (ETDEWEB)
Cai, Y.; Chen, S.S.
1992-02-01
By means of the unsteady-flow theory and a bilinear mathematical model, a theoretical study is presented for chaotic vibrations associated with the fluidelastic instability of nonlinearly supported tubes in a crossflow. Effective tools, including phase portraits, power spectral density, Poincare maps, Lyapunov exponent, fractal dimension, and bifurcation diagrams, are utilized to distinguish periodic and chaotic motions when the tubes vibrate in the instability region. The results show periodic and chaotic motions in the region corresponding to fluid-damping-controlled instability. Nonlinear supports, with symmetric or asymmetric gaps, significantly affect the distribution of periodic, quasiperiodic, and chaotic motions of a tube exposed to various flow velocities in the instability region of the tube-support-plate-inactive mode.
Auto-identifying Diagnostic Symptom of Nonlinear Vibration
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
The technology of diagnostic symptom identification of nonlinear vibration is based on a database of a diagnostic case. This paper defines the periodic degree, quasi-periodic degree, and chaotic degree of a Poincare map, an iterated map, and adopts the image-identification theory, so the three states of periodic, quasi-periodic, and chaotic running states of a machine can be distinguished. It also defines the variable identity, rotating angle and spread degree. The database of diagnostic case is expressed by means of an access database. The diagnostic symptoms are identified using the difference between the Poincare maps of samples and the fault-case. Finally, we demonstrate an identification system of a nonlinear vibration diagnostic symptom of large rotating machinery.
Nonlinear Vibration Analysis of Moving Strip with Inertial Boundary Condition
Directory of Open Access Journals (Sweden)
Chong-yi Gao
2015-01-01
Full Text Available According to the movement mechanism of strip and rollers in tandem mill, the strip between two stands was simplified to axially moving Euler beam and the rollers were simplified to the inertial component on the fixed axis rotation, namely, inertial boundary. Nonlinear vibration mechanical model of Euler beam with inertial boundary conditions was established. The transverse and longitudinal motion equations were derived based on Hamilton’s principle. Kantorovich averaging method was employed to discretize the motion equations and the inertial boundary equations, and the solutions were obtained using the modified iteration method. Depending on numerical calculation, the amplitude-frequency responses of Euler beam were determined. The axial velocity, tension, and rotational inertia have strong influences on the vibration characteristics. The results would provide an important theoretical reference to control and analyze the vertical vibration of moving strip in continuous rolling process.
Stability Analysis of Nonlinear Vibrations of a Deploying Flexible Beam
Institute of Scientific and Technical Information of China (English)
JunfengLI; ZhaolinWANG
1996-01-01
Consider a rigid-flexible coupled system which consists of a central rigid body deploying a flexible appendage,The appendage is modeled as a finite deflection beam having linear constitutive equations.By taking the energy integral as Lyapunov function,it is proved that nonlinear transverse vibrations of the beam undergoing uniform extension or retrieval are stable when there are not controlling moment in the central rigid body and driving force on the beam,according to the partial stablity theorem.
Uncertainty propagation for nonlinear vibrations: A non-intrusive approach
Panunzio, A. M.; Salles, Loic; Schwingshackl, C. W.
2017-02-01
The propagation of uncertain input parameters in a linear dynamic analysis is reasonably well established today, but with the focus of the dynamic analysis shifting towards nonlinear systems, new approaches is required to compute the uncertain nonlinear responses. A combination of stochastic methods (Polynomial Chaos Expansion, PCE) with an Asymptotic Numerical Method (ANM) for the solution of the nonlinear dynamic systems is presented to predict the propagation of random input uncertainties and assess their influence on the nonlinear vibrational behaviour of a system. The proposed method allows the computation of stochastic resonance frequencies and peak amplitudes based on multiple input uncertainties, leading to a series of uncertain nonlinear dynamic responses. One of the main challenges when using the PCE is thereby the Gibbs phenomenon, which can heavily impact the resulting stochastic nonlinear response by introducing spurious oscillations. A novel technique to avoid the Gibbs phenomenon is be presented in this paper, leading to high quality frequency response predictions. A comparison of the proposed stochastic nonlinear analysis technique to traditional Monte Carlo simulations, demonstrates comparable accuracy at a significantly reduced computational cost, thereby validating the proposed approach.
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.
Homotopy analysis approach for nonlinear piezoelectric vibration energy harvesting
Directory of Open Access Journals (Sweden)
Shahlaei-Far Shahram
2016-01-01
Full Text Available Piezoelectric energy harvesting from a vertical geometrically nonlinear cantilever beam with a tip mass subject to transverse harmonic base excitations is analyzed. One piezoelectric patch is placed on the slender beam to convert the tension and compression into electrical voltage. Applying the homotopy analysis method to the coupled electromechanical governing equations, we derive analytical solutions for the horizontal displacement of the tip mass and consequently the output voltage from the piezoelectric patch. Analytical approximation for the frequency response and phase of the geometrically forced nonlinear vibration system are also obtained. The research aims at a rigorous analytical perspective on a nonlinear problem which has previously been solely investigated by numerical and experimental methods.
Asymptotic analysis of a vibrating cantilever with a nonlinear boundary
Institute of Scientific and Technical Information of China (English)
C.; W.; LIM
2009-01-01
Nonlinear vibration of a cantilever in a contact atomic force microscope is analyzed via an asymptotic approach. The asymptotic solution is sought for a beam equation with a nonlinear boundary condition. The steady-state responses are determined in primary resonance and subharmonic resonance. The relations between the response amplitudes and the excitation frequencies and amplitudes are derived from the solvability condition. Multivaluedness occurs in the relations as a consequence of the nonlinearity. The stability of steady-state responses is analyzed by use of the Lyapunov linearized stability theory. The stability analysis predicts the jumping phenomenon for certain parameters. The curves of the response amplitudes changing with the excitation frequencies are numerically compared with those obtained via the method of multiple scales. The calculation results demonstrate that the two methods predict the same varying tendencies while there are small quantitative differences.
Asymptotic analysis of a vibrating cantilever with a nonlinear boundary
Institute of Scientific and Technical Information of China (English)
CHEN LiQun; C.W.LIM; HU QingQuan; DING Hu
2009-01-01
Nonlinear vibration of a cantilever in a contact atomic force microscope is analyzed via an asymptotic approach.The asymptotic solution is sought for a beam equation with a nonlinear boundary condition.The steady-state responses are determined in primary resonance and subharmonic resonance.The relations between the response amplitudes and the excitation frequencies and amplitudes are derived from the solvability condition.Multivaluedness occurs in the relations as a consequence of the nonlinearity.The stability of steady-state responses is analyzed by use of the Lyapunov linearized sta-bility theory.The stability analysis predicts the jumping phenomenon for certain parameters.The curves of the response amplitudes changing with the excitation frequencies are numerically compared with those obtained via the method of multiple scales.The calculation results demonstrate that the two methods predict the same varying tendencies while there are small quantitative differences.
Asymptotic analysis of a vibrating cantilever with a nonlinear boundary
Chen, Liqun; Lim, C. W.; Hu, Qingquan; Ding, Hu
2009-09-01
Nonlinear vibration of a cantilever in a contact atomic force microscope is analyzed via an asymptotic approach. The asymptotic solution is sought for a beam equation with a nonlinear boundary condition. The steady-state responses are determined in primary resonance and subharmonic resonance. The relations between the response amplitudes and the excitation frequencies and amplitudes are derived from the solvability condition. Multivaluedness occurs in the relations as a consequence of the nonlinearity. The stability of steady-state responses is analyzed by use of the Lyapunov linearized stability theory. The stability analysis predicts the jumping phenomenon for certain parameters. The curves of the response amplitudes changing with the excitation frequencies are numerically compared with those obtained via the method of multiple scales. The calculation results demonstrate that the two methods predict the same varying tendencies while there are small quantitative differences.
Nonlinear vibration and rippling instability for embedded carbon nanotubes
Energy Technology Data Exchange (ETDEWEB)
Soltani, Payam; Mehdipour, I. [Islamic Azad University, Semnan (Iran, Islamic Republic of); Farshidianfar, A. [Ferdowsi University of Mashhad, Mashhad (Iran, Islamic Republic of); Ganji, D. D. [Babol University of Technology, Babol (Iran, Islamic Republic of)
2012-04-15
Based on the rippling deformations, a nonlinear continuum elastic model is developed to analyze the transverse vibration of single walled carbon nanotubes (SWCNTs) embedded on a Winkler elastic foundation. The nonlinear natural frequency has been derived analytically for typical boundary conditions using the perturbation method of multi-scales. The results indicate that the nonlinear resonant frequency due to the rippling is related to the stiffness of the foundation, the boundary conditions, the excitation load-to-damping ratio, and the diameter-to-length ratio. Moreover, the rippling instability of carbon nanotubes, as a structural instability, is introduced and the influences of several effective parameters on this kind of instability are widely discussed.
Parametric characteristic of the random vibration response of nonlinear systems
Institute of Scientific and Technical Information of China (English)
Xing-Jian Dong; Zhi-Ke Peng; Wen-Ming Zhang; Guang Meng; Fu-Lei Chu
2013-01-01
Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of non-linear engineering systems and structures that can be represented by a Volterra series model.In the present study,the random vibration of nonlinear systems is investigated using Volterra series.Analytical expressions were derived for the calculation of the output power spectral density (PSD) and input-output cross-PSD for nonlinear systems subjected to Gaussian excitation.Based on these expressions,it was revealed that both the output PSD and the input-output crossPSD can be expressed as polynomial functions of the nonlinear characteristic parameters or the input intensity.Numerical studies were carried out to verify the theoretical analysis result and to demonstrate the effectiveness of the derived relationship.The results reached in this study are of significance to the analysis and design of the nonlinear engineering systems and structures which can be represented by a Volterra series model.
Nonlinear dynamic modeling and resonance tuning of Galfenol vibration absorbers
Scheidler, Justin J.; Dapino, Marcelo J.
2013-08-01
This paper investigates the semi-active control of a magnetically-tunable vibration absorber’s resonance frequency. The vibration absorber that is considered is a metal-matrix composite containing the magnetostrictive material Galfenol (FeGa). A single degree of freedom model for the nonlinear vibration of the absorber is presented. The model is valid under arbitrary stress and magnetic field, and incorporates the variation in Galfenol’s elastic modulus throughout the composite as well as Galfenol’s asymmetric tension-compression behavior. Two boundary conditions—cantilevered and clamped-clamped—are imposed on the composite. The frequency response of the absorber to harmonic base excitation is calculated as a function of the operating conditions to determine the composite’s capacity for resonance tuning. The results show that nearly uniform controllability of the vibration absorber’s resonance frequency is possible below a threshold of the input power amplitude using weak magnetic fields of 0-8 kA m-1. Parametric studies are presented to characterize the effect on resonance tunability of Galfenol volume fraction and Galfenol location within the composite. The applicability of the results to composites of varying geometry and containing different Galfenol materials is discussed.
Nonlinear behavior of vibrating molecules on suspended graphene waveguides
Banerjee, Amrita
2015-01-01
Suspended graphene waveguides were deposited on micron-scale periodic metal (plasmonic) structures. Raman scattering of test molecules (B. Megaterium), deposited on the waveguides' surface, exhibited azimuthal cycles upon rotation: at these micron scales, spontaneous Raman ought to be independent of phase matching conditions. In addition, we observed angular-selective quadratic intensity dependence contrary to the typical linear behavior of spontaneous Raman. The effects were observed at very modest pump laser intensities (<10 MW/cm2 at the sample surface, oftenly used in Raman experiments). We attributed these observations to nonlinear coupling between the vibrating molecules and surface plasmon polariton (SPP) modes at the molecular vibration frequency. It was assessed that the polariton mode propagates through fairly long distances (over 100 microns).
Nonlinear thermoelectric properties of molecular junctions with vibrational coupling
DEFF Research Database (Denmark)
Leijnse, Martin Christian; Wegewijs, M. R.; Flensberg, Karsten
2010-01-01
We present a detailed study of the nonlinear thermoelectric properties of a molecular junction, represented by a dissipative Anderson-Holstein model. A single-orbital level with strong Coulomb interaction is coupled to a localized vibrational mode and we account for both electron and phonon...... exchange with both electrodes, investigating how these contribute to the heat and charge transports. We calculate the efficiency and power output of the device operated as a heat to electric power converter in the regime of weak tunnel coupling and phonon exchange rate and identify the optimal operating...... conditions, which are found to be qualitatively changed by the presence of the vibrational mode. Based on this study of a generic model system, we discuss the desirable properties of molecular junctions for thermoelectric applications....
Nonlinear vibrations of functionally graded doubly curved shallow shells
Alijani, F.; Amabili, M.; Karagiozis, K.; Bakhtiari-Nejad, F.
2011-03-01
Nonlinear forced vibrations of FGM doubly curved shallow shells with a rectangular base are investigated. Donnell's nonlinear shallow-shell theory is used and the shell is assumed to be simply supported with movable edges. The equations of motion are reduced using the Galerkin method to a system of infinite nonlinear ordinary differential equations with quadratic and cubic nonlinearities. Using the multiple scales method, primary and subharmonic resonance responses of FGM shells are fully discussed and the effect of volume fraction exponent on the internal resonance conditions, softening/hardening behavior and bifurcations of the shallow shell when the excitation frequency is (i) near the fundamental frequency and (ii) near two times the fundamental frequency is shown. Moreover, using a code based on arclength continuation method, a bifurcation analysis is carried out for a special case with two-to-one internal resonance between the first and second doubly symmetric modes with respect to the panel's center ( ω13≈2 ω11). Bifurcation diagrams and Poincaré maps are obtained through direct time integration of the equations of motion and chaotic regions are shown by calculating Lyapunov exponents and Lyapunov dimension.
Alippi, A.; Biagioni, A.; Germano, M.; Passeri, D.
2008-06-01
Local probing of nonlinear generation of harmonic vibrations has been done on bone plate samples and the evaluation of the nonlinear term is derived from a limited number of cases of bovine thigh bones, that shows that a low level of nonlinearity is present in bone structures. This is consistent with the assumption that in low level nonlinear samples the distribution of harmonic vibrations matches the corresponding power distribution of the fundamental mode.
Primarily nonlinear effects observed in a driven asymmetrical vibrating wire
Hanson, Roger J.; Macomber, H. Kent; Morrison, Andrew C.; Boucher, Matthew A.
2005-01-01
The purpose of the work reported here is to further experimentally explore the wide variety of behaviors exhibited by driven vibrating wires, primarily in the nonlinear regime. When the wire is driven near a resonant frequency, it is found that most such behaviors are significantly affected by the splitting of the resonant frequency and by the existence of a ``characteristic'' axis associated with each split frequency. It is shown that frequency splitting decreases with increasing wire tension and can be altered by twisting. Two methods are described for determining the orientation of characteristic axes. Evidence is provided, with a possible explanation, that each axis has the same orientation everywhere along the wire. Frequency response data exhibiting nonlinear generation of transverse motion perpendicular to the driving direction, hysteresis, linear generation of perpendicular motion (sometimes tubular), and generation of motion at harmonics of the driving frequency are exhibited and discussed. Also reported under seemingly unchanging conditions are abrupt large changes in the harmonic content of the motion that sometimes involve large subharmonics and harmonics thereof. Slow transitions from one stable state of vibration to another and quasiperiodic motions are also exhibited. Possible musical significance is discussed. .
On the nonlinear models of the vibrating string
Watzky, Alexandre
2005-09-01
Vibrations of strings (threads, wires, cables...) are of great interest because of their various domains of application. In musical acoustics, phenomena which could have been neglected elsewhere take a particular importance since perception, which is very sensitive to nonlinear effects, is involved. Some phenomena can also be emphasized when a string is coupled to a sound-radiating structure. Reliable physical models are thus necessary to account for these phenomena, and to understand the true behavior of a vibrating string. Despite the fact that the first nonlinear models were published more than one century ago, and that accurate equations of motion can be naturally achieved within a finite displacement continuum mechanics framework, general models never received the attention they deserved, most authors focusing on particular phenomena and often settling on approximate models. This can be explained by the awkward multiplicity of the involved phenomena. The aim of this presentation is to discuss the consequences of some common assumptions and the true nature of some observed couplings. Particular attention will be paid to the preponderance of the spatial shape of the modes, which are usually underestimated with respect to their temporal form.
SOME PROBLEMS CONCERNING FREE NON-LINEAR VIBRATIONS OF BEAM STRUCTURES
Directory of Open Access Journals (Sweden)
S. V. Bosakov
2008-01-01
Full Text Available The paper analyzes an influence of physical non-linearity material account on vibrations of single beams with various support fixing. The authors also analyze power criteria for existing stable periodic vibrations and dependence of vibration period on initial power is determined in the paper. Accurate values of an amplitude and non-linear bending vibration period of beams have been also determined as a conservative system with due account of initial conditions. A number of examples are given that clearly illustrate the obtained solutions and show an influence rate of the mentioned effects on amplitude-frequency characteristics of non-linear systems.
Nonlinear vibrational spectroscopy of surfactants at liquid interfaces
Energy Technology Data Exchange (ETDEWEB)
Miranda, Paulo B. [Univ. of California, Berkeley, CA (United States)
1998-12-14
Surfactants are widely used to modify physical and chemical properties of interfaces. They play an important role in many technological problems. Surfactant monolayer are also of great scientific interest because they are two-dimensional systems that may exhibit a very rich phase transition behavior and can also be considered as a model system for biological interfaces. In this Thesis, we use a second-order nonlinear optical technique (Sum-Frequency Generation - SFG) to obtain vibrational spectra of surfactant monolayer at Iiquidhapor and solid/liquid interfaces. The technique has several advantages: it is intrinsically surface-specific, can be applied to buried interfaces, has submonolayer sensitivity and is remarkably sensitive to the confirmational order of surfactant monolayers.
Nonlinear analysis on the coupling process of electromagnetic vibrator and earth
Institute of Scientific and Technical Information of China (English)
CHEN; Zubin; TENG; Jiwen; LIN; Jun; ZHANG; Linhang; JIANG
2005-01-01
The linear model based on the hydraulic pressure vibrator has been no longer adaptable to the electromagnetic vibrator. In order to realize the effective transmission of the limited energy from the vibrator to the ground, it is important to study the coupling model of the electromagnetic vibrator and the earth. In this paper, a nonlinear restore term was introduced to the coupling model because of the existence of a large amount of harmonics in the vibrator baseplate. The nonlinear vibration analysis was applied to the model by the multiscale method. In the course of energy transmission from the vibrator to the ground, ultraharmonic resonance was used to explain the generation of harmonics. An improved scheme was advanced to select the cross correlation reference signal in the vibrator seismic exploration. Good application results were obtained in field experiments.
Non-linear analysis of vibrations of irregular plates
Lobitz, D. W.; Nayfeh, A. H.; Mook, D. T.
1977-01-01
A numerical perturbation method is used to investigate the forced vibrations of irregular plates. Nonlinear terms associated with the midplane stretching are retained in the analysis. The numerical part of the method involves the use of linear, finite element techniques to determine the free oscillation mode shapes and frequencies and to obtain the linear midplane stress resultants caused by the midplane stretching. Representing the solution as an expansion in terms of these linear mode shapes, these modes and the resultants are used to determine the equations governing the time-dependent coefficients of this expansion. These equations are solved by using the method of multiple scales. Specific solutions are given for the main-resonant vibrations of an elliptical plate in the presence of internal resonances. The results indicate that modes other than the driven mode can be drawn into the steady state response. Though the excitation is composed of a single harmonic, the response may not be periodic. Moreover, the particular types of responses that can occur are highly dependent on the mode being excited and are sensitive to small geometrical changes.
Nonlinear Vibrations of Multiwalled Carbon Nanotubes under Various Boundary Conditions
Directory of Open Access Journals (Sweden)
Hossein Aminikhah
2011-01-01
Full Text Available The present work deals with applying the homotopy perturbation method to the problem of the nonlinear oscillations of multiwalled carbon nanotubes embedded in an elastic medium under various boundary conditions. A multiple-beam model is utilized in which the governing equations of each layer are coupled with those of its adjacent ones via the van der Waals interlayer forces. The amplitude-frequency curves for large-amplitude vibrations of single-walled, double-walled, and triple-walled carbon nanotubes are obtained. The influences of some commonly used boundary conditions, changes in material constant of the surrounding elastic medium, and variations of the nanotubes geometrical parameters on the vibration characteristics of multiwalled carbon nanotubes are discussed. The comparison of the generated results with those from the open literature illustrates that the solutions obtained are of very high accuracy and clarifies the capability and the simplicity of the present method. It is worthwhile to say that the results generated are new and can be served as a benchmark for future works.
A 3D printed electromagnetic nonlinear vibration energy harvester
Constantinou, P.; Roy, S.
2016-09-01
A 3D printed electromagnetic vibration energy harvester is presented. The motion of the device is in-plane with the excitation vibrations, and this is enabled through the exploitation of a leaf isosceles trapezoidal flexural pivot topology. This topology is ideally suited for systems requiring restricted out-of-plane motion and benefits from being fabricated monolithically. This is achieved by 3D printing the topology with materials having a low flexural modulus. The presented system has a nonlinear softening spring response, as a result of designed magnetic force interactions. A discussion of fatigue performance is presented and it is suggested that whilst fabricating, the raster of the suspension element is printed perpendicular to the flexural direction and that the experienced stress is as low as possible during operation, to ensure longevity. A demonstrated power of ˜25 μW at 0.1 g is achieved and 2.9 mW is demonstrated at 1 g. The corresponding bandwidths reach up-to 4.5 Hz. The system’s corresponding power density of ˜0.48 mW cm-3 and normalised power integral density of 11.9 kg m-3 (at 1 g) are comparable to other in-plane systems found in the literature.
Nonlinear dynamic model for magnetically-tunable Galfenol vibration absorbers
Scheidler, Justin J.; Dapino, Marcelo J.
2013-03-01
This paper presents a single degree of freedom model for the nonlinear vibration of a metal-matrix composite manufactured by ultrasonic additive manufacturing that contains seamlessly embedded magnetostrictive Galfenol alloys (FeGa). The model is valid under arbitrary stress and magnetic field. Changes in the composite's natural frequency are quantified to assess its performance as a semi-active vibration absorber. The effects of Galfenol volume fraction and location within the composite on natural frequency are quantified. The bandwidth over which the composite's natural frequency can be tuned with a bias magnetic field is studied for varying displacement excitation amplitudes. The natural frequency is tunable for all excitation amplitudes considered, but the maximum tunability occurs below an excitation amplitude threshold of 1 × 10-6 m for the composite geometry considered. Natural frequency shifts between 6% and 50% are found as the Galfenol volume fraction varies from 25% to 100% when Galfenol is located at the composite neutral axis. At a modest 25% Galfenol by volume, the model shows that up to 15% shifts in composite resonance are possible through magnetic bias field modulation if Galfenol is embedded away from the composite midplane. As the Galfenol volume fraction and distance between Galfenol and composite midplane are increased, linear and quadratic increases in tunability result, respectively.
A method for regulating strong nonlinear vibration energy of the flexible arm
Yushu Bian; Ming Wang; Zhihui Gao; Baofeng Yuan; Ming Fan
2015-01-01
For an oscillating system, large amplitude indicates strong vibration energy. In this article, modal interaction is used as a useful means to regulate strong nonlinear vibration energy of the flexible arm undergoing rigid motion. A method is put forward to migrate and dissipate vibration energy based on modal interaction. By means of multiple-scale perturbation analysis, it is proven that internal resonance can be successfully established between modes of the flexible arm and the vibration ab...
Application of HPEM to investigate the response and stability of nonlinear problems in vibration
DEFF Research Database (Denmark)
Mohammadi, M.H.; Mohammadi, A.; Kimiaeifar, A.;
2010-01-01
In this work, a powerful analytical method, called He's Parameter Expanding Methods (HPEM) is used to obtain the exact solution of nonlinear problems in nonlinear vibration. In this work, the governing equation is obtained by using Lagrange method, then the nonlinear governing equation is solved...... and convenient for solving these problems....
The characters of nonlinear vibration in the two-dimensional discrete monoatomic lattice
Institute of Scientific and Technical Information of China (English)
XU Quan; TIAN Qiang
2005-01-01
The two-dimensional discrete monoatomic lattice is analyzed. Taking nearest-neighbor interaction into account, the characters of the nonlinear vibration in two-dimensional discrete monoatomic lattice are described by the two-dimensional cubic nonlinear Schrodinger equation. Considering the quartic nonlinear potential, the two-dimensional discrete-soliton trains and the solutions perturbed by the neck mode are presented.
Directory of Open Access Journals (Sweden)
Ye-Wei Zhang
2013-01-01
Full Text Available Nonlinear targeted energy transfer (TET is applied to suppress the excessive vibration of an axially moving string with transverse wind loads. The coupling dynamic equations used are modeled by a nonlinear energy sink (NES attached to the string to absorb vibrational energy. By a two-term Galerkin procedure, the equations are discretized, and the effects of vibration suppression by numerical methods are demonstrated. Results show that the NES can effectively suppress the vibration of the axially moving string with transverse wind loadings, thereby protecting the string from excessive movement.
Green laser interferometric metrology system with sub-nanometer periodic nonlinearity.
Zhao, Shijie; Wei, Haoyun; Zhu, Minhao; Li, Yan
2016-04-10
This paper describes the design and realization of a heterodyne laser interferometer system that is applicable to metrology comparison. In this research, an iodine-stabilized Nd:YAG laser at 532 nm served as the light source. Two spatially separated beams with different offset frequencies are generated by two acousto-optic modulators to prevent any source mixing and polarization leakage. The interferometry components are integrated to a monolithic prism to reduce the difficulty of the light path adjustment and to guarantee the measuring accuracy. The experimental results show there is a sub-nanometer periodic nonlinearity, which mainly results from the ghost reflection. Placed in a vacuum chamber, the interferometer is applicable for measuring comparison using a piezo nanopositioner and a precision translation stage. Finally, a commercial interferometer is calibrated with the interferometer system.
Chen, Shao-Tuan; Du, Sijun; Arroyo, Emmanuelle; Jia, Yu; Seshia, Ashwin
2017-10-01
This paper presents a novel application of utilising nonlinear air damping as a soft mechanical stopper to increase the shock reliability for microelectromechanical systems (MEMS) vibration energy harvesters. The theoretical framework for nonlinear air damping is constructed for MEMS vibration energy harvesters operating in different air pressure levels, and characterisation experiments are conducted to establish the relationship between air pressure and nonlinear air damping coefficient for rectangular cantilever MEMS micro cantilevers with different proof masses. Design guidelines on choosing the optimal air pressure level for different MEMS vibration energy harvesters based on the trade-off between harvestable energy and the device robustness are presented, and random excitation experiments are performed to verify the robustness of MEMS vibration energy harvesters with nonlinear air damping as soft stoppers to limit the maximum deflection distance and increase the shock reliability of the device.
A method for regulating strong nonlinear vibration energy of the flexible arm
Directory of Open Access Journals (Sweden)
Yushu Bian
2015-07-01
Full Text Available For an oscillating system, large amplitude indicates strong vibration energy. In this article, modal interaction is used as a useful means to regulate strong nonlinear vibration energy of the flexible arm undergoing rigid motion. A method is put forward to migrate and dissipate vibration energy based on modal interaction. By means of multiple-scale perturbation analysis, it is proven that internal resonance can be successfully established between modes of the flexible arm and the vibration absorber. Through examples and analyses, it is verified that this control method is effective in regulating strong vibration energy and can be used to suppress strong nonlinear vibration of the flexible arm undergoing rigid motion.
Robust Optimal Design of a Nonlinear Dynamic Vibration Absorber Combining Sensitivity Analysis
Directory of Open Access Journals (Sweden)
R.A. Borges
2010-01-01
Full Text Available Dynamic vibration absorbers are discrete devices developed in the beginning of the last century used to attenuate the vibrations of different engineering structures. They have been used in several engineering applications, such as ships, power lines, aeronautic structures, civil engineering constructions subjected to seismic induced excitations, compressor systems, etc. However, in the context of nonlinear dynamics, few works have been proposed regarding the robust optimal design of nonlinear dynamic vibration absorbers. In this paper, a robust optimization strategy combined with sensitivity analysis of systems incorporating nonlinear dynamic vibration absorbers is proposed. Although sensitivity analysis is a well known numerical technique, the main contribution intended for this study is its extension to nonlinear systems. Due to the numerical procedure used to solve the nonlinear equations, the sensitivities addressed herein are computed from the first-order finite-difference approximations. With the aim of increasing the efficiency of the nonlinear dynamic absorber into a frequency band of interest, and to augment the robustness of the optimal design, a robust optimization strategy combined with the previous sensitivities is addressed. After presenting the underlying theoretical foundations, the proposed robust design methodology is performed for a two degree-of-freedom system incorporating a nonlinear dynamic vibration absorber. Based on the obtained results, the usefulness of the proposed methodology is highlighted.
Sun, S. S.; Yildirim, T.; Wu, Jichu; Yang, J.; Du, H.; Zhang, S. W.; Li, W. H.
2017-09-01
In this work, a hybrid nonlinear magnetorheological elastomer (MRE) vibration absorber has been designed, theoretically investigated and experimentally verified. The proposed nonlinear MRE absorber has the dual advantages of a nonlinear force-displacement relationship and variable stiffness technology; the purpose for coupling these two technologies is to achieve a large broadband vibration absorber with controllable capability. To achieve a nonlinear stiffness in the device, two pairs of magnets move at a rotary angle against each other, and the theoretical nonlinear force-displacement relationship has been theoretically calculated. For the experimental investigation, the effects of base excitation, variable currents applied to the device (i.e. variable stiffness of the MRE) and semi-active control have been conducted to determine the enhanced broadband performance of the designed device. It was observed the device was able to change resonance frequency with the applied current; moreover, the hybrid nonlinear MRE absorber displayed a softening-type nonlinear response with clear discontinuous bifurcations observed. Furthermore, the performance of the device under a semi-active control algorithm displayed the optimal performance in attenuating the vibration from a primary system to the absorber over a large frequency bandwidth from 4 to 12 Hz. By coupling nonlinear stiffness attributes with variable stiffness MRE technology, the performance of a vibration absorber is substantially improved.
A study on the quintic nonlinear beam vibrations using asymptotic approximate approaches
Sedighi, Hamid M.; Shirazi, Kourosh H.; Attarzadeh, Mohammad A.
2013-10-01
This paper intends to promote the application of modern analytical approaches to the governing equation of transversely vibrating quintic nonlinear beams. Four new studied methods are Stiffness analytical approximation method, Homotopy Perturbation Method with an Auxiliary Term, Max-Min Approach (MMA) and Iteration Perturbation Method (IPM). The powerful analytical approaches are used to obtain the nonlinear frequency-amplitude relationship for dynamic behavior of vibrating beams with quintic nonlinearity. It is demonstrated that the first terms in series expansions of all methods are sufficient to obtain a highly accurate solution. Finally, a numerical example is conducted to verify the integrity of the asymptotic methods.
Zeveleanu, C.
1974-01-01
The insulation of nonlinear and random vibrations is considered for some ore preparing and sorting implements: rotary crushers, resonance screens, hammer mills, etc. The appearance of subharmonic vibrations is analyzed, and the conditions for their appearance are determined. A method is given for calculating the insulation of these vibrations by means of elastic elements made of rubber. The insulation of the random vibrations produced by Symons crushers is calculated by determining the transmissability and deformation of the insulation system for a narrow band random response.
Theoretical analysis on nonlinear vibration of fluid flow in single-walled carbon nanotube
Valipour, P.; Ghasemi, S. E.; Khosravani, Mohammad Reza; Ganji, D. D.
2016-09-01
In this study, the concept of nonlocal continuum theory is used to characterize the nonlinear vibration of an embedded single-walled carbon nanotube. The Pasternak-type model is employed to simulate the interaction of the SWNTs. The parameterized perturbation method is used to solve the corresponding nonlinear differential equation. The effects of the vibration amplitude, flow velocity, nonlocal parameter, and stiffness of the medium on the nonlinear frequency variation are presented. The result shows that by increasing the Winkler constant, the nonlinear frequency decreases, especially for low vibration amplitudes. In addition, it is resulted that influence of the nonlocal parameter is greater at higher flow velocities in comparison with lower flow velocities.
Energy Technology Data Exchange (ETDEWEB)
Dhote, Sharvari, E-mail: sharvari.dhote@mail.utoronto.ca; Zu, Jean; Zhu, Yang [Department of Mechanical and Industrial Engineering, University of Toronto, 5 King' s College Road, Toronto, Ontario M5S-3G8 (Canada)
2015-04-20
In this paper, a nonlinear wideband multi-mode piezoelectric vibration-based energy harvester (PVEH) is proposed based on a compliant orthoplanar spring (COPS), which has an advantage of providing multiple vibration modes at relatively low frequencies. The PVEH is made of a tri-leg COPS flexible structure, where three fixed-guided beams are capable of generating strong nonlinear oscillations under certain base excitation. A prototype harvester was fabricated and investigated through both finite-element analysis and experiments. The frequency response shows multiple resonance which corresponds to a hardening type of nonlinear resonance. By adding masses at different locations on the COPS structure, the first three vibration modes are brought close to each other, where the three hardening nonlinear resonances provide a wide bandwidth for the PVEH. The proposed PVEH has enhanced performance of the energy harvester in terms of a wide frequency bandwidth and a high-voltage output under base excitations.
Phonon mechanisms of nonlinear decay and dephasing of mesoscopic vibrational systems
Atalaya, Juan; Kenny, Thomas W.; Dykman, Mark I.
2015-03-01
The frequencies and the decay rates of mesoscopic oscillators depend on vibration amplitudes. Nonlinear decay has been seen recently in various nano- and micro-mechanical systems. Here we consider a microscopic mechanism of nonlinear decay, the nonlinear coupling of the vibrational mode of interest, for example, a flexural mode, to other vibrations. Typically, the modes of interest have low eigenfrequencies ω0. Their decay comes from the coupling to acoustic-phonon type vibrations with much higher frequency and density of states. Thus, nonlinear decay requires quartic anharmonic coupling or cubic anharmonicity in the higher order. We find the decay rate for the inverse lifetime of the involved phonons, which is determined by the internal nonlinearity and the boundary scattering, being either much larger or smaller than ω0. The results extend the thermo-elastic, Akhiezer, and Landau-Rumer decay theory to nonlinear decay of mesoscopic modes and make specific predictions on the temperature and frequency dependence of the decay rate for different types of systems. We show that nonlinear decay is invariably accompanied by dephasing. We also show that in nano-electro-mechanical systems the decay rate can be electrostatically controlled.
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The nonlinear dynamic behavior of a rubbing rotor system was studied with a mathematical model established with the eccentricity and interaction between bending and torsional vibrations taken into consideration.The nonlinear vibrational response of a rubbing rotor was analyzed using numerical integral,spectroscopic analysis and Poince mapping method,which made it possible to have better understanding of the vibrational characteristics of partial rubbing and complete circular rubbing rotors.The numerical results reveal the response of torsional vibration mainly takes a form of suporchronous motion,and its frequency decreases as the rotational speed increases when partial rubbing occurs,and the response of torsional vibration is synchronous when complete circular rubbing occurs.The comparison of the dynamics of rubbing rotors with and without the interaction between bending and torsional vibrations shows the interaction between bending and torsional vibrations advances the rotational speed,at which the response of bending vibration changes from a synchronous motion into a quasi-periodic motion,and the interaction between bending and torsional vibrations reduces stability of the rubbing rotor.
Method of Green’s function of nonlinear vibration of corrugated shallow shells
Institute of Scientific and Technical Information of China (English)
2008-01-01
Based on the dynamic equations of nonlinear large deflection of axisymmetric shallow shells of revolution, the nonlinear free vibration and forced vibration of a corrugated shallow shell under concentrated load acting at the center have been investigated. The nonlinear partial differential equations of shallow shell were re-duced to the nonlinear integral-differential equations by using the method of Green’s function. To solve the integral-differential equations, the expansion method was used to obtain Green’s function. Then the integral-differential equations were reduced to the form with a degenerate core by expanding Green’s function as a series of characteristic function. Therefore, the integral-differential equations be-came nonlinear ordinary differential equations with regard to time. The ampli-tude-frequency relation, with respect to the natural frequency of the lowest order and the amplitude-frequency response under harmonic force, were obtained by considering single mode vibration. As a numerical example, nonlinear free and forced vibration phenomena of shallow spherical shells with sinusoidal corrugation were studied. The obtained solutions are available for reference to the design of corrugated shells.
Method of Green's function of nonlinear vibration of corrugated shallow shells
Institute of Scientific and Technical Information of China (English)
YUAN Hong
2008-01-01
Based on the dynamic equations of nonlinear large deflection of axisymmetric shallow shells of revolution,the nonlinear free vibration and forced vibration of a corrugated shallow shell under concentrated load acting at the center have been investigated.The nonlinear partial differential equations of shallow shell were re-duced to the nonlinear integral-differential equations by using the method of Green's function.To solve the integral-differential equations,the expansion method was used to obtain Green's function.Then the integral-differential equations were reduced to the form with a degenerate core by expanding Green's function as a series of characteristic function.Therefore,the integral-differential equations be-came nonlinear ordinary differential equations with regard to time.The ampli-tude-frequency relation,with respect to the natural frequency of the lowest order and the amplitude-frequency response under harmonic force,were obtained by considering single mode vibration.As a numerical example,nonlinear free and forced vibration phenomena of shallow spherical shells with sinusoidal corrugation were studied.The obtained solutions are available for reference to the design of corrugated shells.
The Axial Nonlinear Vibration Analysis of Ball-screw about Machine Tool Feeding System
Institute of Scientific and Technical Information of China (English)
ZENG Hao-ran; LIU Nian-cong; YANG Jia-rui; CHEN Jian-long; GENG Wei-tao
2016-01-01
The forced state of the ball⁃screw of machine tool feeding system is analyzed. The ball⁃screw is simplified as Timoshenko beam and the differential equation of motion for the ball⁃screw is built. To obtain the axial vibration equation, the differential equation of motion is simplified using the assumed mode method. Axial vibration equation is in form of Duffing equation and has the characteristics of nonlinearity. The numerical simulation of Duffing equation is proceeded by MATLAB/Simulink. The effect of screw length, exciting force and damping coefficient are researched, and the axial vibration phase track diagram and Poincare section are obtained. The stability and period of the axial vibration are analyzed. The limit cycle of phase track diagram is enclosed. Axial vibration has two type⁃center singularity distributions on both sides of the origin. The singularity attracts vibration to reach a stable state, and Poincare section shows that axial vibration appears chaotic motion and quasi periodic motion or periodic motion. Singularity position changes with the vibration system parameters, while the distribution doesn′t change. The period of the vibration is enhanced with increasing frequency and damping coefficient. Test of the feeding system ball⁃screw axial vibration exists chaos movement. This paper provides a certain theoretical basis for the dynamic characteristic analysis of machine feeding system ball⁃screw and optimization of structural parameters.
Zhu, H.; Shan, G. C.; Shek, C. H.; Lee, J. E.-Y.
2012-07-01
The frequency response of a single crystal silicon resonator under nonlinear vibration is investigated and related to the shear property of the material. The shear stress-strain relation of bulk silicon is studied using a first-principles approach. By incorporating the calculated shear property into a device-level model, our simulation closely predicts the frequency response of the device obtained by experiments and further captures the nonlinear features. These results indicate that the observed nonlinearity stems from the material's mechanical property. Given the high quality factor (Q) of the device reported here (˜2 × 106), this makes it highly susceptible to such mechanical nonlinear effects.
Performance, robustness and sensitivity analysis of the nonlinear tuned vibration absorber
Detroux, T.; Habib, G.; Masset, L.; Kerschen, G.
2015-08-01
The nonlinear tuned vibration absorber (NLTVA) is a recently developed nonlinear absorber which generalizes Den Hartog's equal peak method to nonlinear systems. If the purposeful introduction of nonlinearity can enhance system performance, it can also give rise to adverse dynamical phenomena, including detached resonance curves and quasiperiodic regimes of motion. Through the combination of numerical continuation of periodic solutions, bifurcation detection and tracking, and global analysis, the present study identifies boundaries in the NLTVA parameter space delimiting safe, unsafe and unacceptable operations. The sensitivity of these boundaries to uncertainty in the NLTVA parameters is also investigated.
Analysis of factors influencing fire damage to concrete using nonlinear resonance vibration method
Energy Technology Data Exchange (ETDEWEB)
Park, Gang Kyu; Park, Sun Jong; Kwak, Hyo Gyoung [Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology, KAIST, Daejeon (Korea, Republic of); Yim, Hong Jae [Dept. of Construction and Disaster Prevention Engineering, Kyungpook National University, Sangju (Korea, Republic of)
2015-04-15
In this study, the effects of different mix proportions and fire scenarios (exposure temperatures and post-fire-curing periods) on fire-damaged concrete were analyzed using a nonlinear resonance vibration method based on nonlinear acoustics. The hysteretic nonlinearity parameter was obtained, which can sensitively reflect the damage level of fire-damaged concrete. In addition, a splitting tensile strength test was performed on each fire-damaged specimen to evaluate the residual property. Using the results, a prediction model for estimating the residual strength of fire-damaged concrete was proposed on the basis of the correlation between the hysteretic nonlinearity parameter and the ratio of splitting tensile strength.
Nonlinear size-dependent longitudinal vibration of carbon nanotubes embedded in an elastic medium
Fernandes, R.; El-Borgi, S.; Mousavi, S. M.; Reddy, J. N.; Mechmoum, A.
2017-04-01
In this paper, we study the longitudinal linear and nonlinear free vibration response of a single walled carbon nanotube (CNT) embedded in an elastic medium subjected to different boundary conditions. This formulation is based on a large deformation analysis in which the linear and nonlinear von Kármán strains and their gradient are included in the expression of the strain energy and the velocity and its gradient are taken into account in the expression of the kinetic energy. Therefore, static and kinetic length scales associated with both energies are introduced to model size effects. The governing motion equation along with the boundary conditions are derived using Hamilton's principle. Closed-form solutions for the linear free vibration problem of the embedded CNT rod are first obtained. Then, the nonlinear free vibration response is investigated for various values of length scales using the method of multiple scales.
Nonlinear instability and convection in a vertically vibrated granular bed
Shukla, P.; Ansari, I.H.; van der Meer, Roger M.; Lohse, Detlef; Alam, M.
2014-01-01
The nonlinear instability of the density-inverted granular Leidenfrost state and the resulting convective motion in strongly shaken granular matter are analysed via a weakly nonlinear analysis of the hydrodynamic equations. The base state is assumed to be quasi-steady and the effect of harmonic
Vibrations of Nonlinear Systems. The Method of Integral Equations,
Many diverse applied methods of investigating oscillations of nonlinear systems often in different mathematical formulations and outwardly not...parameter classical methods and the methods of investigating nonlinear systems of automatic control based on the so-called filter hypothesis, and to
Nonlinear instability and convection in a vertically vibrated granular bed
Shukla, P.; Ansari, I.H.; Meer, van der R.M.; Lohse, D.; Alam, M.
2014-01-01
The nonlinear instability of the density-inverted granular Leidenfrost state and the resulting convective motion in strongly shaken granular matter are analysed via a weakly nonlinear analysis of the hydrodynamic equations. The base state is assumed to be quasi-steady and the effect of harmonic shak
Transverse nonlinear vibrations of a circular spinning disk with a varying rotating speed
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
We analyze the transverse nonlinear vibrations of a rotating flexible disk subjected to a rotating point force with a periodically varying rotating speed. Based on Hamilton’s principle, the nonlinear governing equations of motion (coupled equations among the radial, tangential and transverse displacements) are derived for the rotating flexible disk. When the in-plane inertia is ignored and a stress function is introduced, the three nonlinearly coupled partial differential equations are reduced to two nonlinearly coupled partial differential equations. According to Galerkin’s approach, a four-degree-of-freedom nonlinear system governing the weakly split resonant modes is derived. The resonant case considered here is 1:1:2:2 internal resonance and a critical speed resonance. The primary parametric resonance for the first-order sin and cos modes and the fundamental parametric resonance for the second-order sin and cos modes are also considered. The method of multiple scales is used to obtain a set of eight-dimensional nonlinear averaged equations. Based on the averaged equations, using numerical simulations, the influence of different parameters on the nonlinear vibrations of the spinning disk is detected. It is concluded that there exist complicated nonlinear behaviors including the periodic, period-n and multi-pulse type chaotic motions for the spinning disk with a varying rotating speed. It is also found that among all parameters, the damping and excitation have great influence on the nonlinear responses of the spinning disk with a varying rotating speed.
Research on strip hysteretic behavior and mill vertical vibration system nonlinear dynamics
Fan, Xiaobin; Zang, Yong; Jin, Ke
2016-10-01
Rolling mill vibration is a technical problem in the iron and steel industry for many years and has serious impact and harm on production. There were serious vibrations in the middle mills when rolling thin container strip for the compact strip production (CSP) strip hot rolling process. This paper studied the hysteretic characteristic of rolled strip and established the vertical vibration system single-degree-of-freedom dynamics model of the F3 mill rollers. The influence of parameters on the system characteristics was studied, such as the linear damping coefficient, linear stiffness coefficient, nonlinear displacement coefficient, nonlinear velocity coefficient and exciting force, and then, the vibration source and vibration-restraining measure were studied from the roll gap. The results show that with increasing linear stiffness, damping and hysteresis coefficient, it can reduce the possibility of chaotic system; the linear stiffness coefficient had the greatest influence, and hysteresis damping coefficient had minimal influence on chaotic threshold. In order to reduce rolling mill vibration amplitude, we should reduce the external excitation force firstly, and in order to improve the dynamic performance of the system, we should control the speed of nonlinear coefficient values. The contrast experiments were carried out at the production scene finally.
Nonlinear vibration of a hemispherical dome under external water pressure
Ross, C. T. F.; McLennan, A.; Little, A. P. F.
2011-07-01
The aim of this study was to analyse the behaviour of a hemi-spherical dome when vibrated under external water pressure, using the commercial computer package ANSYS 11.0. In order to achieve this aim, the dome was modelled and vibrated in air and then in water, before finally being vibrated under external water pressure. The results collected during each of the analyses were compared to the previous studies, and this demonstrated that ANSYS was a suitable program and produced accurate results for this type of analysis, together with excellent graphical displays. The analysis under external water pressure, clearly demonstrated that as external water pressure was increased, the resonant frequencies decreased and a type of dynamic buckling became likely; because the static buckling eigenmode was similar to the vibration eigenmode. ANSYS compared favourably with the in-house software, but had the advantage that it produced graphical displays. This also led to the identification of previously undetected meridional modes of vibration; which were not detected with the in-house software.
Non-linear Vibration of Oscillation Systems using Frequency-Amplitude Formulation
DEFF Research Database (Denmark)
Fereidoon, A.; Ghadimi, M.; Barari, Amin
2012-01-01
In this paper we study the periodic solutions of free vibration of mechanical systems with third and fifthorder nonlinearity for two examples using He’s Frequency Amplitude Formulation (HFAF).The effectiveness and convenience of the method is illustrated in these examples. It will be shown...... that the solutions obtained with current method have a fabulous conformity with those achieved from time marching solution. HFAF is easy with powerful concepts and the high accuracy, so it can be found widely applicable in vibrations, especially strong nonlinearity oscillatory problems....
Energy Technology Data Exchange (ETDEWEB)
Naei, Mohammad Hassan; Rastgoo, Abbas [University of Tehran, Tehran (Iran, Islamic Republic of); Ebrahimi, Farzad [Faculty of Engineering and Technology, lmam Khomeini International University, Qazvin (Iran, Islamic Republic of)
2009-08-15
A theoretical model for geometrically nonlinear vibration analysis of piezoelectrically actuated circular plates made of functionally grade material (FGM) is presented based on Kirchhoff's-Love hypothesis with von-Karman type geometrical large nonlinear deformations. To determine the initial stress state and pre-vibration deformations of the smart plate a nonlinear static problem is solved followed by adding an incremental dynamic state to the pre-vibration state. The derived governing equations of the structure are solved by exact series expansion method combined with perturbation approach. The material properties of the FGM core plate are assumed to be graded in the thickness direction according to the power-law distribution in terms of the volume fractions of the constituents. Control of the FGM plate's nonlinear deflections and natural frequencies using high control voltages is studied and their nonlinear effects are evaluated. Numerical results for FG plates with various mixture of ceramic and metal are presented in dimensionless forms. In a parametric study the emphasis is placed on investigating the effect of varying the applied actuator voltage as well as gradient index of FGM plate on vibration characteristics of the smart structure
CALCULATIONS OF STRETCHING VIBRATIONAL ENERGYLEVELS OF THE CH3I MOLECULE BY A NONLINEAR MODEL
Institute of Scientific and Technical Information of China (English)
ZHU JUN; GOU QING-QUAN
2001-01-01
A nonlinear model, i.e. the quantized discrete self-trapping equation, is applied to calculate the highly excited CH stretching vibrational energy levels of the CH3I molecule in the liquid phase at the electronic ground state up to n=8. The obtained results agree well with the experimental data and with those obtained from local mode model calculations. We note that the dominant feature of the methyl CH stretching vibrational energy levels of the CH3I molecule is a pattern of local mode pairs. When n ＞ 7, all the vibrational energy of the CH3 group can nearly be localized on a single CH bond.
Institute of Scientific and Technical Information of China (English)
XIAO Yong-gang; FU Yi-ming; ZHA Xu-dong
2005-01-01
Based on Reissner plate theory and Hamilton variational principle, the nonlinear equations of motion were derived for the moderate thickness rectangular plates with transverse surface penetrating crack on the two-parameter foundation. Under the condition of free boundary, a set of trial functions satisfying all boundary conditions and crack's continuous conditions were proposed. By employing the Galerkin method and the harmonic balance method, the nonlinear vibration equations were solved and the nonlinear vibration behaviors of the plate were analyzed. In numerical computation, the effects of the different location and depth of crack, the different structural parameters of plates and the different physical parameters of foundation on the nonlinear amplitude frequency response curves of the plate were discussed.
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.
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.
Directory of Open Access Journals (Sweden)
H. Bayıroğlu
2012-01-01
Full Text Available Vibrational conveyers with a centrifugal vibration exciter transmit their load based on the jumping method. Common unbalanced-mass driver oscillates the trough. The motion is strictly related to the vibrational parameters. The transition over resonance of a vibratory system, excited by rotating unbalances, is important in terms of the maximum vibrational amplitude produced and the power demand on the drive for the crossover. The mechanical system is driven by the DC motor. In this study, the working ranges of oscillating shaking conveyers with nonideal vibration exciter have been analyzed analytically for superharmonic and subharmonic resonances by the method of multiple scales and numerically. The analytical results obtained in this study agree well with the numerical results.
Analysis on Forced Vibration of Thin-Wall Cylindrical Shell with Nonlinear Boundary Condition
Directory of Open Access Journals (Sweden)
Qiansheng Tang
2016-01-01
Full Text Available Forced vibration of thin-wall cylindrical shell under nonlinear boundary condition was discussed in this paper. The nonlinear boundary was modeled as supported clearance in one end of shell and the restraint was assumed as linearly elastic in the radial direction. Based on Sanders’ shell theory, Lagrange equation was utilized to derive the nonlinear governing equations of cylindrical shell. The displacements in three directions were represented by beam functions and trigonometric functions. In the study of nonlinear dynamic responses of thin-wall cylindrical shell with supported clearance under external loads, the Newmark method is used to obtain time history, frequency spectrum plot, phase portraits, Poincare section, bifurcation diagrams, and three-dimensional spectrum plot with different parameters. The effects of external loads, supported clearance, and support stiffness on nonlinear dynamics behaviors of cylindrical shell with nonlinear boundary condition were discussed.
Rahmouni, A.; Beidouri, Z.; Benamar, R.
2013-09-01
The purpose of the present paper was the development of a physically discrete model for geometrically nonlinear free transverse constrained vibrations of beams, which may replace, if sufficient degrees of freedom are used, the previously developed continuous nonlinear beam constrained vibration models. The discrete model proposed is an N-Degrees of Freedom (N-dof) system made of N masses placed at the ends of solid bars connected by torsional springs, presenting the beam flexural rigidity. The large transverse displacements of the bar ends induce a variation in their lengths giving rise to axial forces modelled by longitudinal springs. The calculations made allowed application of the semi-analytical model developed previously for nonlinear structural vibration involving three tensors, namely the mass tensor mij, the linear rigidity tensor kij and the nonlinearity tensor bijkl. By application of Hamilton's principle and spectral analysis, the nonlinear vibration problem is reduced to a nonlinear algebraic system, examined for increasing numbers of dof. The results obtained by the physically discrete model showed a good agreement and a quick convergence to the equivalent continuous beam model, for various fixed boundary conditions, for both the linear frequencies and the nonlinear backbone curves, and also for the corresponding mode shapes. The model, validated here for the simply supported and clamped ends, may be used in further works to present the flexural linear and nonlinear constrained vibrations of beams with various types of discontinuities in the mass or in the elasticity distributions. The development of an adequate discrete model including the effect of the axial strains induced by large displacement amplitudes, which is predominant in geometrically nonlinear transverse constrained vibrations of beams [1]. The investigation of the results such a discrete model may lead to in the case of nonlinear free vibrations. The development of the analogy between the
Analysis of Nonlinear Vibration of Hard Coating Thin Plate by Finite Element Iteration Method
Directory of Open Access Journals (Sweden)
Hui Li
2014-01-01
Full Text Available This paper studies nonlinear vibration mechanism of hard coating thin plate based on macroscopic vibration theory and proposes finite element iteration method (FEIM to theoretically calculate its nature frequency and vibration response. First of all, strain dependent mechanical property of hard coating is briefly introduced and polynomial method is adopted to characterize the storage and loss modulus of coating material. Then, the principle formulas of inherent and dynamic response characteristics of the hard coating composite plate are derived. And consequently specific analysis procedure is proposed by combining ANSYS APDL and self-designed MATLAB program. Finally, a composite plate coated with MgO + Al2O3 is taken as a study object and both nonlinear vibration test and analysis are conducted on the plate specimen with considering strain dependent mechanical parameters of hard coating. Through comparing the resulting frequency and response results, the practicability and reliability of FEIM have been verified and the corresponding analysis results can provide an important reference for further study on nonlinear vibration mechanism of hard coating composite structure.
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.
Effects of heat exchange and nonlinearity on acoustic streaming in a vibrating cylindrical cavity.
Gubaidullin, Amir A; Yakovenko, Anna V
2015-06-01
Acoustic streaming in a gas filled cylindrical cavity subjected to the vibration effect is investigated numerically. Both thermally insulated walls and constant temperature walls are considered. The range of vibration frequencies from low frequencies, at which the process can be described by an approximate analytical solution, to high frequencies giving rise to strong nonlinear effects is studied. Frequencies lower than the resonant one are chosen, and nonlinearity is achieved due to the large amplitude. The problem is solved in an axisymmetric statement. The dependence of acoustic streaming in narrow channels at vibration frequencies lower than the resonant one on the type of thermal boundary conditions is shown. The streaming vortices' directions of rotation in the case of constant temperature walls are found to be opposite to those in the case of thermally insulated walls. Different nonlinear effects, which increase with the frequency of vibration, are obtained. Nonlinear effects manifesting as the nonuniformity of average temperature, pressure, and density are in turn found to be influencing the streaming velocity and streaming structure.
Nonlinear free vibrations of beams in space due to internal resonance
Stoykov, S.; Ribeiro, P.
2011-08-01
The geometrically nonlinear free vibrations of beams with rectangular cross section are investigated using a p-version finite element method. The beams may vibrate in space, hence they may experience longitudinal, torsional and non-planar bending deformations. The model is based on Timoshenko's theory for bending and assumes that, under torsion, the cross section rotates as a rigid body and is free to warp in the longitudinal direction, as in Saint-Venant's theory. The geometrical nonlinearity is taken into account by considering Green's nonlinear strain tensor. Isotropic and elastic beams are investigated and generalised Hooke's law is used. The equation of motion is derived by the principle of virtual work. Mostly clamped-clamped beams are investigated, although other boundary conditions are considered for validation purposes. Employing the harmonic balance method, the differential equations of motion are converted into a nonlinear algebraic form and then solved by a continuation method. One constant term, odd and even harmonics are assumed in the Fourier series and convergence with the number of harmonics is analysed. The variation of the amplitude of vibration with the frequency of vibration is determined and presented in the form of backbone curves. Coupling between modes is investigated, internal resonances are found and the ensuing multimodal oscillations are described. Some of the couplings discovered lead from planar oscillations to oscillations in the three dimensional space.
Hu, Zhan; Zheng, Gangtie
2016-08-01
A combined analysis method is developed in the present paper for studying the dynamic properties of a type of geometrically nonlinear vibration isolator, which is composed of push-pull configuration rings. This method combines the geometrically nonlinear theory of curved beams and the Harmonic Balance Method to overcome the difficulty in calculating the vibration and vibration transmissibility under large deformations of the ring structure. Using the proposed method, nonlinear dynamic behaviors of this isolator, such as the lock situation due to the coulomb damping and the usual jump resulting from the nonlinear stiffness, can be investigated. Numerical solutions based on the primary harmonic balance are first verified by direct integration results. Then, the whole procedure of this combined analysis method is demonstrated and validated by slowly sinusoidal sweeping experiments with different amplitudes of the base excitation. Both numerical and experimental results indicate that this type of isolator behaves as a hardening spring with increasing amplitude of the base excitation, which makes it suitable for isolating both steady-state vibrations and transient shocks.
Directory of Open Access Journals (Sweden)
Hailong Xu
2016-01-01
Full Text Available Rotated blades are key mechanical components in turbomachinery and high cycle fatigues often induce blade cracks. Accurate detection of small cracks in rotated blades is very significant for safety, reliability, and availability. In nature, a breathing crack model is fit for a small crack in a rotated blade rather than other models. However, traditional vibration displacements-based methods are less sensitive to nonlinear characteristics due to small breathing cracks. In order to solve this problem, vibration power flow analysis (VPFA is proposed to analyze nonlinear dynamic behaviors of rotated blades with small breathing cracks in this paper. Firstly, local flexibility due to a crack is derived and then time-varying dynamic model of the rotated blade with a small breathing crack is built. Based on it, the corresponding vibration power flow model is presented. Finally, VPFA-based numerical simulations are done to validate nonlinear behaviors of the cracked blade. The results demonstrate that nonlinear behaviors of a crack can be enhanced by power flow analysis and VPFA is more sensitive to a small breathing crack than displacements-based vibration analysis. Bifurcations will occur due to breathing cracks and subharmonic resonance factors can be defined to identify breathing cracks. Thus the proposed method can provide a promising way for detecting and predicting small breathing cracks in rotated blades.
Experimental Methods to Characterize Nonlinear Vibration of Flapping Wing Micro Air Vehicles
2007-03-01
the following terminology when referring to flapping wing MAVs; bird flight machines are also known as ornithopters and robotic insects are also...15. SUBJECT TERMS Flapping Wing Micro Air Vehicle, flapping-wing MAV, MAV, ornithopter , entomopter, nonlinear vibration, beam resonance
Rahman, T.; Jansen, E.L.; Tiso, P.
2011-01-01
In this paper, a finite element-based approach for nonlinear vibration analysis of shell structures is presented. The approach makes use of a perturbation method that gives an approximation for the amplitude-frequency relation of the structure. The method is formulated using a functional notation an
Rahman, T.; Jansen, E.L.; Tiso, P.
2011-01-01
In this paper, a finite element-based approach for nonlinear vibration analysis of shell structures is presented. The approach makes use of a perturbation method that gives an approximation for the amplitude-frequency relation of the structure. The method is formulated using a functional notation
Non-linear system identification in flow-induced vibration
Energy Technology Data Exchange (ETDEWEB)
Spanos, P.D.; Zeldin, B.A. [Rice Univ., Houston, TX (United States); Lu, R. [Hudson Engineering Corp., Houston, TX (United States)
1996-12-31
The paper introduces a method of identification of non-linear systems encountered in marine engineering applications. The non-linearity is accounted for by a combination of linear subsystems and known zero-memory non-linear transformations; an equivalent linear multi-input-single-output (MISO) system is developed for the identification problem. The unknown transfer functions of the MISO system are identified by assembling a system of linear equations in the frequency domain. This system is solved by performing the Cholesky decomposition of a related matrix. It is shown that the proposed identification method can be interpreted as a {open_quotes}Gram-Schmidt{close_quotes} type of orthogonal decomposition of the input-output quantities of the equivalent MISO system. A numerical example involving the identification of unknown parameters of flow (ocean wave) induced forces on offshore structures elucidates the applicability of the proposed method.
Suppression of limit cycle oscillations using the nonlinear tuned vibration absorber
Habib, G.; Kerschen, G.
2015-01-01
The objective of this study is to mitigate, or even completely eliminate, the limit cycle oscillations in mechanical systems using a passive nonlinear absorber, termed the nonlinear tuned vibration absorber (NLTVA). An unconventional aspect of the NLTVA is that the mathematical form of its restoring force is not imposed a priori, as it is the case for most existing nonlinear absorbers. The NLTVA parameters are determined analytically using stability and bifurcation analyses, and the resulting design is validated using numerical continuation. The proposed developments are illustrated using a Van der Pol–Duffing primary system. PMID:27547085
Nonlinear thickness-stretch vibration of thin-film acoustic wave resonators
Ji, Xiaojun; Fan, Yanping; Han, Tao; Cai, Ping
2016-03-01
We perform a theoretical analysis on nonlinear thickness-stretch free vibration of thin-film acoustic wave resonators made from AlN and ZnO. The third-order or cubic nonlinear theory by Tiersten is employed. Using Green's identify, under the usual approximation of neglecting higher time harmonics, a perturbation analysis is performed from which the resonator frequency-amplitude relation is obtained. Numerical calculations are made. The relation can be used to determine the linear operating range of these resonators. It can also be used to compare with future experimental results to determine the relevant thirdand/or fourth-order nonlinear elastic constants.
Application of HPEM to investigate the response and stability of nonlinear problems in vibration
DEFF Research Database (Denmark)
Mohammadi, M.H.; Mohammadi, A.; Kimiaeifar, A.
2010-01-01
In this work, a powerful analytical method, called He's Parameter Expanding Methods (HPEM) is used to obtain the exact solution of nonlinear problems in nonlinear vibration. In this work, the governing equation is obtained by using Lagrange method, then the nonlinear governing equation is solved...... analytically by He's Parameter Expanding Methods. It is shown that one term in series expansions is sufficient to obtain a highly accurate solution which is valid for the whole domain. Comparison of the obtained solutions with those obtained using numerical method shows that this method is effective...
Eltanany, Ali M.; Yoshimura, Takeshi; Fujimura, Norifumi; Elsayed, Nour Z.; Ebied, Mohamed R.; Ali, Mohamed G. S.
2015-10-01
The role of nonlinear stiffness in the performance of the piezoelectric vibrational energy harvester (pVEH) was discussed. Harmonic balance and numerical methods are applied to characterize the electromechanical response of pVEHs based on Duffing oscillator at a deterministic harmonic excitation of fundamental vibration characteristics (2 Hz, 1 m·s-2), which corresponds to human walking. Then, the response to a vibration with two harmonic waves, which has a fixed fundamental frequency (2 Hz, 1 m·s-2) and a frequency varied from 1.5 to 2.5 Hz. The numerical results obtained in this study indicate that nonlinearity does not have a significant advantage on the energy harvesting from human walking.
Control of an extending nonlinear elastic cable with an active vibration control strategy
Dai, L.; Sun, L.; Chen, C.
2014-10-01
An active control strategy based on the fuzzy sliding mode control (FSMC) is developed in this research for controlling the large-amplitude vibrations of an extending nonlinear elastic cable. The geometric nonlinearity of the cable and the fixed-fixed boundary of the cable are considered. For effectively and accurately control the motion of the cable with the active control strategy developed, the governing equation of the elastic cable is established and transformed into a multi-dimensional dynamic system with the 3rd order Galerkin method. The active control strategy is developed on the basis of the dynamic system, and the control strategy is applicable to multi-dimensional dynamic systems. In the numerical simulation, large-amplitude vibrations of the cable are effectively controlled with the control strategy. The results of the research demonstrate significances for controlling the cable vibrations of an elevator in practice.
Royston, T. J.; Singh, R.
1996-07-01
While significant non-linear behavior has been observed in many vibration mounting applications, most design studies are typically based on the concept of linear system theory in terms of force or motion transmissibility. In this paper, an improved analytical strategy is presented for the design optimization of complex, active of passive, non-linear mounting systems. This strategy is built upon the computational Galerkin method of weighted residuals, and incorporates order reduction and numerical continuation in an iterative optimization scheme. The overall dynamic characteristics of the mounting system are considered and vibratory power transmission is minimized via adjustment of mount parameters by using both passive and active means. The method is first applied through a computational example case to the optimization of basic passive and active, non-linear isolation configurations. It is found that either active control or intentionally introduced non-linearity can improve the mount's performance; but a combination of both produces the greatest benefit. Next, a novel experimental, active, non-linear isolation system is studied. The effect of non-linearity on vibratory power transmission and active control are assessed via experimental measurements and the enhanced Galerkin method. Results show how harmonic excitation can result in multiharmonic vibratory power transmission. The proposed optimization strategy offers designers some flexibility in utilizing both passive and active means in combination with linear and non-linear components for improved vibration mounts.
Strozzi, Matteo; Smirnov, Valeri V.; Manevitch, Leonid I.; Milani, Massimo; Pellicano, Francesco
2016-10-01
In this paper, the nonlinear vibrations and energy exchange of single-walled carbon nanotubes (SWNTs) are studied. The Sanders-Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration. The SWNT deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported, clamped and free boundary conditions are considered. The circumferential flexural modes (CFMs) are investigated. Two different approaches based on numerical and analytical models are compared. In the numerical model, an energy method based on the Lagrange equations is used to reduce the nonlinear partial differential equations of motion to a set of nonlinear ordinary differential equations, which is solved by using the implicit Runge-Kutta numerical method. In the analytical model, a reduced form of the Sanders-Koiter theory assuming small circumferential and tangential shear deformations is used to get the nonlinear ordinary differential equations of motion, which are solved by using the multiple scales analytical method. The transition from energy beating to energy localization in the nonlinear field is studied. The effect of the aspect ratio on the analytical and numerical values of the nonlinear energy localization threshold for different boundary conditions is investigated. Time evolution of the total energy distribution along the axis of a simply supported SWNT
Qing Wang, Yan; Zu, Jean W.
2017-10-01
This work investigates the porosity-dependent nonlinear forced vibrations of functionally graded piezoelectric material (FGPM) plates by using both analytical and numerical methods. The FGPM plates contain porosities owing to the technical issues during the preparation of FGPMs. Two types of porosity distribution, namely, even and uneven distribution, are considered. A modified power law model is adopted to describe the material properties of the porous FGPM plates. Using D’Alembert’s principle, the out-of-plane equation of motion is derived by taking into account the Kármán nonlinear geometrical relations. After that, the Galerkin method is used to discretize the equation of motion, resulting in a set of ordinary differential equations with respect to time. These ordinary differential equations are solved analytically by employing the harmonic balance method. The approximate analytical results are verified by using the adaptive step-size fourth-order Runge–Kutta method. By means of the perturbation technique, the stability of approximate analytical solutions is examined. An interesting nonlinear broadband vibration phenomenon is detected in the FGPM plates with porosities. Nonlinear frequency-response characteristics of the present smart structures are investigated for various system parameters including the porosity type, the porosity volume fraction, the electric potential, the external excitation, the damping and the constituent volume fraction. It is found that these parameters have significant effects on the nonlinear vibration characteristics of porous FGPM plates.
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.
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
Bab, Saeed; Khadem, S. E.; Shahgholi, Majid; Abbasi, Amirhassan
2017-02-01
The current paper investigates the effects of a number of smooth nonlinear energy sinks (NESs) located on the disk and bearings on the vibration attenuation of a rotor-blisk-journal bearing system under excitation of a mass eccentricity force. The blade and rotor are modeled using the Euler-Bernoulli beam theory. The nonlinear energy sinks on the bearing have a linear damping and an essentially nonlinear stiffness. The nonlinear energy sinks on the disk have a linear damping, linear stiffness, and an essentially nonlinear stiffness. It can be seen that the linear stiffness of the NESs on the disk is eliminated by the negative stiffness induced by the centrifugal force, and the collection of the NESs can be tuned to a required rotational speed of the rotor by varying the linear stiffness of the NESs. Furthermore, the remained stiffness of the NESs on the disk after elimination of their linear stiffness, would be essentially a nonlinear (nonlinearizable) one. Two nonlinear energy sinks in the vertical axes are positioned on the bearing housing and nnd NESs are located on the perimeter of the disk. The equations of motion are extracted using the extended Hamilton principle. The modal coordinates and complex transformations are employed to decrease the number of equations of motion. A genetic algorithm is used to optimize the parameters of the nonlinear energy sinks and its objective function is considered as minimizing the vibration of the rotating system within an operating speed range. In order to examine the periodic and non-periodic solutions of the system, time history, bifurcation diagram, Poincaré map, phase portrait, Lyapunov exponent, and power spectra analyses are performed. System shows periodic and quasi-periodic motions for different values of the system parameters. It is shown that the NESs on the disk and bearings have almost local effects on vibration reduction of rotating system. In addition, the optimum NESs remove the instability region from the
PI-type Iterative Learning Control for Nonlinear Electro-hydraulic Servo Vibrating System
Institute of Scientific and Technical Information of China (English)
LUO Xiaohui; ZHU Yuquan; HU Junhua
2009-01-01
For the electro-hydraulic servo vibrating system(ESVS) with the characteristics of non-linearity and repeating motion, a novel method, PI-type iterative learning control(ILC), is proposed on the basis of traditional PID control. By using memory ability of computer, the method keeps last time's tracking error of the system and then applies the error information to the next time's control process. At the same time, a forgetting factor and a D-type learning law of feedforward fuzzy-inferring referenced displacement error under the optimal objective are employed to enhance the systemic robustness and tracking accuracy. The results of simulation and test reveal that the algorithm has a trait of high repeating precision, and could restrain the influence of nonlinear factors like leaking, external disturbance, aerated oil, etc. Compared with traditional PID control, it could better meet the requirement of nonlinear electro-hydraulic servo vibrating system.
THERMOELASTICALLY COUPLED AXISYMMETRIC NONLINEAR VIBRATION OF SHALLOW SPHERICAL AND CONICAL SHELLS
Institute of Scientific and Technical Information of China (English)
王永岗; 戴诗亮
2004-01-01
The problem of axisymmetric nonlinear vibration for shallow thin spherical and conical shells when temperature and strain fields are coupled is studied. Based on the large deflection theories of von Krmn and the theory of thermoelasticity, the whole governing equations and their simplified type are derived. The time-spatial variables are separated by Galerkin's technique, thus reducing the governing equations to a system of time-dependent nonlinear ordinary differential equation. By means of regular perturbation method and multiple-scales method, the first-order approximate analytical solution for characteristic relation of frequency vs amplitude parameters along with the decay rate of amplitude are obtained, and the effects of different geometric parameters and coupling factors as well as boundary conditions on thermoelastically coupled nonlinear vibration behaviors are discussed.
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.
Nonlinear Vibration of Rotor Rubbing Stator Caused by Initial Perturbation
Institute of Scientific and Technical Information of China (English)
张小章; 隆锦胜; 李正光
2001-01-01
The vibration of a rotor rubbing a stator caused by an initial perturbation was studied analytically.The analytical model consists of a simple disc shaft rotor and a fixed stator. The perturbation is aninstantaneous change of the radial velocity when the rotor is operating in its normal steady state. The analysisshowed that the rotor may continue rubbing the stator for small clearance, even if the initial perturbation nolonger exists. For the interest of engineering applications, we investigated various rotating speeds,perturbation amplitudes and clearances between the rotor and the stator. Various friction coefficients on thecontact surface were also considered. The graphical results can be used for the design of rotating machines.``
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
Directory of Open Access Journals (Sweden)
Peng Guo
2012-12-01
Full Text Available With appropriate vibration modeling and analysis the incipient failure of key components such as the tower, drive train and rotor of a large wind turbine can be detected. In this paper, the Nonlinear State Estimation Technique (NSET has been applied to model turbine tower vibration to good effect, providing an understanding of the tower vibration dynamic characteristics and the main factors influencing these. The developed tower vibration model comprises two different parts: a sub-model used for below rated wind speed; and another for above rated wind speed. Supervisory control and data acquisition system (SCADA data from a single wind turbine collected from March to April 2006 is used in the modeling. Model validation has been subsequently undertaken and is presented. This research has demonstrated the effectiveness of the NSET approach to tower vibration; in particular its conceptual simplicity, clear physical interpretation and high accuracy. The developed and validated tower vibration model was then used to successfully detect blade angle asymmetry that is a common fault that should be remedied promptly to improve turbine performance and limit fatigue damage. The work also shows that condition monitoring is improved significantly if the information from the vibration signals is complemented by analysis of other relevant SCADA data such as power performance, wind speed, and rotor loads.
Effect of nonlinearity of connecting dampers on vibration control of connected building structures
Directory of Open Access Journals (Sweden)
Masatoshi eKasagi
2016-01-01
Full Text Available The connection of two building structures with dampers is one of effective vibration control systems. In this vibration control system, both buildings have to possess different vibration properties in order to provide a higher vibration reduction performance. In addition to such condition of different vibration properties of both buildings, the connecting dampers also play an important role in the vibration control mechanism. In this paper, the effect of nonlinearity of connecting dampers on the vibration control of connected building structures is investigated in detail. A high-damping rubber damper and an oil damper with and without relief mechanism are treated. It is shown that, while the high-damping rubber damper is effective in a rather small deformation level, the linear oil damper is effective in a relatively large deformation level. It is further shown that, while the oil dampers reduce the response in the same phase as the case without dampers, the high-damping rubber dampers change the phase. The merit is that the high-damping rubber can reduce the damper deformation and keep the sufficient space between both buildings. This can mitigate the risk of building pounding.
Influences on nonlinear judder vibrations of railway brakes
Heckmann, Andreas; Kurzeck, Bernhard; Carrarini, Antonio; Günther, Frank; Schroeder-Bodenstein, Kaspar
2010-06-01
The paper reports on a joined research project of Knorr-Bremse, Siemens Mobility and the Institute of Robotics and Mechatronics. The goal of the project was to analyse the dynamical behaviour of friction brakes for high-speed trains. It was intended to gain insight into possible vibration mechanisms and to assess the potential for lay-out and operation improvements for future light-weight designs. In particular, the frequency range up to 250 Hz has been addressed, since the corresponding excitation is unavoidable at least to some extent and has to be considered when the brake system is designed. The study includes a comprehensive multibody simulation study and its comparison to experimental results at the test rig of Knorr-Bremse in Munich. The simulation model is adapted step by step in order to clearly identify and separate the influences on the dynamical properties of the complete brake system including its mounting. Additionally a minimal model is introduced that demonstrates some characteristics of the brake system. It turned out that the underlying knowledge is essential for the mechanical lay-out, which could be demonstrated by solving a particular vibration problem in an actual high-speed project.
Influence of combined fundamental potentials in a nonlinear vibration energy harvester
Podder, Pranay; Mallick, Dhiman; Amann, Andreas; Roy, Saibal
2016-11-01
Ambient mechanical vibrations have emerged as a viable energy source for low-power wireless sensor nodes aiming the upcoming era of the ‘Internet of Things’. Recently, purposefully induced dynamical nonlinearities have been exploited to widen the frequency spectrum of vibration energy harvesters. Here we investigate some critical inconsistencies between the theoretical formulation and applications of the bistable Duffing nonlinearity in vibration energy harvesting. A novel nonlinear vibration energy harvesting device with the capability to switch amidst individually tunable bistable-quadratic, monostable-quartic and bistable-quartic potentials has been designed and characterized. Our study highlights the fundamentally different large deflection behaviors of the theoretical bistable-quartic Duffing oscillator and the experimentally adapted bistable-quadratic systems, and underlines their implications in the respective spectral responses. The results suggest enhanced performance in the bistable-quartic potential in comparison to others, primarily due to lower potential barrier and higher restoring forces facilitating large amplitude inter-well motion at relatively lower accelerations.
Lin, Zhiming; Chen, Jun; Li, Xiaoshi; Li, Jun; Liu, Jun; Awais, Qasim; Yang, Jin
2016-12-01
Vibration, widely existing in an ambient environment with a variety of forms and wide-range of scales, recently becomes an attractive target for energy harvesting. However, its time-varying directions and frequencies render a lack of effective energy technology to scavenge it. Here, we report a rationally designed nonlinear magnetoelectric generator for broadband and multi-directional vibration energy harvesting. By using a stabilized three-dimensional (3D) magnetic interaction and spring force, the device working bandwidth was largely broadened, which was demonstrated both experimentally and theoretically. The multidirectional vibration energy harvesting was enabled by three identical suspended springs with equal intersection angles, which are all connected to a cylindrical magnet. Numerical simulations and experimental results show that the nonlinear harvester can sustain large-amplitude oscillations over a wide frequency range, and it can generate power efficiently in an arbitrary direction. Moreover, the experimental data suggest that the proposed nonlinear energy harvester has the potential to scavenge vibrational energy over a broad range of ambient frequencies in 3D space.
Grain size effects on stability of nonlinear vibration with nanocrystalline NiTi shape memory alloy
Xia, Minglu; Sun, Qingping
2017-10-01
Grain size effects on stability of thermomechanical responses for a nonlinear torsional vibration system with nanocrystalline superelastic NiTi bar are investigated in the frequency and amplitude domains. NiTi bars with average grain size from 10 nm to 100 nm are fabricated through cold-rolling and subsequent annealing. Thermomechanical responses of the NiTi bar as a softening nonlinear damping spring in the torsional vibration system are obtained by synchronised acquisition of rotational angle and temperature under external sinusoidal excitation. It is shown that nonlinearity and damping capacity of the NiTi bar decrease as average grain size of the material is reduced below 100 nm. Therefore jump phenomena of thermomechanical responses become less significant or even vanish and the vibration system becomes more stable. The work in this paper provides a solid experimental base for manipulating the undesired jump phenomena of thermomechanical responses and stabilising the mechanical vibration system through grain refinement of NiTi SMA.
Mei, Chuh; Shen, Mo-How
1987-01-01
Multiple-mode nonlinear forced vibration of a beam was analyzed by the finite element method. Inplane (longitudinal) displacement and inertia (IDI) are considered in the formulation. By combining the finite element method and nonlinear theory, more realistic models of structural response are obtained more easily and faster.
Global Dynamic Characteristic of Nonlinear Torsional Vibration System under Harmonically Excitation
Institute of Scientific and Technical Information of China (English)
SHI Peiming; LIU Bin; HOU Dongxiao
2009-01-01
Torsional vibration generally causes serious instability and damage problems in many rotating machinery parts. The global dynamic characteristic of nonlinear torsional vibration system with nonlinear rigidity and nonlinear friction force is investigated. On the basis of the generalized dissipation Lagrange's equation, the dynamics equation of nonlinear torsional vibration system is deduced. The bifurcation and chaotic motion in the system subjected to an external harmonic excitation is studied by theoretical analysis and numerical simulation. The stability of unperturbed system is analyzed by using the stability theory of equilibrium positions of Hamiltonian systems. The criterion of existence of chaos phenomena under a periodic perturbation is given by means of Melnikov's method. It is shown that the existence of homoclinic and heteroclinic orbits in the unperturbed system implies chaos arising from breaking of homoclinic or heteroclinic orbits under perturbation. The validity of the result is checked numerically. Periodic doubling bifurcation route to chaos, quasi-periodic route to chaos, intermittency route to chaos are found to occur due to the amplitude varying in some range. The evolution of system dynamic responses is demonstrated in detail by Poincare maps and bifurcation diagrams when the system undergoes a sequence of periodic doubling or quasi-periodic bifurcations to chaos. The conclusion can provide reference for deeply researching the dynamic behavior of mechanical drive systems.
Active Vibration Control of a Nonlinear Beam with Self- and External Excitations
Directory of Open Access Journals (Sweden)
J. Warminski
2013-01-01
Full Text Available An application of the nonlinear saturation control (NSC algorithm for a self-excited strongly nonlinear beam structure driven by an external force is presented in the paper. The mathematical model accounts for an Euler-Bernoulli beam with nonlinear curvature, reduced to first mode oscillations. It is assumed that the beam vibrates in the presence of a harmonic excitation close to the first natural frequency of the beam, and additionally the beam is self-excited by fluid flow, which is modelled by a nonlinear Rayleigh term for self-excitation. The self- and externally excited vibrations have been reduced by the application of an active, saturation-based controller. The approximate analytical solutions for a full structure have been found by the multiple time scales method, up to the first-order approximation. The analytical solutions have been compared with numerical results obtained from direct integration of the ordinary differential equations of motion. Finally, the influence of a negative damping term and the controller's parameters for effective vibrations suppression are presented.
Lei, Jing; Jiang, Zuo; Li, Ya-Li; Li, Wu-Xin
2014-10-01
The problem of nonlinear vibration control for active vehicle suspension systems with actuator delay is considered. Through feedback linearization, the open-loop nonlinearity is eliminated by the feedback nonlinear term. Based on the finite spectrum assignment, the quarter-car suspension system with actuator delay is converted into an equivalent delay-free one. The nonlinear control includes a linear feedback term, a feedforward compensator, and a control memory term, which can be derived from a Riccati equation and a Sylvester equation, so that the effects produced by the road disturbances and the actuator delay are compensated, respectively. A predictor is designed to implement the predictive state in the designed control. Moreover, a reduced-order observer is constructed to solve its physical unrealisability problem. The stability proofs for the zero dynamics and the closed-loop system are provided. Numerical simulations illustrate the effectiveness and the simplicity of the designed control.
Bich, Dao Huy; Xuan Nguyen, Nguyen
2012-12-01
In the present work, the study of the nonlinear vibration of a functionally graded cylindrical shell subjected to axial and transverse mechanical loads is presented. Material properties are graded in the thickness direction of the shell according to a simple power law distribution in terms of volume fractions of the material constituents. Governing equations are derived using improved Donnell shell theory ignoring the shallowness of cylindrical shells and kinematic nonlinearity is taken into consideration. One-term approximate solution is assumed to satisfy simply supported boundary conditions. The Galerkin method, the Volmir's assumption and fourth-order Runge-Kutta method are used for dynamical analysis of shells to give explicit expressions of natural frequencies, nonlinear frequency-amplitude relation and nonlinear dynamic responses. Numerical results show the effects of characteristics of functionally graded materials, pre-loaded axial compression and dimensional ratios on the dynamical behavior of shells. The proposed results are validated by comparing with those in the literature.
Vibration control of a nonlinear quarter-car active suspension system by reinforcement learning
Bucak, İ. Ö.; Öz, H. R.
2012-06-01
This article presents the investigation of performance of a nonlinear quarter-car active suspension system with a stochastic real-valued reinforcement learning control strategy. As an example, a model of a quarter car with a nonlinear suspension spring subjected to excitation from a road profile is considered. The excitation is realised by the roughness of the road. The quarter-car model to be considered here can be approximately described as a nonlinear two degrees of freedom system. The experimental results indicate that the proposed active suspension system suppresses the vibrations greatly. A simulation of a nonlinear quarter-car active suspension system is presented to demonstrate the effectiveness and examine the performance of the learning control algorithm.
Saviz, M. R.
2015-11-01
In this paper a nonlinear approach to studying the vibration characteristic of laminated composite plate with surface-bonded piezoelectric layer/patch is formulated, based on the Green Lagrange type of strain-displacements relations, by incorporating higher-order terms arising from nonlinear relations of kinematics into mathematical formulations. The equations of motion are obtained through the energy method, based on Lagrange equations and by using higher-order shear deformation theories with von Karman-type nonlinearities, so that transverse shear strains vanish at the top and bottom surfaces of the plate. An isoparametric finite element model is provided to model the nonlinear dynamics of the smart plate with piezoelectric layer/ patch. Different boundary conditions are investigated. Optimal locations of piezoelectric patches are found using a genetic algorithm to maximize spatial controllability/observability and considering the effect of residual modes to reduce spillover effect. Active attenuation of vibration of laminated composite plate is achieved through an optimal control law with inequality constraint, which is related to the maximum and minimum values of allowable voltage in the piezoelectric elements. To keep the voltages of actuator pairs in an allowable limit, the Pontryagin’s minimum principle is implemented in a system with multi-inequality constraint of control inputs. The results are compared with similar ones, proving the accuracy of the model especially for the structures undergoing large deformations. The convergence is studied and nonlinear frequencies are obtained for different thickness ratios. The structural coupling between plate and piezoelectric actuators is analyzed. Some examples with new features are presented, indicating that the piezo-patches significantly improve the damping characteristics of the plate for suppressing the geometrically nonlinear transient vibrations.
Nonlinear vibrations and imperfection sensitivity of a cylindrical shell containing axial fluid flow
del Prado, Z.; Gonçalves, P. B.; Païdoussis, M. P.
2009-10-01
The high imperfection sensitivity of cylindrical shells under static compressive axial loads is a well-known phenomenon in structural stability. On the other hand, less is known of the influence of imperfections on the nonlinear vibrations of these shells under harmonic axial loads. The aim of this work is to study the simultaneous influence of geometric imperfections and an axial fluid flow on the nonlinear vibrations and instabilities of simply supported circular cylindrical shells under axial load. The fluid is assumed to be non-viscous and incompressible and the flow to be isentropic and irrotational. The behavior of the thin-walled shell is modeled by Donnell's nonlinear shallow-shell equations. It is subjected to a static uniform compressive axial pre-load plus a harmonic axial load. A low-dimensional modal expansion, which satisfies the relevant boundary and continuity conditions, and takes into account all relevant nonlinear modal interactions observed in the past in the nonlinear vibrations of cylindrical shells with and without flow is used together with the Galerkin method to derive a set of eight coupled nonlinear ordinary differential equations of motion which are, in turn, solved by the Runge-Kutta method. The shell is considered to be initially at rest, in a position corresponding to a pre-buckling configuration. Then, a harmonic excitation is applied and conditions for parametric instability and dynamic snap-through are sought. The results clarify the marked influence of geometric imperfections and fluid flow on the dynamic stability boundaries, bifurcations and basins of attraction.
The Nonlinear Behavior of Vibrational Conveyers with Single-Mass Crank-and-Rod Exciters
Directory of Open Access Journals (Sweden)
G. Füsun Alışverişçi
2012-01-01
Full Text Available The single-mass, crank-and-rod exciters vibrational conveyers have a trough supported on elastic stands which are rigidly fastened to the trough and a supporting frame. The trough is oscillated by a common crank drive. This vibration causes the load to move forward and upward. The moving loads jump periodically and move forward with relatively small vibration. The movement is strictly related to vibrational parameters. This is applicable in laboratory conditions in the industry which accommodate a few grams of loads, up to those that accommodate tons of loading capacity. In this study I explore the transitional behavior across resonance, during the starting of a single degree of freedom vibratory system excited by crank-and-rod. A loaded vibratory conveyor is more safe to start than an empty one. Vibrational conveyers with cubic nonlinear spring and ideal vibration exciter have been analyzed analytically for primary and secondary resonance by the Method of Multiple Scales, and numerically. The approximate analytical results obtained in this study have been compared with the numerical results and have been found to be well matched.
Acceleration Control in Nonlinear Vibrating Systems based on Damped Least Squares
Pilipchuk, V N
2011-01-01
A discrete time control algorithm using the damped least squares is introduced for acceleration and energy exchange controls in nonlinear vibrating systems. It is shown that the damping constant of least squares and sampling time step of the controller must be inversely related to insure that vanishing the time step has little effect on the results. The algorithm is illustrated on two linearly coupled Duffing oscillators near the 1:1 internal resonance. In particular, it is shown that varying the dissipation ratio of one of the two oscillators can significantly suppress the nonlinear beat phenomenon.
Nonlinear Analysis of Cable Vibration of a Multispan Cable-Stayed Bridge under Transverse Excitation
Kun Lin; Dujian Zou; Minghai Wei
2014-01-01
The nonlinear vibrations of cable in a multispan cable-stayed bridge subjected to transverse excitation are investigated. The MECS (multielements cable system) model, where multielements per cable stay are used, is built up and used to analyze the model properties of the multispan cable-stayed bridges. Then, a simplified two-degrees-of-freedom (2-DOFs) model, where the tower or the deck is reduced to a beam, is proposed to analyze the nonlinear dynamic behaviors of the beam and cable. The res...
Indian Academy of Sciences (India)
S Gunasekaran; G Anand; R Arun Balaji; J Dhanalakshmi; S Kumaresan
2010-10-01
Single crystals of urea thiourea mercuric sulphate (UTHS) and urea thiourea mercuric chloride (UTHC), semi-organic nonlinear optical materials, were grown by low-temperature solution growth technique by slow evaporation method using water as the solvent. Good quality single crystals were grown within three weeks. The nonlinear nature of the crystals was confirmed by SHG test. The UV–Vis spectrum showed the transmitting ability of the crystals in the entire visible region. FTIR spectrum was recorded and vibrational assignments were made. The degree of dopant inclusion was ascertained by AAS. The TGA–DTA studies showed the thermal properties of the crystals.
Effect of transverse shears on complex nonlinear vibrations of elastic beams
Krysko, V. A.; Zhigalov, M. V.; Saltykova, O. A.; Krysko, A. V.
2011-09-01
Models of geometrically nonlinear Euler-Bernoulli, Timoshenko, and Sheremet'ev-Pelekh beams under alternating transverse loading were constructed using the variational principle and the hypothesis method. The obtained differential equation systems were analyzed based on nonlinear dynamics and the qualitative theory of differential equations with using the finite difference method with the approximation O(h2) and the Bubnov-Galerkin finite element method. It is shown that for a relative thickness λ ⩽ 50, accounting for the rotation and bending of the beam normal leads to a significant change in the beam vibration modes.
Two Degrees of Freedom Non-linear Model to Study the Automobile’s Vibrations
Nicolae–Doru Stănescu
2010-01-01
In this paper we present a non-linear model for the study of an automobile's vibrations. The model has two degrees of freedom and it is highly non-linear. The forces in the springs are considered to be given by a polynomial potential. The equations of motion are obtained using the Lagrange second order equations. We determined the equilibrium positions. We proved the conditions for the uniqueness of the equilibrium. In our paper we studied the stability of the equilibrium and the stability of...
Two Degrees of Freedom Non-linear Model to Study the Automobile’s Vibrations
Directory of Open Access Journals (Sweden)
Nicolae–Doru Stănescu
2010-01-01
Full Text Available In this paper we present a non-linear model for the study of an automobile's vibrations. The model has two degrees of freedom and it is highly non-linear. The forces in the springs are considered to be given by a polynomial potential. The equations of motion are obtained using the Lagrange second order equations. We determined the equilibrium positions. We proved the conditions for the uniqueness of the equilibrium. In our paper we studied the stability of the equilibrium and the stability of the motion. Finally a numerical application is presented.
Institute of Scientific and Technical Information of China (English)
Ronghua Huan; Lincong Chen; Weiliang Jin; Weiqiu Zhu
2009-01-01
An optimal vibration control strategy for partially observable nonlinear quasi Hamil-tonian systems with actuator saturation is proposed. First, a controlled partially observable non-linear system is converted into a completely observable linear control system of finite dimension based on the theorem due to Charalambous and Elliott. Then the partially averaged Ito stochas-tic differential equations and dynamical programming equation associated with the completely observable linear system are derived by using the stochastic averaging method and stochastic dynamical programming principle, respectively. The optimal control law is obtained from solving the final dynamical programming equation. The results show that the proposed control strategy has high control effectiveness and control efficiency.
Abed, I.; Kacem, N.; Bouhaddi, N.; Bouazizi, M. L.
2016-02-01
We propose a multi-modal vibration energy harvesting approach based on arrays of coupled levitated magnets. The equations of motion which include the magnetic nonlinearity and the electromagnetic damping are solved using the harmonic balance method coupled with the asymptotic numerical method. A multi-objective optimization procedure is introduced and performed using a non-dominated sorting genetic algorithm for the cases of small magnet arrays in order to select the optimal solutions in term of performances by bringing the eigenmodes close to each other in terms of frequencies and amplitudes. Thanks to the nonlinear coupling and the modal interactions even for only three coupled magnets, the proposed method enable harvesting the vibration energy in the operating frequency range of 4.6-14.5 Hz, with a bandwidth of 190% and a normalized power of 20.2 {mW} {{cm}}-3 {{{g}}}-2.
Vibration mitigation of a bridge cable using a nonlinear energy sink: design and experiment
Directory of Open Access Journals (Sweden)
Weiss Mathieu
2015-01-01
Full Text Available This work deals with the design and experiment of a cubic nonlinear energy sink (NES for horizontal vibration mitigation of a bridge cable. Modal analysis of horizontal linear modes of the cable is experimentally performed using accelerometers and displacement sensors. A theoretical simplified 2-dof model of the coupled cable-NES system is used to analytically design the NES by mean of multi-time scale systems behaviours and detection its invariant manifold, equilibrium and singular points which stand for periodic and strongly modulated regimes, respectively. Numerical integration is used to confirm the efficiency of the designed NES for the system under step release excitation. Then, the prototype system is built using geometrical cubic nonlinearity as the potential of the NES. Efficiency of the prototype system for mitigation of horizontal vibrations of the cable under for step release and forced excitations is experimentally demonstrated.
Wang, Y. Q.; Guo, X. H.; Li, Y. G.; Li, J.
2010-03-01
This is a study of nonlinear traveling wave response of a cantilever circular cylindrical shell subjected to a concentrated harmonic force moving in a concentric circular path at a constant velocity. Donnell's shallow-shell theory is used, so that moderately large vibrations are analyzed. The problem is reduced to a system of ordinary differential equations by means of the Galerkin method. Frequency-responses for six different mode expansions are studied and compared with that for single mode to find the more contracted and accurate mode expansion investigating traveling wave vibration. The method of harmonic balance is applied to study the nonlinear dynamic response in forced oscillations of this system. Results obtained with analytical method are compared with numerical simulation, and the agreement between them bespeaks the validity of the method developed in this paper. The stability of the period solutions is also examined in detail.
Vibrational spectroscopic and non-linear optical activity studies on nicotinanilide : A DFT approach
Energy Technology Data Exchange (ETDEWEB)
Premkumar, S.; Mathavan, T.; Dhas, M. Kumara; Benial, A. Milton Franklin, E-mail: miltonfranklin@yahoo.com [Department of Physics, N.M.S.S.V.N. College, Madurai-625 019, Tamil Nadu (India); Jawahar, A. [Department of Chemistry, N.M.S.S.V.N. College, Madurai-625 019, Tamil Nadu (India)
2015-06-24
The molecular structure of nicotinanilide was optimized by the DFT/B3LYP method with cc-pVTZ basis set using Gaussian 09 program. The first order hyperpolarizability of the molecule was calculated, which exhibits the higher nonlinear optical activity. The natural bond orbital analysis confirms the presence of intramolecular charge transfer and the hydrogen bonding interaction, which leads to the higher nonlinear optical activity of the molecule. The Frontier molecular orbitals analysis of the molecule shows that the delocalization of electron density occurs within the molecule. The lower energy gap indicates that the hydrogen bond formation between the charged species. The vibrational frequencies were calculated and assigned on the basis of potential energy distribution calculation using the VEDA 4.0 program and the corresponding vibrational spectra were simulated. Hence, the nicotinanilide molecule can be a good candidate for second-order NLO material.
STEADY-STATE RESPONSES AND THEIR STABILITY OF NONLINEAR VIBRATION OF AN AXIALLY ACCELERATING STRING
Institute of Scientific and Technical Information of China (English)
吴俊; 陈立群
2004-01-01
The steady-state transverse vibration of an axially moving string with geometric nonlinearity was investigated. The transport speed was assumed to be a constant mean speed with small harmonic variations. The nonlinear partial-differential equation that governs the transverse vibration of the string was derived by use of the Hamilton principle. The method of multiple scales was applied directly to the equation. The solvability condition of eliminating the secular terms was established. Closed form solutions for the amplitude and the existence conditions of nontrivial steady-state response of the two-to-one parametric resonance were obtained. Some numerical examples showing effects of the mean transport speed, the amplitude and the frequency of speed variation were presented. The Liapunov linearized stability theory was employed to derive the instability conditions of the trivial solution and the nontrivial solutions for the two-to-one parametric resonance. Some numerical examples highlighting influences of the related parameters on the instability conditions were presented.
Trautmann, L.; Rabenstein, R.
2004-12-01
The functional transformation method (FTM) is a well-established mathematical method for accurate simulations of multidimensional physical systems from various fields of science, including optics, heat and mass transfer, electrical engineering, and acoustics. This paper applies the FTM to real-time simulations of transversal vibrating strings. First, a physical model of a transversal vibrating lossy and dispersive string is derived. Afterwards, this model is solved with the FTM for two cases: the ideally linearly vibrating string and the string interacting nonlinearly with the frets. It is shown that accurate and stable simulations can be achieved with the discretization of the continuous solution at audio rate. Both simulations can also be performed with a multirate approach with only minor degradations of the simulation accuracy but with preservation of stability. This saves almost 80% of the computational cost for the simulation of a six-string guitar and therefore it is in the range of the computational cost for digital waveguide simulations.
Nonlinear Control Strategies for Bioprocesses: Sliding Mode Control versus Vibrational Control
Selisteanu, Dan; Petre, Emil; Popescu, Dorin; Bobasu, Eugen
2008-01-01
In this work, two nonlinear high-frequency control strategies for bioprocesses are proposed: a feedback sliding mode control law and a vibrational control strategy. In order to implement these strategies, a prototype bioprocess that is carried out in a Continuous Stirred Tank Bioreactor was considered. First, a discontinuous feedback law was designed using the exact linearization and by imposing a SMC that stabilizes the output of the bioprocess. When some state variables used in the control ...
Advances in nonlinear vibration analysis of structures. Part-I. Beams
Indian Academy of Sciences (India)
Sudhakar R Marur
2001-06-01
The development of nonlinear vibration formulations for beams in the literature can be seen to have gone through distinct phases — earlier continuum solutions, development of appropriate forms, extra-variational simplifications, debate and discussions, variationally correct formulations and finally applications. A review of work in each of these phases is very necessary in order to have a complete understanding of the process of evolution of this field. This paper attempts to achieve precisely this objective.
Nonlinear Vibration Characteristics of a Flexible Blade with Friction Damping due to Tip-Rub
Directory of Open Access Journals (Sweden)
Dengqing Cao
2011-01-01
Full Text Available An approximate approach is proposed in this paper for analyzing the two-dimensional friction contact problem so as to compute the dynamic response of a structure constrained by friction interfaces due to tip-rub. The dynamical equation of motion for a rotational cantilever blade in a centrifugal force field is established. Flow-induced distributed periodic forces and the internal material damping in the blade are accounted for in the governing equation of motion. The Galerkin method is employed to obtain a three-degree-of-freedom oscillator with friction damping due to tip-rub. The combined motion of impact and friction due to tip-rub produced a piecewise linear vibration which is actually nonlinear. Thus, a complete vibration cycle is divided into successive intervals. The system possesses linear vibration characteristic during each of these intervals, which can be determined using analytical solution forms. Numerical simulation shows that the parameters such as gap of the tip and the rotational speed of the blades have significant effects on the dynamical responses of the system. Finally, the nonlinear vibration characteristics of the blade are investigated in terms of the Poincare graph, and the frequency spectrum of the responses and the amplitude-frequency curves.
Flow-induced vibrations of long circular cylinders modeled by coupled nonlinear oscillators
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The dynamics of long slender cylinders undergoing vortex-induced vibrations (VIV) is studied in this work. Long slender cylinders such as risers or tension legs are widely used in the field of ocean engineering. When the sea current flows past a cylinder, it will be excited due to vortex shedding. A three-dimensional time domain model is formulated to describe the response of the cylinder, in which the in-line (IL) and cross-flow (CF) deflections are coupled. The wake dynamics, including in-line and cross-flow vibrations, is represented using a pair of non-linear oscillators distributed along the cylinder. The wake oscillators are coupled to the dynamics of the long cylinder with the acceleration coupling term. A non-linear fluid force model is accounted for to reflect the relative motion of cylinder to current. The model is validated against the published data from a tank experiment with the free span riser. The comparisons show that some aspects due to VIV of long flexible cylinders can be reproduced by the proposed model, such as vibrating frequency, dominant mode number, occurrence and transition of the standing or traveling waves. In the case study, the simulations show that the IL curvature is not smaller than CF curvature, which indicates that both IL and CF vibrations are important for the structural fatigue damage.
Tavakolpour-Saleh, A. R.; Haddad, M. A.
2017-03-01
In this paper, a novel robust vibration control scheme, namely, one degree-of-freedom fuzzy active force control (1DOF-FAFC) is applied to a nonlinear electromagnetic-actuated flexible plate system. First, the flexible plate with clamped-free-clamped-free (CFCF) boundary conditions is modeled and simulated. Then, the validity of the simulation platform is evaluated through experiment. A nonlinear electromagnetic actuator is developed and experimentally modeled through a parametric system identification scheme. Next, the obtained nonlinear model of the actuator is applied to the simulation platform and performance of the proposed control technique in suppressing unwanted vibrations is investigated via simulation. A fuzzy controller is applied to the robust 1DOF control scheme to tune the controller gain using acceleration feedback. Consequently, an intelligent self-tuning vibration control strategy based on an inexpensive acceleration sensor is proposed in the paper. Furthermore, it is demonstrated that the proposed acceleration-based control technique owns the benefits of the conventional velocity feedback controllers. Finally, an experimental rig is developed to investigate the effectiveness of the 1DOF-FAFC scheme. It is found that the first, second, and third resonant modes of the flexible system are attenuated up to 74%, 81%, and 90% respectively through which the effectiveness of the proposed control scheme is affirmed.
Noid, W G; Loring, Roger F
2004-10-15
Observables in coherent, multiple-pulse infrared spectroscopy may be computed from a vibrational nonlinear response function. This response function is conventionally calculated quantum-mechanically, but the challenges in applying quantum mechanics to large, anharmonic systems motivate the examination of classical mechanical vibrational nonlinear response functions. We present an approximate formulation of the classical mechanical third-order vibrational response function for an anharmonic solute oscillator interacting with a harmonic solvent, which establishes a clear connection between classical and quantum mechanical treatments. This formalism permits the identification of the classical mechanical analog of the pure dephasing of a quantum mechanical degree of freedom, and suggests the construction of classical mechanical analogs of the double-sided Feynman diagrams of quantum mechanics, which are widely applied to nonlinear spectroscopy. Application of a rotating wave approximation permits the analytic extraction of signals obeying particular spatial phase matching conditions from a classical-mechanical response function. Calculations of the third-order response function for an anharmonic oscillator coupled to a harmonic solvent are compared to numerically correct classical mechanical results.
Nonlinear Analysis of Cable Vibration of a Multispan Cable-Stayed Bridge under Transverse Excitation
Directory of Open Access Journals (Sweden)
Kun Lin
2014-01-01
Full Text Available The nonlinear vibrations of cable in a multispan cable-stayed bridge subjected to transverse excitation are investigated. The MECS (multielements cable system model, where multielements per cable stay are used, is built up and used to analyze the model properties of the multispan cable-stayed bridges. Then, a simplified two-degrees-of-freedom (2-DOFs model, where the tower or the deck is reduced to a beam, is proposed to analyze the nonlinear dynamic behaviors of the beam and cable. The results of MECS model analysis show that the main tower in the multispan cable-stayed bridge is prone to the transverse vibration, and the local vibration of cables only has a little impact on the frequency values of the global modes. The results of simplified model analysis show that the energy can be transformed between the modes of the beam and cable when the nature frequencies of them are very close. On the other hand, with the transverse excitation changing, the cable can exhibit richer quasi-periodic or chaotic motions due to the nonlinear terms caused by the coupled mode between the beam and cable.
Directory of Open Access Journals (Sweden)
Y. Y. Lee
2014-01-01
Full Text Available This study includes the first work about the absorption of a panel absorber under the effects of microperforation, air pumping, and linear and nonlinear vibrations. In practice, thin perforated panel absorber is backed by a flexible wall to enhance the acoustic performance within the room. The panel is easily excited to vibrate nonlinearly and the wall can vibrate linearly. However, the assumptions of linear panel vibration and no wall vibration are adopted in many research works. The development of the absorption formula is based on the classical approach and the electroacoustic analogy, in which the impedances of microperforation, air pumping, and linear and nonlinear vibrations are in parallel and connected to that of the air cavity in series. Unlike those finite element, numerical integration, and multiscale solution methods and so forth, the analytic formula to calculate the absorption of a panel absorber does not require heavy computation effort and is suitable for engineering calculation purpose. The theoretical result obtained from the proposed method shows reasonable agreement with that from a previous numerical integration method. It can be concluded that the overall absorption bandwidth of a panel absorber with an appropriate configuration can be optimized and widened by making use of the positive effects of microperforation, air pumping, and panel vibration.
Nonlinear nonuniform torsional vibrations of bars by the boundary element method
Sapountzakis, E. J.; Tsipiras, V. J.
2010-05-01
In this paper a boundary element method is developed for the nonuniform torsional vibration problem of bars of arbitrary doubly symmetric constant cross-section taking into account the effect of geometrical nonlinearity. The bar is subjected to arbitrarily distributed or concentrated conservative dynamic twisting and warping moments along its length, while its edges are supported by the most general torsional boundary conditions. The transverse displacement components are expressed so as to be valid for large twisting rotations (finite displacement-small strain theory), thus the arising governing differential equations and boundary conditions are in general nonlinear. The resulting coupling effect between twisting and axial displacement components is considered and torsional vibration analysis is performed in both the torsional pre- or post-buckled state. A distributed mass model system is employed, taking into account the warping, rotatory and axial inertia, leading to the formulation of a coupled nonlinear initial boundary value problem with respect to the variable along the bar angle of twist and to an "average" axial displacement of the cross-section of the bar. The numerical solution of the aforementioned initial boundary value problem is performed using the analog equation method, a BEM based method, leading to a system of nonlinear differential-algebraic equations (DAE), which is solved using an efficient time discretization scheme. Additionally, for the free vibrations case, a nonlinear generalized eigenvalue problem is formulated with respect to the fundamental mode shape at the points of reversal of motion after ignoring the axial inertia to verify the accuracy of the proposed method. The problem is solved using the direct iteration technique (DIT), with a geometrically linear fundamental mode shape as a starting vector. The validity of negligible axial inertia assumption is examined for the problem at hand.
Vibration of piezoelectric nanobeams with an internal residual stress and a nonlinear strain
Energy Technology Data Exchange (ETDEWEB)
Jiang, Hao; Wang, Chengyuan, E-mail: cywang@ujs.edu.cn; Luo, Ying
2015-10-23
This Letter reports the effect of an internal residual stress and the local geometric nonlinearity on the vibration of piezoelectric nanowires (NWs). A dynamic equation is derived based on Hamilton's principle, which enables one to capture the above-mentioned effects and the influence of all lateral surfaces of a rectangular NW. Vibration frequencies are obtained for the NWs under an electrical voltage and compared with those given by the existing Young–Laplace model where zero internal stress, a linear strain and the effects of top and bottom surfaces of rectangular NWs are considered. It is found that the internal residual stress can extinguish the effect of the surface-induced residual stress and substantially down shift the frequency or qualitatively alter the size-dependence of the frequency. In addition, with a nonlinear strain the piezoelectric effect is found to be able to exert a direct impact on the bending stiffness of piezoelectric NWs. - Highlights: • A dynamic equation is derived for piezoelectric nanowires (PNs) by considering a nonlinear strain and an internal stress. • A nonlinear strain extends the piezoelectric effects to the bending stiffness of the PNs. • An internal stress decreases PN frequency and alters its thickness-dependence. • All lateral surfaces of PNs contribute substantially to the effect of surface piezoelectricity.
Internal Resonance in a Vibrating Beam: A Zoo of Nonlinear Resonance Peaks.
Mangussi, Franco; Zanette, Damián H
2016-01-01
In oscillating mechanical systems, nonlinearity is responsible for the departure from proportionality between the forces that sustain their motion and the resulting vibration amplitude. Such effect may have both beneficial and harmful effects in a broad class of technological applications, ranging from microelectromechanical devices to edifice structures. The dependence of the oscillation frequency on the amplitude, in particular, jeopardizes the use of nonlinear oscillators in the design of time-keeping electronic components. Nonlinearity, however, can itself counteract this adverse response by triggering a resonant interaction between different oscillation modes, which transfers the excess of energy in the main oscillation to higher harmonics, and thus stabilizes its frequency. In this paper, we examine a model for internal resonance in a vibrating elastic beam clamped at its two ends. In this case, nonlinearity occurs in the form of a restoring force proportional to the cube of the oscillation amplitude, which induces resonance between modes whose frequencies are in a ratio close to 1:3. The model is based on a representation of the resonant modes as two Duffing oscillators, coupled through cubic interactions. Our focus is put on illustrating the diversity of behavior that internal resonance brings about in the dynamical response of the system, depending on the detailed form of the coupling forces. The mathematical treatment of the model is developed at several approximation levels. A qualitative comparison of our results with previous experiments and numerical calculations on elastic beams is outlined.
Internal Resonance in a Vibrating Beam: A Zoo of Nonlinear Resonance Peaks
Mangussi, Franco
2016-01-01
In oscillating mechanical systems, nonlinearity is responsible for the departure from proportionality between the forces that sustain their motion and the resulting vibration amplitude. Such effect may have both beneficial and harmful effects in a broad class of technological applications, ranging from microelectromechanical devices to edifice structures. The dependence of the oscillation frequency on the amplitude, in particular, jeopardizes the use of nonlinear oscillators in the design of time-keeping electronic components. Nonlinearity, however, can itself counteract this adverse response by triggering a resonant interaction between different oscillation modes, which transfers the excess of energy in the main oscillation to higher harmonics, and thus stabilizes its frequency. In this paper, we examine a model for internal resonance in a vibrating elastic beam clamped at its two ends. In this case, nonlinearity occurs in the form of a restoring force proportional to the cube of the oscillation amplitude, which induces resonance between modes whose frequencies are in a ratio close to 1:3. The model is based on a representation of the resonant modes as two Duffing oscillators, coupled through cubic interactions. Our focus is put on illustrating the diversity of behavior that internal resonance brings about in the dynamical response of the system, depending on the detailed form of the coupling forces. The mathematical treatment of the model is developed at several approximation levels. A qualitative comparison of our results with previous experiments and numerical calculations on elastic beams is outlined. PMID:27648829
Masuda, Arata; Sato, Takeru
2016-04-01
This paper presents an experimental verification of a wideband nonlinear vibration energy harvester which has a globally stabilized high-energy resonating response. For the conventional linear vibration energy harvester, the maximum performance of the power generation and its bandwidth are in a relation of trade-off. The resonance frequency band can be expanded by introducing a Duffing-type nonlinear resonator in order to enable the harvester to generate larger electric power in a wider frequency range. However, since such nonlinear resonators often have multiple stable steady-state solutions in the resonance band, it is diﬃcult for the nonlinear harvester to maintain the high performance of the power generation constantly. The principle of self-excitation and entrainment has been utilized to provide the global stability to the highest-energy solution by destabilizing other unexpected lower-energy solutions by introducing a switching circuit of the load resistance between positive and the negative values depending on the response amplitude of the oscillator. In this study, an experimental verification of this concept are carried out. An experimental prototype harvester is designed and fabricated and the performance of the proposed harvester is experimentally verified. It has been shown that the numerical and experimental results agreed very well, and the highest-energy solutions above the threshold value were successfully stabilized globally.
Sundararajan, N; Ganapathi, M; 10.1016/j.finel.2005.06.001
2011-01-01
The nonlinear formulation developed based on von Karman's assumptions is employed to study the free vibration characteristics of functionally graded material (FGM) plates subjected to thermal environment. Temperature field is assumed to be a uniform distribution over the plate surface and varied in the thickness direction. The material is assumed to be temperature dependent and graded in the thickness direction according to the power-law distribution in terms of volume fractions of the constituents. The effective material properties are estimated from the volume fractions and the material properties of the constituents using Mori-Tanaka homogenization method. The nonlinear governing equations obtained using Lagrange's equations of motion are solved using finite element procedure coupled with the direct iteration technique. The variation of nonlinear frequency ratio with amplitude is highlighted considering various parameters such as gradient index, temperature, thickness and aspect ratios, and skew angle. For...
Nonlinear free vibration of single walled Carbone NanoTubes conveying fluid
Directory of Open Access Journals (Sweden)
Azrar A.
2014-04-01
Full Text Available Nonlinear free vibration of single-walled carbon nanotubes (CNTs conveying fluid are modeled and numerically simulated based on von Kármán geometric nonlinearity and Eringen’s nonlocal elasticity theory. The CNTs are modelled as nanobeams where the effects of transverse shear deformation and rotary inertia are considered within the framework of Timoshenko beam theory. The governing equations and boundary conditions are derived using the Hamilton’s principle and the nonlinear equation of motion is solved by the Galerkin’s method. The small scale parameter and the fluid-tube interaction effects on the dynamic behaviours of the CNT-fluid system as well as the instabilities induced by the fluid-velocity can be investigated. The critical fluid-velocity and frequency-amplitude relationships as well as the flutter and divergence instability types and the associated time responses are obtained based on the presented methodological approach.
Nonlinear nonlocal vibration of embedded DWCNT conveying fluid using shell model
Energy Technology Data Exchange (ETDEWEB)
Ghorbanpour Arani, A., E-mail: aghorban@kashanu.ac.ir [Faculty of Mechanical Engineering, University of Kashan, Kashan (Iran, Islamic Republic of); Institute of Nanoscience and Nanotechnology, University of Kashan, Kashan (Iran, Islamic Republic of); Zarei, M.Sh.; Amir, S.; Khoddami Maraghi, Z. [Faculty of Mechanical Engineering, University of Kashan, Kashan (Iran, Islamic Republic of)
2013-02-01
In this work nonlinear vibration of double-walled carbon nanotube (DWCNT) embedded in an elastic medium and subjected to an axial fluid flow (incompressible and non-viscose) is investigated. The elastic medium is simulated using Pasternak foundation in which adjacent layer interactions are assumed to have been coupled by van der Waals (VdW) force. The higher-order equation of motion is derived using Hamilton's principle and nonlocal-nonlinear shell theory. Galerkin and averaging methods are adopted to solve the higher-order governing equations. Elastic medium, small scale parameter, velocity and fluid density are taken into account to calculate the effects of axial and circumferential wave numbers in this study. Results reveal that increasing circumferential wave number, leads to enhanced nonlinearity. Critical flow velocities of DWCNT are inversely related to the non-local parameter (e{sub 0}a), so that increase in the later lead to reduced critical flow velocities.
On the Nonlinear Behavior of the Piezoelectric Coupling on Vibration-Based Energy Harvesters
Directory of Open Access Journals (Sweden)
Luciana L. Silva
2015-01-01
Full Text Available Vibration-based energy harvesting with piezoelectric elements has an increasing importance nowadays being related to numerous potential applications. A wide range of nonlinear effects is observed in energy harvesting devices and the analysis of the power generated suggests that they have considerable influence on the results. Linear constitutive models for piezoelectric materials can provide inconsistencies on the prediction of the power output of the energy harvester, mainly close to resonant conditions. This paper investigates the effect of the nonlinear behavior of the piezoelectric coupling. A one-degree of freedom mechanical system is coupled to an electrical circuit by a piezoelectric element and different coupling models are investigated. Experimental tests available in the literature are employed as a reference establishing the best matches of the models. Subsequently, numerical simulations are carried out showing different responses of the system indicating that nonlinear piezoelectric couplings can strongly modify the system dynamics.
Flow-Induced Vibration of A Nonlinearly Restrained Curved Pipe Conveying Fluid
Institute of Scientific and Technical Information of China (English)
王琳; 倪樵; 黄玉盈
2004-01-01
Investigated in this study is the flow-induced vibration of a nonlinearly restrained curved pipe conveying fluid. The nonlinear equation of motion is derived by equilibrium of forces on microelement of the system under consideration. The spatial coordinate of the system is discretized by DQM (differential quadrature method). On the basis of the boundary conditions, the dynamic equation is solved by the Newton-Raphson iteration method. The numerical solutions reveal several complex dynamic motions for the variation of the fluid velocity parameter, such as limit cycle motion, buckling and so on. The result obtained also shows that the sub parameter regions corresponding to the several motions may change with the variation of some parameters of the curved pipe. The present study supplies a new reference for investigating the nonlinear dynamic response of some other structures.
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.
Fast and slow dynamics in a nonlinear elastic bar excited by longitudinal vibrations
Favrie, Nicolas; Payan, Cédric
2014-01-01
Heterogeneous materials, such as rocks and concrete, have a complex dynamics including hysteresis, nonlinear elasticity and viscoelasticity. It is very sensitive to microstructural changes and damage. The goal of this paper is to propose a physical model describing the longitudinal vibrations of this class of material, and to develop a numerical strategy for solving the evolution equations. The theory relies on the coupling between two processes with radically-different time scales: a fast process at the frequency of the excitation, governed by nonlinear elasticity and viscoelasticity; a slow process, governed by the evolution of defects. The evolution equations are written as a nonlinear hyperbolic system with relaxation. A time-domain numerical scheme is developed, based on a splitting strategy. The numerical simulations show qualitative agreement with the features observed experimentally by Dynamic Acousto-Elastic Testing.
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.
Global Nonlinear Analysis of Piezoelectric Energy Harvesting from Ambient and Aeroelastic Vibrations
Abdelkefi, Abdessattar
Converting vibrations to a usable form of energy has been the topic of many recent investigations. The ultimate goal is to convert ambient or aeroelastic vibrations to operate low-power consumption devices, such as microelectromechanical systems, heath monitoring sensors, wireless sensors or replacing small batteries that have a finite life span or would require hard and expensive maintenance. The transduction mechanisms used for transforming vibrations to electric power include: electromagnetic, electrostatic, and piezoelectric mechanisms. Because it can be used to harvest energy over a wide range of frequencies and because of its ease of application, the piezoelectric option has attracted significant interest. In this work, we investigate the performance of different types of piezoelectric energy harvesters. The objective is to design and enhance the performance of these harvesters. To this end, distributed-parameter and phenomenological models of these harvesters are developed. Global analysis of these models is then performed using modern methods of nonlinear dynamics. In the first part of this Dissertation, global nonlinear distributed-parameter models for piezoelectric energy harvesters under direct and parametric excitations are developed. The method of multiple scales is then used to derive nonlinear forms of the governing equations and associated boundary conditions, which are used to evaluate their performance and determine the effects of the nonlinear piezoelectric coefficients on their behavior in terms of softening or hardening. In the second part, we assess the influence of the linear and nonlinear parameters on the dynamic behavior of a wing-based piezoaeroelastic energy harvester. The system is composed of a rigid airfoil that is constrained to pitch and plunge and supported by linear and nonlinear torsional and flexural springs with a piezoelectric coupling attached to the plunge degree of freedom. Linear analysis is performed to determine the
ELECTRICALLY FORCED THICKNESS-SHEAR VIBRATIONS OF QUARTZ PLATE WITH NONLINEAR COUPLING TO EXTENSION
Institute of Scientific and Technical Information of China (English)
Rongxing Wu; Jiashi Yang; Jianke Du; Ji Wang
2008-01-01
We study electrically forced nonlinear thickness-shear vibrations of a quartz plate resonator with relatively large amplitude. It is shown that thickness-shear is nonlinearly coupled to extension due to the well-known Poynting effect in nonlinear elasticity. This coupling is relatively strong when the resonant frequency of the extensional mode is about twice the resonant frequency of the thickness-shear mode. This happens when the plate length/thickness ratio assumes certain values. With this nonlinear coupling, the thickness-shear motion is no longer sinusoidal. Coupling to extension also affects energy trapping which is related to device mounting. When damping is 0.01, nonlinear coupling causes a frequency shift of the order of 10-e which is not insignificant,and an amplitude change of the order of 10-8. The effects are expected to be stronger under real damping of 10-5 or larger. To avoid nonlinear coupling to extension, certain values of the aspect ratio of the plate should be avoided.
Cartmell, Matthew P.
2016-09-01
The Editor wishes to make the reader aware that the paper "A new method for predicting nonlinear structural vibrations induced by ground impact loading" by Jun Liu, Yu Zhang, Bin Yun, Journal of Sound and Vibration, 331 (2012) 2129-2140, did not contain a direct citation of the fundamental and original work in this field by Dr. Mark Svinkin. The Editor regrets that this omission was not noted at the time that the above paper was accepted and published.
A review of development and implementation of an active nonlinear vibration absorber
Energy Technology Data Exchange (ETDEWEB)
Oueini, S.S.; Nayfeh, A.H. [Virginia Polytechnic Inst. and State Univ., Blacksburg, VA (United States). Dept. of Engineering Science and Mechanics; Pratt, J.R. [Manufacturing Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899-001 (United States)
1999-10-01
We present an account of an implementation of an active nonlinear vibration absorber that we have developed. The control technique exploits the saturation phenomenon that is known to occur in quadratically-coupled multi-degree-of-freedom systems subjected to primary excitation and possessing a two-to-one internal resonance. The technique is based on introducing an absorber and coupling it with the structure through a sensor and an actuator, where the feedback and control signals are quadratic. First, we consider the case of controlling the vibrations of a single-degree-of-freedom system. We develop the equations governing the response of the closed-loop system and use the method of multiple scales to obtain an approximate solution. We investigate the performance of the control strategy by studying its steady-state and transient characteristics. Additionally, we compare the performance of the quadratic absorber with that of a linear absorber. Then, we present theoretical and experimental results that demonstrate the versatility of the technique. We design an electronic circuit to emulate the absorber and use a variety of sensors and actuators to implement the active control strategy. First, we use a motor and a potentiometer to control the vibration of a rigid beam. We develop a plant model that includes Coulomb friction and demonstrate that the closed-loop system exhibits the saturation phenomenon. Second, we extend the strategy to multi-degree-of-freedom systems. We use PZT ceramics and strain gages to suppress vibrations of flexible steel beams when subjected to single- and simultaneous two-mode excitations. Third, we employ Terfenol-D, a nonlinear actuator, and accelerometers to control the vibrations of flexible beams. In all instances, the technique is successful in reducing the response amplitude of the structures. (orig.)
Issa, Jimmy S.; Shaw, Steven W.
2015-07-01
In this work we investigate the nonlinear dynamic response of systems composed of a primary inertia to which multiple identical vibration absorbers are attached. This problem is motivated by observations of systems of centrifugal pendulum vibration absorbers that are designed to reduce engine order torsional vibrations in rotating systems, but the results are relevant to translational systems as well. In these systems the total absorber mass is split into multiple equal masses for purposes of distribution and/or balance, and it is generally expected that the absorbers will act in unison, corresponding to a synchronous response. In order to capture nonlinear effects of the responses of the absorbers, specifically, their amplitude-dependent frequency, we consider them to possess nonlinear stiffness. The equations of motion for the system are derived and it is shown how one can uncouple the equations for the absorbers from that for the primary inertia, resulting in a system of identical resonators that are globally coupled. These symmetric equations are scaled for weak nonlinear effects, near resonant forcing, and small damping. The method of averaging is applied, from which steady-state responses and their stability are investigated. The response of systems with two, three, and four absorbers are considered in detail, demonstrating a rich variety of bifurcations of the synchronous response, resulting in responses with various levels of symmetry in which sub-groups of absorbers are mutually synchronous. It is also shown that undamped models with more than two absorbers possess a degenerate response, which is made robust by the addition of damping to the model. Design guidelines are proposed based on the nature of the system response, with the aim of minimizing the acceleration of the primary system. It is shown that the desired absorber parameters are selected so that the system achieves a stable synchronous response which does not undergo jumps via saddle
Energy Technology Data Exchange (ETDEWEB)
Singh, B.N., E-mail: bnsingh@aero.iitkgp.ernet.i [Department of Aerospace Engineering, IIT Kharagpur 721 302, West Bengal (India); Lal, Achchhe [Department of Mechanical Engineering, SVNIT, Surat 395007 (India)
2010-10-15
This study deals with the stochastic post-buckling and nonlinear free vibration analysis of a laminated composite plate resting on a two parameters Pasternak foundation with Winkler cubic nonlinearity having uncertain system properties. The system properties are modeled as basic random variables. A C{sup 0} nonlinear finite element formulation of the random problem based on higher-order shear deformation theory in the von Karman sense is presented. A direct iterative method in conjunction with a stochastic nonlinear finite element method proposed earlier by the authors is extended to analyze the effect of uncertainty in system properties on the post-buckling and nonlinear free vibration of the composite plates having Winler type of geometric nonlinearity. Mean as well as standard deviation of the responses have been obtained for various combinations of geometric parameters, foundation parameters, stacking sequences and boundary conditions and compared with those available in the literature and Monte Carlo simulation.
Directory of Open Access Journals (Sweden)
Ruilan Tian
2016-06-01
Full Text Available The coupled system of smooth and discontinuous absorber and beam bridge under moving loads is constructed in order to detect the effectiveness of smooth and discontinuous absorber. It is worth pointing out that the coupled system contains an irrational restoring force which is a barrier for conventional nonlinear techniques. Hence, the harmonic balance method and Fourier expansion are used to obtain the approximate solutions of the system. The first and the second kind of generalized complete elliptic integrals are introduced. Furthermore, using power flow approach, the performance of smooth and discontinuous absorber in vibration reduction is estimated through the input energy, the dissipated energy, and the damping efficiency. It is interesting that only depending on the value of the smoothness parameter, the efficiency parameter of vibration reduction is optimized. Therefore, smooth and discontinuous absorber can adapt itself to effectively reducing the amplitude of the vibration of the beam bridge, which provides an insight to the understanding of the applications of smooth and discontinuous oscillator in engineering and power flow characteristics in nonlinear system.
Furumachi, S.; Ueno, T.
2016-04-01
We study magnetostrictive vibration based power generator using iron-gallium alloy (Galfenol). The generator is advantages over conventional, such as piezoelectric material in the point of high efficiency highly robust and low electrical impedance. Generally, the generator exhibits maximum power when its resonant frequency matches the frequency of ambient vibration. In other words, the mismatch of these frequencies results in significant decrease of the output. One solution is making the spring characteristics nonlinear using magnetic force, which distorts the resonant peak toward higher or lower frequency side. In this paper, vibrational generator consisting of Galfenol plate of 6 by 0.5 by 13 mm wound with coil and U shape-frame accompanied with plates and pair of permanent magnets was investigated. The experimental results show that lean of resonant peak appears attributed on the non-linear spring characteristics, and half bandwidth with magnets is 1.2 times larger than that without. It was also demonstrated that the addition of proof mass is effective to increase the sensitivity but also the bandwidth. The generator with generating power of sub mW order is useful for power source of wireless heath monitoring for bridge and factory machine.
Non-linear vibrational modes in biomolecules: A periodic orbits description
Energy Technology Data Exchange (ETDEWEB)
Kampanarakis, Alexandros [Department of Chemistry, University of Crete, and Institute of Electronic Structure and Laser, Foundation for Research and Technology-Hellas (FORTH), Vasilika Vouton, Heraklion 71110, Crete (Greece); Farantos, Stavros C., E-mail: farantos@iesl.forth.gr [Department of Chemistry, University of Crete, and Institute of Electronic Structure and Laser, Foundation for Research and Technology-Hellas (FORTH), Vasilika Vouton, Heraklion 71110, Crete (Greece); Daskalakis, Vangelis; Varotsis, Constantinos [Department of Environmental Science and Technology, Cyprus University of Technology, 31 Archbishop Kyprianos St., P.O. Box 50329, 3603 Lemesos (Cyprus)
2012-05-03
Graphical abstract: Vibrational frequency shifts in Fe{sup IV} = O species of the active site of cytochrome c oxidase are attributed to changes in the surrounding Coulomb field. Periodic orbits analysis assists to find the most anharmonic modes in model biomolecules. Highlights: Black-Right-Pointing-Pointer Periodic orbits are extended to multidimensional potentials of biomolecules. Black-Right-Pointing-Pointer Highly anharmonic vibrational modes and center-saddle bifurcations are detected. Black-Right-Pointing-Pointer Vibrational frequencies shifts in Oxoferryl species of CcO are observed. - Abstract: The vibrational harmonic normal modes of a molecule, which are valid at energies close to an equilibrium point (a minimum, maximum or saddle of the potential energy surface), are extended by periodic orbits to high energies where anharmonicity and coupling of the degrees of freedom are significant. In this way the assignment of the spectra, and thus the extraction of dynamics in highly excited molecules, can be obtained. New vibrational modes emanating from bifurcations of periodic orbits and long living localized trajectories signal the birth and localization of new quantum states. In this article we review and further study non-linear vibrational modes for model biomolecules such as alanine dipeptide and the active site in the oxoferryl oxidation state of the enzyme cytochrome c oxidase. We locate periodic orbits which exhibit high anhamonicity and lead to center-saddle bifurcations. These modes are associated to an isomerization process in alanine dipeptide and to frequency shifts in the oxoferryl observed by modifying the Coulomb field around the Imidazole-Fe{sup IV} = O species.
Nonlinear vibrations of shallow shells with complex boundary: R-functions method and experiments
Kurpa, Lidia; Pilgun, Galina; Amabili, Marco
2007-10-01
Geometrically nonlinear vibrations of shallow circular cylindrical panels with complex shape of the boundary are considered. The R-functions theory and variational methods are used to study the problem. The R-functions method (RFM) allows constructing in analytical form the sequence of basis functions satisfying the given boundary conditions in case of complex shape of the boundary. The problem is reduced to a single second-order differential equation with quadratic and cubic nonlinear terms. The method developed has been initially applied to study free vibrations of shallow circular cylindrical panels with rectangular base for different boundary conditions: (i) clamped edges, (ii) in-plane immovable simply supported edges, (iii) classically simply supported edges, and (iv) in-plane free simply supported edges. Then, the same approach is applied to a shell with complex shape of the boundary. Experiments have been conducted on an aluminum panel with complex shape of the boundary in order to identify the nonlinear response of the fundamental mode; these experimental results have been compared to numerical results.
Lohar, Hareram; Mitra, Anirban; Sahoo, Sarmila
2016-09-01
In the present study non-linear free vibration analysis is performed on a tapered Axially Functionally Graded (AFG) beam resting on an elastic foundation with different boundary conditions. Firstly the static problem is carried out through an iterative scheme using a relaxation parameter and later on the subsequent dynamic problem is solved as a standard eigen value problem. Minimum potential energy principle is used for the formulation of the static problem whereas for the dynamic problem Hamilton's principle is utilized. The free vibrational frequencies are tabulated for different taper profile, taper parameter and foundation stiffness. The dynamic behaviour of the system is presented in the form of backbone curves in dimensionless frequency-amplitude plane.
Nonlinear vibration and buckling of circular sandwich plate under complex load
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The nonlinear vibration fundamental equation of circular sandwich plate under uniformed load and circumjacent load and the loosely clamped boundary condition were established by von Karman plate theory, and then accordingly exact solution of static load and its numerical results were given. Based on time mode hypothesis and the variational method, the control equation of the space mode was derived, and then the amplitude frequency-load character relation of circular sandwich plate was obtained by the modified iteration method. Consequently the rule of the effect of the two kinds of load on the vibration character of the circular sandwich plate was investigated. When circumjacent load makes the lowest natural frequency zero, critical load is obtained.
Suppression of chaotic vibrations in a nonlinear half-car model
Tusset, Ángelo Marcelo; Piccirillo, Vinícius; Janzen, Frederic Conrad; Lenz, Wagner Barth; Balthazar, José Manoel; da Fonseca Brasil, Reyolando M. L. R.
2014-12-01
The present work investigates the nonlinear response of a half-car model. The disturbances of the road are assumed to be sinusoidal. After constructing the bifurcation diagram, we using the 0-1 test for identify the chaotic motion. The principal objective of this study is to eliminate the chaotic behaviour of the chassis and reduce its vibration, and for this reason a control system for semi-active vehicle suspension with magnetorheological damper is proposed. The control mechanism is designed based on SDRE technique, where the control parameter is the voltage applied to the coil of the damper. Numerical results show that the proposed control method is effective in significantly reducing of the chassis vibration, increasing therefore, passenger comfort.
Suppression of chaotic vibrations in a nonlinear half-car model
Energy Technology Data Exchange (ETDEWEB)
Tusset, Ângelo Marcelo, E-mail: tusset@utfpr.edu.br, E-mail: piccirillo@utfpr.edu.br, E-mail: fcjanzen@utfpr.edu.br, E-mail: wagner-barth@hotmail.com; Piccirillo, Vinícius, E-mail: tusset@utfpr.edu.br, E-mail: piccirillo@utfpr.edu.br, E-mail: fcjanzen@utfpr.edu.br, E-mail: wagner-barth@hotmail.com; Janzen, Frederic Conrad, E-mail: tusset@utfpr.edu.br, E-mail: piccirillo@utfpr.edu.br, E-mail: fcjanzen@utfpr.edu.br, E-mail: wagner-barth@hotmail.com; Lenz, Wagner Barth, E-mail: tusset@utfpr.edu.br, E-mail: piccirillo@utfpr.edu.br, E-mail: fcjanzen@utfpr.edu.br, E-mail: wagner-barth@hotmail.com [UTFPR- PONTA GROSSA, PR (Brazil); Balthazar, José Manoel, E-mail: jmbaltha@rc.unesp.br [UNESP-BAURU, SP (Brazil); Fonseca Brasil, Reyolando M. L. R. da, E-mail: reyolando.brasil@ufabc.edu.br [UFABC-SANTO ANDRE, SP (Brazil)
2014-12-10
The present work investigates the nonlinear response of a half-car model. The disturbances of the road are assumed to be sinusoidal. After constructing the bifurcation diagram, we using the 0-1 test for identify the chaotic motion. The principal objective of this study is to eliminate the chaotic behaviour of the chassis and reduce its vibration, and for this reason a control system for semi-active vehicle suspension with magnetorheological damper is proposed. The control mechanism is designed based on SDRE technique, where the control parameter is the voltage applied to the coil of the damper. Numerical results show that the proposed control method is effective in significantly reducing of the chassis vibration, increasing therefore, passenger comfort.
Robust energy harvesting from walking vibrations by means of nonlinear cantilever beams
Kluger, Jocelyn M.; Sapsis, Themistoklis P.; Slocum, Alexander H.
2015-04-01
In the present work we examine how mechanical nonlinearity can be appropriately utilized to achieve strong robustness of performance in an energy harvesting setting. More specifically, for energy harvesting applications, a great challenge is the uncertain character of the excitation. The combination of this uncertainty with the narrow range of good performance for linear oscillators creates the need for more robust designs that adapt to a wider range of excitation signals. A typical application of this kind is energy harvesting from walking vibrations. Depending on the particular characteristics of the person that walks as well as on the pace of walking, the excitation signal obtains completely different forms. In the present work we study a nonlinear spring mechanism that is composed of a cantilever wrapping around a curved surface as it deflects. While for the free cantilever, the force acting on the free tip depends linearly on the tip displacement, the utilization of a contact surface with the appropriate distribution of curvature leads to essentially nonlinear dependence between the tip displacement and the acting force. The studied nonlinear mechanism has favorable mechanical properties such as low frictional losses, minimal moving parts, and a rugged design that can withstand excessive loads. Through numerical simulations we illustrate that by utilizing this essentially nonlinear element in a 2 degrees-of-freedom (DOF) system, we obtain strongly nonlinear energy transfers between the modes of the system. We illustrate that this nonlinear behavior is associated with strong robustness over three radically different excitation signals that correspond to different walking paces. To validate the strong robustness properties of the 2DOF nonlinear system, we perform a direct parameter optimization for 1DOF and 2DOF linear systems as well as for a class of 1DOF and 2DOF systems with nonlinear springs similar to that of the cubic spring that are physically realized
Advanced non-linear flow-induced vibration and fretting-wear analysis capabilities
Energy Technology Data Exchange (ETDEWEB)
Toorani, M.; Pan, L.; Li, R.; Idvorian, N. [Babcock and Wilcox Canada Ltd., Cambridge, Ontario (Canada); Vincent, B.
2009-07-01
Fretting wear is a potentially significant degradation mechanism in nuclear steam generators and other shell and tube heat transfer equipment as well. This paper presents an overview of the recently developed code FIVDYNA which is used for the non-linear flow-induced vibration and fretting wear analysis for operating steam generators (OTSG and RSG) and shell-and-tube heat exchangers. FIVDYNA is a non-linear time-history Flow-Induced Vibration (FIV) analysis computer program that has been developed by Babcock and Wilcox Canada to advance the understanding of tube vibration and tube to tube-support interaction. In addition to the dynamic fluid induced forces the program takes into account other tube static forces due to axial and lateral tube preload and thermal interaction loads. The program is capable of predicting the location where the fretting wear is most likely to occur and its magnitude taking into account the support geometry including gaps. FIVDYNA uses the general purpose finite element computer code ABAQUS as its solver. Using ABAQUS gives the user the flexibility to add additional forces to the tube ranging from tube preloads and the support offsets to thermal loads. The forces currently being modeled in FIVDYNA are the random turbulence, steady drag force, fluid-elastic forces, support offset and pre-strain force (axial loads). This program models the vibration of tubes and calculates the structural dynamic characteristics, and interaction forces between the tube and the tube supports. These interaction forces are then used to calculate the work rate at the support and eventually the predicted depth of wear scar on the tube. A very good agreement is found with experiments and also other computer codes. (author)
DEFF Research Database (Denmark)
Kimiaeifar, Amin; Lund, Erik; Thomsen, Ole Thybo;
2010-01-01
In this work, an analytical method, which is referred to as Parameter-expansion Method is used to obtain the exact solution for the problem of nonlinear vibrations of an inextensible beam. It is shown that one term in the series expansion is sufficient to obtain a highly accurate solution, which ...... is valid for the whole domain of the problem. A comparison of the obtained the numerical solution demonstrates that PEM is effective and convenient for solving such problems. After validation of the obtained results, the system response and stability are also discussed....
Nonlinear vibrations of cylindrical shells with initial imperfections in a supersonic flow
Kurilov, E. A.; Mikhlin, Yu. V.
2007-09-01
The paper studies the dynamics of nonlinear elastic cylindrical shells using the theory of shallow shells. The aerodynamic pressure on the shell in a supersonic flow is found using piston theory. The effect of the flow and initial deflections on the vibrations of the shell is analyzed in the flutter range. The normal modes of both perfect shells in a flow and shells with initial imperfections are studied. In the latter case, the trajectories of normal modes in the configuration space are nearly rectilinear, only one mode determined by the initial imperfections being stable
Communication: atomic force detection of single-molecule nonlinear optical vibrational spectroscopy.
Saurabh, Prasoon; Mukamel, Shaul
2014-04-28
Atomic Force Microscopy (AFM) allows for a highly sensitive detection of spectroscopic signals. This has been first demonstrated for NMR of a single molecule and recently extended to stimulated Raman in the optical regime. We theoretically investigate the use of optical forces to detect time and frequency domain nonlinear optical signals. We show that, with proper phase matching, the AFM-detected signals closely resemble coherent heterodyne-detected signals. Applications are made to AFM-detected and heterodyne-detected vibrational resonances in Coherent Anti-Stokes Raman Spectroscopy (χ((3))) and sum or difference frequency generation (χ((2))).
Sudharsana, N.; Nagalakshmi, R.; Krishnakumar, V.; Sharma, A.; Fausto, R.; Row, T. N. Guru; Pal, Rumpa
2012-06-01
Single crystals of hydroxyethylammonium picrate (C8 H10N4O8; HEAP) have been grown for the first time by slow evaporation solution growth technique at room temperature, using ethanol as solvent. FT-IR and Raman spectra were recorded for HEAP at room temperature. The main vibrational bands related to NH3+ and CO- (picrate) groups, involved in charge transfer, are discussed. Second-order hyperpolarizability(γ) for the single crystal was evaluated theoretically to be 3.48×10-28 e.s.u. A Z-scan study of HEAP showed that the relative third-order nonlinear refractive index is -9.2×10-5cm2/W. The measured third-order nonlinear properties confirm the suitability of the crystal for optical limiting and switching applications.
Deng, Linhua
2015-07-01
Three nonlinear analysis techniques, including cross-recurrence plot, line of synchronization, and cross-wavelet transform, are proposed to estimate the coherent phase vibrations of nonlinear and non-stationary time series. The case study utilizes the monthly averages of sunspot areas during the time interval from May 1874 to August 2014. The following prominent results are found: (1) the phase-leading hemisphere of long-term sunspot areas has changed twice in the past 140 years, indicating that the hemispheric imbalances and apparent phase differences on both hemispheres are a prevalent behavior and are not anomalous; (2) the alternating regularity of hemispheric asynchronism exhibits a cyclical pattern of 4.5+3.5 cycles, and the magnetic flux excess in a certain hemisphere during the ascending branch of a cycle can be taken as an indication of the phase-leading hemisphere in this cycle. We firmly believe that powerful nonlinear approaches are more advanced than classical linear methods when they are combined to determine the dynamic complexity of nonlinear physical systems.
Directory of Open Access Journals (Sweden)
Yan-Lei Zhang
2016-01-01
Full Text Available Nonlinear vibration of a fluid-conveying pipe subjected to a transverse external harmonic excitation is investigated in the case with two-to-one internal resonance. The excitation amplitude is in the same magnitude of the transverse displacement. The fluid in the pipes flows in the speed larger than the critical speed so that the straight configuration becomes an unstable equilibrium and two curved configurations bifurcate as stable equilibriums. The motion measured from each of curved equilibrium configurations is governed by a nonlinear integro-partial-differential equation with variable coefficients. The Galerkin method is employed to discretize the governing equation into a gyroscopic system consisting of a set of coupled nonlinear ordinary differential equations. The method of multiple scales is applied to analyze approximately the gyroscopic system. A set of first-order ordinary differential equations governing the modulations of the amplitude and the phase are derived via the method. In the supercritical regime, the subharmonic, superharmonic, and combination resonances are examined in the presence of the 2 : 1 internal resonance. The steady-state responses and their stabilities are determined. The various jump phenomena in the amplitude-frequency response curves are demonstrated. The effects of the viscosity, the excitation amplitude, the nonlinearity, and the flow speed are observed. The analytical results are supported by the numerical integration.
Jiao, J. P.; Drinkwater, B. W.; Neild, S. A.; Wilcox, P. D.
2009-06-01
Guided wave structural health monitoring offers the prospect of continuous interrogation of large plate-like structures with a sparse network of permanently attached sensors. Currently, the most common approach is to monitor changes in the received signals by subtraction from a reference signal obtained when the structure was known to be defect-free. In this paper a comparison is made between this defect-free subtraction approach and a technique in which low-frequency vibration modulation of guided wave signals is used to detect nonlinear scatterers. The modulation technique potentially overcomes the need for the defect-free reference measurement as the subtraction is now made between different parts of an externally applied low-frequency vibration. Linear defects were simulated by masses bonded onto a plate and nonlinear scatterers were simulated by loading a similar mass against the plate. The experimental results show that the defect-free subtraction technique performs well in detecting the bonded mass whereas the modulation technique is able to discriminate between the bonded and loaded masses. Furthermore, because the modulation technique does not require a defect-free reference, it is shown to be relatively independent of temperature effects, a significant problem for reference based subtraction techniques.
Nonlinear TeraHertz Coherent Excitation of Vibrational Modes of Liquids
Allodi, Marco A; Blake, Geoffrey A
2015-01-01
We report the first coherent excitation of intramolecular vibrational modes via the nonlinear interaction of a TeraHertz (THz) light field with molecular liquids. A TeraHertz-TeraHertz-Raman pulse sequence prepares the coherences with a broadband, high-energy, (sub)picosecond TeraHertz pulse, that are then measured in a TeraHertz Kerr effect spectrometer via phase-sensitive, heterodyne detection with an optical pulse. The spectrometer reported here has broader TeraHertz frequency coverage and an increased sensitivity relative to previously reported TeraHertz Kerr effect experiments. Vibrational coherences are observed in liquid diiodomethane at 3.66 THz (122 cm$^{-1}$), and in carbon tetrachloride at 6.50 THz (217 cm$^{-1}$), in exact agreement with literature values of those intramolecular modes. This work opens the door to 2D spectroscopies, nonlinear in TeraHertz field, that can study the dynamics of condensed-phase molecular systems, as well as coherent control at TeraHertz frequencies.
Eiras, J N; Vu, Q A; Lott, M; Payá, J; Garnier, V; Payan, C
2016-07-01
This study demonstrates the feasibility of the dynamic acousto-elastic effect of a continuous high frequency wave for investigating the material nonlinearity upon transient vibration. The approach is demonstrated on a concrete sample measuring 15×15×60cm(3). Two ultrasonic transducers (emitter and receiver) are placed at its middle span. A continuous high frequency wave of 500kHz propagates through the material and is modulated with a hammer blow. The position of the hammer blow on the sample is configured to promote the first bending mode of vibration. The use of a continuous wave allows discrete time extraction of the nonlinear behavior by a short-time Fourier transform approach, through the simultaneous comparison of a reference non-modulated signal and an impact-modulated signal. The hammer blow results in phase shifts and variations of signal amplitude between reference and perturbed signals, which are driven by the resonant frequency of the sample. Finally, a comprehensive analysis of the relaxation mechanisms (modulus and attenuation recovery) is conducted to untangle the coupled fast and slow hysteretic effects. Copyright © 2016 Elsevier B.V. All rights reserved.
Nguyen, Khoi Tan; Le Clair, Stéphanie V; Ye, Shuji; Chen, Zhan
2009-09-10
In this paper, we systematically presented the orientation determination of protein helical secondary structures using vibrational spectroscopic methods, particularly, nonlinear sum frequency generation (SFG) vibrational spectroscopy, along with linear vibrational spectroscopic techniques such as infrared spectroscopy and Raman scattering. SFG amide I signals can be collected using different polarization combinations of the input laser beams and output signal beam to measure the second-order nonlinear optical susceptibility components of the helical amide I modes, which are related to their molecular hyperpolarizability elements through the orientation distribution of these helices. The molecular hyperpolarizability elements of amide I modes of a helix can be calculated based on the infrared transition dipole moment and Raman polarizability tensor of the helix; these quantities are determined by using the bond additivity model to sum over the individual infrared transition dipole moments and Raman polarizability tensors, respectively, of the peptide units (or the amino acid residues). The computed overall infrared transition dipole moment and Raman polarizability tensor of a helix can be validated by experimental data using polarized infrared and polarized Raman spectroscopy on samples with well-aligned helical structures. From the deduced SFG hyperpolarizability elements and measured SFG second-order nonlinear susceptibility components, orientation information regarding helical structures can be determined. Even though such orientation information can also be measured using polarized infrared or polarized Raman amide I signals, SFG has a much lower detection limit, which can be used to study the orientation of a helix when its surface coverage is much lower than a monolayer. In addition, the combination of different vibrational spectroscopic techniques, for example, SFG and attenuated total reflectance Fourier transform infrared spectroscopy, provides more
Directory of Open Access Journals (Sweden)
R. Rabenstein
2004-06-01
Full Text Available The functional transformation method (FTM is a well-established mathematical method for accurate simulations of multidimensional physical systems from various fields of science, including optics, heat and mass transfer, electrical engineering, and acoustics. This paper applies the FTM to real-time simulations of transversal vibrating strings. First, a physical model of a transversal vibrating lossy and dispersive string is derived. Afterwards, this model is solved with the FTM for two cases: the ideally linearly vibrating string and the string interacting nonlinearly with the frets. It is shown that accurate and stable simulations can be achieved with the discretization of the continuous solution at audio rate. Both simulations can also be performed with a multirate approach with only minor degradations of the simulation accuracy but with preservation of stability. This saves almost 80% of the computational cost for the simulation of a six-string guitar and therefore it is in the range of the computational cost for digital waveguide simulations.
Nonlinear coupled rotor-fuselage helicopter vibration studies with higher harmonic control
Friedmann, P. P.; Venkatesan, C.; Papavassiliou, I.
1990-01-01
This paper addresses the problem of vibration prediction and vibration reduction in helicopters by means of active control methodologies. The nonlinear equations of a coupled rotor/flexible-fuselage system have been derived using computer algebra, thus relegating this tedious task to the computer. In the solution procedure the trim state and vibratory response of the helicopter are obtained in a single pass by using a harmonic balance technique and simultaneously satisfying the trim and the vibratory response of the helicopter in all the rotor and fuselage degrees of freedom. Using this solution procedure, the influence of the fuselage flexibility on the vibratory response is studied. In addition, it is shown that the conventional single frequency HHC is capable of reducing either the hub loads or only the fuselage vibrations but not both simultaneously. A new scheme called MHHC, having multiple higher harmonic pitch inputs, was used to accomplish this task of simultaneously reducing both the vibratory hub loads and fuselage vibratory response. In addition, the uniqueness of this MHHC scheme is explained in detail.
Institute of Scientific and Technical Information of China (English)
Liqun Chen; C.W.Lim; Hu Ding
2008-01-01
Nonlinear three-dimensional vibration of axially moving strings is investigated in the view of energetics. The governing equation is derived from the Eulerian equation of motion of a continuum for axially accelerating strings. The time-rate of the total mechanical energy associated with the vibration is calculated for the string with its ends moving in a prescribed way. For a string moving in a constant axial speed and constrained by two fixed ends, a conserved quan-tity is proved to remain unchanged during three-dimensional vibration, while the string energy is not conserved. An approximate conserved quantity is derived from the con-served quantity in the neighborhood of the straight equilib-rium configuration. The approximate conserved quantity is applied to verify the Lyapunov stability of the straight equi-librium configuration. Numerical simulations are performed for a rubber string and a steel string. The results demonstrate the variation of the total mechanical energy and the invari-ance of the conserved quantity.
Institute of Scientific and Technical Information of China (English)
Guogang LIU; Yi ZHAO
2004-01-01
The one-dimensional linear wave equation with a van der Pol nonlinear boundary condition is one of the simplest models that may cause isotropic or nonisotropic chaotic vibrations.It characterizes the nonisotropic chaotic vibration by means of the total variation theory.Some results are derived on the exponential growth of total variation of the snapshots on the spatial interval in the long-time horizon when the map and the initial condition satisfy some conditions.
Ben Ahmed, A; Feki, H; Abid, Y; Boughzala, H; Minot, C
2010-01-01
This paper presents the results of our calculations on the geometric parameters, vibrational spectra and hyperpolarizability of a non-linear optical material L-histidine chloride monohydrate. Due to the lack of sufficiently precise information on geometric parameters available in literature, theoretical calculations were preceded by re-determination of the crystal X-ray structure. Single crystal of L-histidine chloride monohydrate has been growing by slow evaporation of an aqueous solution at room temperature. The compound crystallizes in the non-Centro-symmetric space group P2(1)2(1)2(1) of orthorhombic system. IR spectrum has been recorded in the range [400-4000 cm(-1)]. All the experimental vibrational bands have been discussed and assigned to normal mode or to combinations on the basis of our calculations. The optimized geometric bond lengths and bond angles obtained by using DFT//B3LYP/6-31G (d) method show a good agreement with the experimental data. The calculated vibrational spectra are in well agreement with the experimental one. To investigate microscopic second-order non-linear optical NLO behavior of the examined complex, the electric dipole mu, the polarizability alpha and the hyperpolarizability beta were computed using DFT//B3LYP/6-31G (d) method. The time-dependent density functional theory (TD-DFT) was employed to descript the molecular electron structure of the title compound using the B3LYP/6-31G (d) method. According to our calculations, L-histidine chloride monohydrate exhibits non-zero beta value revealing microscopic second-order NLO behavior. Copyright 2009 Elsevier B.V. All rights reserved.
Ahmed, A. Ben; Feki, H.; Abid, Y.; Boughzala, H.; Minot, C.
2010-01-01
This paper presents the results of our calculations on the geometric parameters, vibrational spectra and hyperpolarizability of a non-linear optical material L-histidine chloride monohydrate. Due to the lack of sufficiently precise information on geometric parameters available in literature, theoretical calculations were preceded by re-determination of the crystal X-ray structure. Single crystal of L-histidine chloride monohydrate has been growing by slow evaporation of an aqueous solution at room temperature. The compound crystallizes in the non-Centro-symmetric space group P2 12 12 1 of orthorhombic system. IR spectrum has been recorded in the range [400-4000 cm -1]. All the experimental vibrational bands have been discussed and assigned to normal mode or to combinations on the basis of our calculations. The optimized geometric bond lengths and bond angles obtained by using DFT//B3LYP/6-31G (d) method show a good agreement with the experimental data. The calculated vibrational spectra are in well agreement with the experimental one. To investigate microscopic second-order non-linear optical NLO behavior of the examined complex, the electric dipole μ, the polarizability α and the hyperpolarizability β were computed using DFT//B3LYP/6-31G (d) method. The time-dependent density functional theory (TD-DFT) was employed to descript the molecular electron structure of the title compound using the B3LYP/6-31G (d) method. According to our calculations, L-histidine chloride monohydrate exhibits non-zero β value revealing microscopic second-order NLO behavior.
Institute of Scientific and Technical Information of China (English)
ZHANG; Yimin; (张义民); WANG; Shun; (王; 顺); LIU; Qiaoling; (刘巧伶); WEN; Bangchun; (闻邦椿)
2003-01-01
Based on the generalized probabilistic finite element method, this paper presents an approximate solution technique for general multi-degree-of-freedom nonlinear random vibration systems with random parameters. The fourth-moment technique, maximum entropy theory and incomplete probability information theory are employed to systematically develop a reliability analysis method for dynamic random structural systems with correlation failure modes under unavailable joint probability density functions of basic random variables. The first passage problem of multi-degree-of-freedom nonlinear random vibration systems is solved.
Energy Technology Data Exchange (ETDEWEB)
Chen, Shun-Li; Fu, Li; Chase, Zizwe A.; Gan, Wei; Wang, Hong-Fei
2016-11-10
Vibrational spectral lineshape contains important detailed information of molecular vibration and reports its specific interactions and couplings to its local environment. In this work, recently developed sub-1 cm-1 high-resolution broadband sum frequency generation vibrational spectroscopy (HR-BB-SFG-VS) was used to measure the -C≡N stretch vibration in the 4-n-octyl-4’-cyanobiphenyl (8CB) Langmuir or Langmuir-Blodgett (LB) monolayer as a unique vibrational probe, and the spectral lineshape analysis revealed the local environment and interactions at the air/water, air/glass, air/calcium fluoride and air/-quartz interfaces for the first time. The 8CB Langmuir or LB film is uniform and the vibrational spectral lineshape of its -C≡N group has been well characterized, making it a good choice as the surface vibrational probe. Lineshape analysis of the 8CB -C≡N stretch SFG vibrational spectra suggests the coherent vibrational dynamics and the structural and dynamic inhomogeneity of the -C≡N group at each interface are uniquely different. In addition, it is also found that there are significantly different roles for water molecules in the LB films on different substrate surfaces. These results demonstrated the novel capabilities of the surface nonlinear spectroscopy in characterization and in understanding the specific structures and chemical interactions at the liquid and solid interfaces in general.
Directory of Open Access Journals (Sweden)
Iman Eshraghi
2016-09-01
Full Text Available Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive governing equations of motion. Spatial discretization of governing equations and associated boundary conditions is performed using differential quadrature (DQ method and the corresponding nonlinear eigenvalue problem is iteratively solved. Effects of amplitude and location of the geometric imperfection, and the nonlocal small-scale parameter on the nonlinear frequency for various boundary conditions are investigated. The results show that the geometric imperfection and non-locality play a significant role in the nonlinear vibration characteristics of curved SWCNTs.
Nonlinear vibration and radiation from a panel with transition to chaos induced by acoustic waves
Maestrello, Lucio; Frendi, Abdelkader; Brown, Donald E.
1992-01-01
The dynamic response of an aircraft panel forced at resonance and off-resonance by plane acoustic waves at normal incidence is investigated experimentally and numerically. Linear, nonlinear (period doubling) and chaotic responses are obtained by increasing the sound pressure level of the excitation. The response time history is sensitive to the input level and to the frequency of excitation. The change in response behavior is due to a change in input conditions, triggered either naturally or by modulation of the bandwidth of the incident waves. Off-resonance, bifurcation is diffused and difficult to maintain, thus the panel response drifts into a linear behavior. The acoustic pressure emanated by the panel is either linear or nonlinear as is the vibration response. The nonlinear effects accumulate during the propagation with distance. Results are also obtained on the control of the panel response using damping tape on aluminum panel and using a graphite epoxy panel having the same size and weight. Good agreement is obtained between the experimental and numerical results.
Energy Technology Data Exchange (ETDEWEB)
Chen, Jia Nen; Liu, Jun [Tianjin Key Laboratory of the Design and Intelligent Control of the Advanced Mechatronical System, Tianjin University of Technology, Tianjin (China); Zhang, Wei; Yao, Ming Hui [College of Mechanical Engineering, Beijing University of Technology, Beijing (China); Sun, Min [School of Science, Tianjin Chengjian University, Tianjin (China)
2016-09-15
Nonlinear vibrations of carbon fiber reinforced composite sandwich plate with pyramidal truss core are investigated. The governing equation of motion for the sandwich plate is derived by using a Zig-Zag theory under consideration of geometrically nonlinear. The natural frequencies of sandwich plates with different dimensions are calculated and compared with those obtained from the classic laminated plate theory and Reddy's third-order shear deformation plate theory. The frequency responses and waveforms of the sandwich plate when 1:3 internal resonance occurs are obtained, and the characteristics of the internal resonance are discussed. The influences of layer number of face sheet, strut radius, core height and inclination angle on the nonlinear responses of the sandwich plate are analyzed. The results demonstrate that the strut radius and inclination angle mainly affect the resonance frequency band of the sandwich plate, and the layer number and core height not only influence the resonance frequency band but also significantly affect the response amplitude.
Rahman, Md. Saifur; Lee, Yiu-Yin
2017-10-01
In this study, a new modified multi-level residue harmonic balance method is presented and adopted to investigate the forced nonlinear vibrations of axially loaded double beams. Although numerous nonlinear beam or linear double-beam problems have been tackled and solved, there have been few studies of this nonlinear double-beam problem. The geometric nonlinear formulations for a double-beam model are developed. The main advantage of the proposed method is that a set of decoupled nonlinear algebraic equations is generated at each solution level. This heavily reduces the computational effort compared with solving the coupled nonlinear algebraic equations generated in the classical harmonic balance method. The proposed method can generate the higher-level nonlinear solutions that are neglected by the previous modified harmonic balance method. The results from the proposed method agree reasonably well with those from the classical harmonic balance method. The effects of damping, axial force, and excitation magnitude on the nonlinear vibrational behaviour are examined.
You, Bin Di; Wen, Jian Min; Zhao, Yang
2014-03-01
In this paper, a nonlinear dynamic modeling method for a rigid-flexible coupling satellite antenna system composed of laminated shell reflector is proposed undergoing a large overall motion. For the study of the characteristics of the reflector using laminated shell structure, the displacement field description of a point in a 3-noded shell element is acquired in conjunction with the length stretch, lateral bending and torsional deformation. Hence, a nonlinear dynamic model of the satellite antenna system is deduced based on Lagrange's equations. The complete expressions of nonlinear terms of elastic deformation and coupling terms between rigid motion and large deflection are considered in the dynamic equations, and the dynamic behavior of the rigid-flexible coupling system is analyzed using linear model and nonlinear model, respectively. In order to eliminate the system vibration, the PD with vibration force feedback control strategy is used to achieve its desired angles and velocity in a much shorter duration, and can further accomplish reduction of residual vibration. Then, the asymptotic stability of the system is proved based on the Lyapunov method. Through numerical computation, the results show that the linear model cannot capture the motion-induced coupling terms and geometric nonlinearity variations. However, the nonlinear model is suitable for dealing with large deformation rigid-flexible problem undergoing large overall motions. Hence, the satellite antenna pointing accuracy would be predicted based on the nonlinear model. Furthermore, the results also show that the proposed control strategy can suppress system vibration quickly. The above conclusions would have important academic significance and engineering value.
Nonlinear Vibration Analysis of Helical Face-Gear Transmission System with Multi-Factor
Directory of Open Access Journals (Sweden)
Liu Bo
2016-01-01
Full Text Available A systematic analysis of the dynamics of a helical face-gear system with 8 degree of freedom is performed in this study under complex excitation. The nonlinear dynamic system is solved by the Runge-Kutta method. The bifurcation and dynamic load characteristics of the system is identified from a series of diagrams. The effect of multi-factor on bifurcation diagrams is also analysed. The results real that with the increase of dimensionless frequency, the system undergoes the process of periodic, chaotic and periodic motions. The amplitude of the dynamic load gradually increases in a certain range and begins to decrease at a certain value. A higher mesh damping coefficient or a higher input torque or a lower gear backlash can reduce the vibration or eliminate chaotic responses.
Non-linear Vibrations of Deep Cylindrical Shells by the p-Version Finite Element Method
Directory of Open Access Journals (Sweden)
Pedro Ribeiro
2010-01-01
Full Text Available A p-version shell finite element based on the so-called shallow shell theory is for the first time employed to study vibrations of deep cylindrical shells. The finite element formulation for deep shells is presented and the linear natural frequencies of different shells, with various boundary conditions, are computed. These linear natural frequencies are compared with published results and with results obtained using a commercial software finite element package; good agreement is found. External forces are applied and the displacements in the geometrically non-linear regime computed with the p-model are found to be close to the ones computed using a commercial FE package. In all numerical tests the p-FE model requires far fewer degrees of freedom than the regular FE models. A numerical study on the dynamic behaviour of deep shells is finally carried out.
Directory of Open Access Journals (Sweden)
Yong Zhao
1996-01-01
Full Text Available The large strain ratcheting in cyclic plasticity of a typical pressurized pipe elbow in a realistic nuclear piping system was investigated in a more quantitative manner than previously. The elbow was modeled using a fine mesh of shell elements that can provide the completed information of detailed time varying strain distributions in the whole elbow area. The nonlinear time history stress analyses performed were based on a pseudostatic concept using the vector-valued stochastic displacement response time series loaded at the elbow ends. The response time series were synthesized using a simulation approach based on the random vibration analyses of the piping system and its supporting building. After a finite element mesh convergence study, parametric analyses were conducted that included the effects due to the magnitude changes in excitation level, internal pressure, material yield stress, and material strain hardening.
Suweken, G.; van Horssen, W.T.
2002-01-01
In this paper the weakly nonlinear, transversal vibrations of a conveyor belt will be considered. The belt is assumed to move with a low and time-varying speed. Using Kirchhoff's approach a single equation of motion will be derived from a coupled system of partial differential equations describing
Vibration Control of Structures using Vibro-Impact Nonlinear Energy Sinks
Directory of Open Access Journals (Sweden)
M. Ahmadi
2016-09-01
Full Text Available Using Vibro-Impact Nonlinear Energy Sinks (VI NESs is one of the novel strategies to control structural vibrations and mitigate their seismic response. In this system, a mass is tuned on the structure floor, so that it has a specific distance from an inelastic constraint connected to the floor mass. In case of structure stimulation, the displaced VI NES mass collides with the inelastic constraint and upon impacts, energy is dissipated. In the present work, VI NES is studied when its parameters, including clearance and stiffness ratio, are simultaneously optimized. Harmony search as a recent meta-heuristic algorithm is efficiently specialized and utilized for the aforementioned continuous optimization problem. The optimized attached VI NES is thus shown to be capable of interacting with the primary structure over a wide range of frequencies. The resulting controlled response is then investigated, in a variety of low and medium rise steel moment frames, via nonlinear dynamic time history analyses. Capability of the VI NES to dissipate siesmic input energy of earthquakes and their capabilitiy in reducing response of srtructures effectively, through vibro-impacts between the energy sink’s mass and the floor mass, is discussed by extracting several performance indices and the corresponding Fourier spectra. Results of the numerical simulations done on some structural model examples reveal that the optimized VI NES has caused successive redistribution of energy from low-frequency high-amplitude vibration modes to high-frequency low-amplitude modes, bringing about the desired attenuation of the structural responses.
Chiu, Yi; Hong, Hao-Chiao; Hsu, Wei-Hung
2016-12-01
A wideband vibrational electromagnetic energy harvester employing nonlinear spring effects is proposed and demonstrated. The harvesters were designed and fabricated by commercial rigid-flex printed circuit boards technology. Rigid FR-4 boards were used for mechanical support and coil winding, whereas flexible polyimide films were patterned for mechanical springs and mass platforms. Two sets of coils were patterned and fabricated in the harvester with an internal coil resistance of about 16 Ω each. Two rare-earth magnets were attached to the central platform as shuttle mass. The total dimension of the harvester was 20 × 20 × 4 mm3. In vibration tests, nonlinearity could be observed even at 0.1 grms vibration level due to the spring hardening effect. The frequency for peak induced voltage increased from 187 Hz at low vibration to 382 Hz at 5 grms vibration. The effective half-power bandwidth increased from 8 Hz at 0.1 grms to 32 Hz at 1 grms and 52 Hz at 5 grms due to the hysteresis in frequency response. For a matched load and 1 grms vibration at 250 Hz, the maximum output power was 160 nW, corresponding to a power density of 100 nW cm-3.
Nonlinear Vibration Analysis for a Jeffcott Rotor with Seal and Air-Film Bearing Excitations
Directory of Open Access Journals (Sweden)
Yuefang Wang
2010-01-01
Full Text Available The nonlinear coupling vibration and bifurcation of a high-speed centrifugal compressor with a labyrinth seal and two air-film journal bearings are presented in this paper. The rotary shaft and disk are modeled as a rigid Jeffcott rotor. Muszynska's model is used to express the seal force with multiple parameters. For air-film journal bearings, the model proposed by Zhang et al. is adopted to express unsteady bearing forces. The Runge-Kutta method is used to numerically determine the vibration responses of the disk center and the bearings. Bifurcation diagrams for transverse motion of the rotor are presented with parameters of rotation speed and pressure drop of the seal. Multiple subharmonic, periodic, and quasiperiodic motions are presented with two seal-pressure drops. The bifurcation characteristics show inherent interactions between forces of the air-film bearings and the seal, presenting more complicated rotor dynamics than the one with either of the forces alone. Bifurcation diagrams are obtained with parameters of pressure drop and seal length determined for the sake of operation safety.
Asath, R. Mohamed; Premkumar, S.; Rekha, T. N.; Jawahar, A.; Mathavan, T.; Benial, A. Milton Franklin
2016-05-01
The conformational analysis was carried out for 6-aminonicotinamide (ANA) using potential energy surface scan method and the most stable optimized conformer was predicted. The theoretical vibrational frequencies were calculated for the optimized geometry using DFT/B3LYP cc-pVQZ basis set by Gaussian 09 Program. The vibrational frequencies were assigned on the basis of potential energy distribution calculation using VEDA 4.0 program. The Mulliken atomic charge values were calculated. In the Frontier molecular orbitals analysis, the molecular reactivity, kinetic stability, intermolecular charge transfer studies and the related molecular properties were calculated. The ultraviolet-visible spectrum was simulated for both in the gas phase and liquid phase (ethanol) and the л to л* electronic transition was predicted. The nonlinear optical (NLO) activity was studied by means of the first order hyperpolarizability value, which was 8.61 times greater than the urea and the natural bond orbital analysis was also performed to confirm the NLO activity of the molecule. Hence, the ANA molecule is a promising candidate for the NLO materials.
Nonlinear Free Vibration Analysis of Thin-walled Curved Beam with Non-symmetric Open Cross Section
Institute of Scientific and Technical Information of China (English)
DUAN Hai-juan; SONG Zhen-sen
2008-01-01
A finite element formulation was presented for the nonlinear free vibration of thin-walled curved beams with non-symmetric open across section. The kinetic and potential energies were derived by the virtual principle. The energy function includes the effect of flexural-torsional coupling, the torsion warping and the shear centre location. For finite element analysis, cubic polynomials were utilized as the shape functions of the two nodal thin-walled curved elements. Each node possesses seven degrees freedom including the warping degree of freedom. The nonlinear eigenvalue problem was solved by the direct iteration technique. The results are compared with those for straight beams as available in the literature. The results for nonlinear free vibration analysis of curved beams for various radii and subtended angle are presented.
Meera, M. R.; Dipuna Das, C. N.; Bena Jothy, V.; Rayar, S. L.
2016-10-01
Nonlinear optics is a topic of much current interest that exhibits a great diversity. This is due to the technological potentials of certain nonlinear optical effects for photonic based technologies. Many NLO crystals grown by mixing amino acids with various organic and inorganic acids have been reported in the literature. Hence, glycine mixed semi-organic material will be of special interest as a fundamental building block to develop many complex crystals with improved NLO properties. In this context, the present work it is attempted to grow NLO active Triglycine phosphate [(NH2CH2COOH)3H3PO4](TGP) crystal from aqueous solution at room temperature by slow evaporation method. The geometry, intermolecular hydrogen bonding and harmonic vibrational wavenumbers of TGP was investigated with the help of B3LYP density functional theory (DFT) methods. Natural Bond Orbital (NBO) analysis confirms the occurrence of strong intermolecular N-H...O hydrogen bond. Second harmonic frequency generation was examined by Kurtz and Perry powder test. Theoretical first order hyperpolarizability value was calculated.
Nonlinear free vibrations of centrifugally stiffened uniform beams at high angular velocity
Bekhoucha, F.; Rechak, S.; Duigou, L.; Cadou, J. M.
2016-09-01
In this paper, we study the bending nonlinear free vibrations of a centrifugally stiffened beam with uniform cross-section and constant angular velocity. The nonlinear intrinsic equations of motion used here are geometrically exact and specific to beams exhibiting large amplitude displacements and rotations associated with small strains. Based on the Timoshenko beam model, these equations are derived from Hamilton's principle, in which the warping is considered. All coupling terms are considered including Coriolis terms. The studied beams are isotropic with clamped-free boundary conditions. By combining the Galerkin method with the harmonic balance method, the equations of motion are converted into a quadratic function treated with a continuation method: the Asymptotic Numerical Method, where the generalized displacement vector is presented as a series expansion. While analysing the effect of the angular velocity, we determine the amplitude versus frequency variations which are plotted as backbone curves. Considering the first lagging and flapping modes, the changes in beam behaviour from hardening to softening are investigated and identified as a function of the angular velocity and the effect of shear. Particular attention is paid to high angular velocities for both Euler-Bernoulli and Timoshenko beams and the natural frequencies so obtained are compared with the results available in the literature.
Radio Interferometric Calibration Using a Riemannian Manifold
Yatawatta, Sarod
2013-01-01
In order to cope with the increased data volumes generated by modern radio interferometers such as LOFAR (Low Frequency Array) or SKA (Square Kilometre Array), fast and efficient calibration algorithms are essential. Traditional radio interferometric calibration is performed using nonlinear optimization techniques such as the Levenberg-Marquardt algorithm in Euclidean space. In this paper, we reformulate radio interferometric calibration as a nonlinear optimization problem on a Riemannian manifold. The reformulated calibration problem is solved using the Riemannian trust-region method. We show that calibration on a Riemannian manifold has faster convergence with reduced computational cost compared to conventional calibration in Euclidean space.
Abdikarimov, R.; Bykovtsev, A.; Khodzhaev, D.; Research Team Of Geotechnical; Structural Engineers
2010-12-01
Long-period earthquake ground motions (LPEGM) with multiple oscillations have become a crucial consideration in seismic hazard assessment because of the rapid increase of tall buildings and special structures (SP).Usually, SP refers to innovative long-span structural systems. More specifically, they include many types of structures, such as: geodesic showground; folded plates; and thin shells. As continuation of previous research (Bykovtsev, Abdikarimov, Khodzhaev 2003, 2010) analysis of nonlinear vibrations (NV) and dynamic stability of SP simulated as shells with variable rigidity in geometrically nonlinear statement will be presented for two cases. The first case will represent NV example of a viscoelastic orthotropic cylindrical shell with radius R, length L and variable thickness h=h(x,y). The second case will be NV example of a viscoelastic shell with double curvature, variable thickness, and bearing the concentrated masses. In both cases we count, that the SP will be operates under seismic load generated by LPEGM with multiple oscillations. For different seismic loads simulations, Bykovtsev’s Model and methodology was used for generating LPEGM time history. The methodology for synthesizing LPEGM from fault with multiple segmentations was developed by Bykovtev (1978-2010) and based on 3D-analytical solutions by Bykovtsev-Kramarovskii (1987&1989) constructed for faults with multiple segmentations. This model is based on a kinematics description of displacement function on the fault and included in consideration of all possible combinations of 3 components of vector displacement (two slip vectors and one tension component). The opportunities to take into consideration fault segmentations with both shear and tension vector components of displacement on the fault plane provide more accurate LPEGM evaluations. Radiation patterns and directivity effects were included in the model and more physically realistic results for simulated LPEGM were considered. The
Dijkstra, Arend G
2015-01-01
We study hole, electron and exciton transport in a charge transfer system in the presence of underdamped vibrational motion. We analyze the signature of these processes in the linear and third-, and fifth-order nonlinear electronic spectra. Calculations are performed with a numerically exact hierarchical equations of motion method for an underdamped Brownian oscillator spectral density. We find that combining electron, hole and exciton transfer can lead to non-trivial spectra with more structure than with excitonic coupling alone. Traces taken during the waiting time of a two-dimensional spectrum are dominated by vibrational motion and do not reflect the electron, hole, and exciton dynamics directly. We find that the fifth-order nonlinear response is particularly sensitive to the charge transfer process. While third-order 2D spectroscopy detects the correlation between two coherences, fifth-order 2D spectroscopy (2D population spectroscopy) is here designed to detect correlations between the excited states du...
Morgan, Sarah E; Chin, Alex W
2016-01-01
Collective protein modes are expected to be important for facilitating energy transfer in the Fenna-Matthews-Olson (FMO) complex, however to date little work has focussed on the microscopic details of these vibrations. The nonlinear network model (NNM) provides a computationally inexpensive approach to studying vibrational modes at the microscopic level, whilst incorporating anharmonicity in the inter-residue interactions which can influence protein dynamics. We apply the NNM to the FMO complex and find evidence for the existence of nonlinear discrete breather modes. These modes tend to transfer energy to the highly connected core pigments, potentially opening up alternative excitation energy transfer routes. Incorporating localised modes based on these discrete breathers in the optical spectra calculations for FMO using ab initio site energies and excitonic couplings can substantially improve their agreement with experimental results.
Morgan, Sarah E.; Cole, Daniel J.; Chin, Alex W.
2016-11-01
Collective protein modes are expected to be important for facilitating energy transfer in the Fenna-Matthews-Olson (FMO) complex of photosynthetic green sulphur bacteria, however to date little work has focussed on the microscopic details of these vibrations. The nonlinear network model (NNM) provides a computationally inexpensive approach to studying vibrational modes at the microscopic level in large protein structures, whilst incorporating anharmonicity in the inter-residue interactions which can influence protein dynamics. We apply the NNM to the entire trimeric FMO complex and find evidence for the existence of nonlinear discrete breather modes. These modes tend to transfer energy to the highly connected core pigments, potentially opening up alternative excitation energy transfer routes through their influence on pigment properties. Incorporating localised modes based on these discrete breathers in the optical spectra calculations for FMO using ab initio site energies and excitonic couplings can substantially improve their agreement with experimental results.
Directory of Open Access Journals (Sweden)
Fan-Ping Qing
2014-02-01
Full Text Available The study derives the kinetics equation of the system and analyzes vibration performance considering the nonlinear factors like time-varying mesh stiffness, gear back lash, mesh error. With the time-varying mesh stiffness of the gear increasing, the vibration of the gear system is more intense. The gear backlash has little effect on the aperiodic behaviour. However, with the clearance increasing, the system response quickly converts to chaos response from single frequency response with the increase of gap and the mesh impact is more serious. The excitation frequency is close to the resonance frequency of system, the system appears chaotic response and the vibration amplitude increases. When the frequency is far from the natural frequency, the response of the system tends to be steady. So it is easy to predict the dynamic performance in the design and make the system avoid the resonance frequency. In the following profile modification of gear, it also provides the data sources.
Recurrence plot analysis of nonlinear vibrational dynamics in H sub 3 sup + molecule
Babinec, P
2003-01-01
An ab initio classical trajectories obtained from the simulation of vibrational mode dynamics of H sub 3 sup + molecule were analyzed by Fourier transform and recurrence plot analysis. As has been found, at a particular value of energy supplied to vibrational modes (slightly above the zero point energy) the character of vibrational motion changes from regular to chaotic.
Institute of Scientific and Technical Information of China (English)
Ta Na; Qiu Jiajun; Cai Ganhua
2005-01-01
Zero mode natural frequency (ZMNF) is found during experiments. The ZMNF and vibrations resulted by it are studied. First, calculating method of the ZMNF excited by electromagnetic in vibrational system of coupled mechanics and electrics are given from the view of magnetic energy.Laws that the ZMNF varies with active power and exciting current are obtained and are verified by experiments. Then, coupled lateral and torsional vibration of rotor shaft system is studied by considering rest eccentricity, rotating eccentricity and swing eccentricity. Using Largrange-Maxwell equation when three phases are asymmetric derives differential equation of the coupled vibration. With energy method of nonlinear vibration, amplitude-frequency characteristics of resonance are studied when rotating speed of rotor equals to ZMNF. The results show that ZMNF will occur in turbine generators by the action of electromagnetic. Because ZMNF varies with electromagnetic parameters,resonance can occur when exciting frequency of the rotor speed is fixed whereas exciting current change. And also find that a generator is in the state of large amplitude in rated exciting current.
Lenci, Stefano; Rega, Giuseppe
2016-06-01
The nonlinear free oscillations of a straight planar Timoshenko beam are investigated analytically by means of the asymptotic development method. Attention is focused for the first time, to the best of our knowledge, on the nonlinear coupling between the axial and the transversal oscillations of the beam, which are decoupled in the linear regime. The existence of coupled and uncoupled motion is discussed. Furthermore, the softening versus hardening nature of the backbone curves is investigated in depth. The results are summarized by means of behaviour charts that illustrate the different possible classes of motion in the parameter space. New, and partially unexpected, phenomena, such as the changing of the nonlinear behaviour from softening to hardening by adding/removing the axial vibrations, are highlighted.
Wierschem, Nicholas E.; Hubbard, Sean A.; Luo, Jie; Fahnestock, Larry A.; Spencer, Billie F.; McFarland, D. Michael; Quinn, D. Dane; Vakakis, Alexander F.; Bergman, Lawrence A.
2017-02-01
Limiting peak stresses and strains in a structure subjected to high-energy, short-duration transient loadings, such as blasts, is a challenging problem, largely due to the well-known insensitivity of the first few cycles of the structural response to damping. Linear isolation, while a potential solution, requires a very low fundamental natural frequency to be effective, resulting in large nearly-rigid body displacement of the structure, while linear vibration absorbers have little or no effect on the early-time response where relative motions, and thus stresses and strains, are at their highest levels. The problem has become increasingly important in recent years with the expectation of blast-resistance as a design requirement in new construction. In this paper, the problem is examined experimentally and computationally in the context of offset-blast loading applied to a custom-built nine story steel frame structure. A fully-passive response mitigation system consisting of six lightweight, essentially nonlinear vibration absorbers (termed nonlinear energy sinks - NESs) is optimized and deployed on the upper two floors of this structure. Two NESs have vibro-impact nonlinearities and the other four possess smooth but essentially nonlinear stiffnesses. Results of the computational and experimental study demonstrate the efficacy of the proposed passive nonlinear mitigation system to rapidly and efficiently attenuate the global structural response, even at early time (i.e., starting at the first response cycle), thus minimizing the peak demand on the structure. This is achieved by nonlinear redistribution of the blast energy within the modal space through low-to-high energy scattering due to the action of the NESs. The experimental results validate the theoretical predictions.
Bao, Bin; Guyomar, Daniel; Lallart, Mickaël
2017-01-01
Smart periodic structures covered by periodically distributed piezoelectric patches have drawn more and more attention in recent years for wave propagation attenuation and corresponding structural vibration suppression. Since piezoelectric materials are special type of energy conversion materials that link mechanical characteristics with electrical characteristics, shunt circuits coupled with such materials play a key role in the wave propagation and/or vibration control performance in smart periodic structures. Conventional shunt circuit designs utilize resistive shunt (R-shunt) and resonant shunt (RL-shunt). More recently, semi-passive nonlinear approaches have also been developed for efficiently controlling the vibrations of such structures. In this paper, an innovative smart periodic beam structure with nonlinear interleaved-switched electric networks based on synchronized switching damping on inductor (SSDI) is proposed and investigated for vibration reduction and wave propagation attenuation. Different from locally resonant band gap mechanism forming narrow band gaps around the desired resonant frequencies, the proposed interleaved electrical networks can induce new broadly low-frequency stop bands and broaden primitive Bragg stop bands by virtue of unique interleaved electrical configurations and the SSDI technique which has the unique feature of realizing automatic impedance adaptation with a small inductance. Finite element modeling of a Timoshenko electromechanical beam structure is also presented for validating dispersion properties of the structure. Both theoretical and experimental results demonstrate that the proposed beam structure not only shows better vibration and wave propagation attenuation than the smart beam structure with independent switched networks, but also has technical simplicity of requiring only half of the number of switches than the independent switched network needs.
Ding, Hu; Zu, Jean W.
2013-11-01
This study focuses on the nonlinear steady-state response of a belt-drive system with a one-way clutch. A dynamic model is established to describe the rotations of the driving pulley, the driven pulley, and the accessory shaft. Moreover, the model considers the transverse vibration of the translating belt spans for the first time in belt-drive systems coupled with a one-way clutch. The excitation of the belt-drive system is derived from periodic fluctuation of the driving pulley. In automotive systems, this kind of fluctuation is induced by the engine firing harmonic pulsations. The derived coupled discrete-continuous nonlinear equations consist of integro-partial-differential equations and piece-wise ordinary differential equations. Using the Galerkin truncation, a set of nonlinear ordinary differential equations is obtained from the integro-partial-differential equations. Applying the Runge-Kutta time discretization, the time histories of the dynamic response are numerically solved for the driven pulley and the accessory shaft and the translating belt spans. The resonance areas of the coupled belt-drive system are determined using the frequency sweep. The effects of the one-way clutch on the belt-drive system are studied by comparing the frequency-response curves of the translating belt with and without one-way clutch device. Furthermore, the results of 2-term and 4-term Galerkin truncation are compared to determine the numerical convergence. Moreover, parametric studies are conducted to understand the effects of the system parameters on the nonlinear steady-state response. It is concluded that one-way clutch not only decreases the resonance amplitude of the driven pulley and shaft's rotational vibration, but also reduces the resonance region of the belt's transverse vibration.
Madsen, Niels K; Godtliebsen, Ian H; Christiansen, Ove
2017-04-07
Vibrational coupled-cluster (VCC) theory provides an accurate method for calculating vibrational spectra and properties of small to medium-sized molecules. Obtaining these properties requires the solution of the non-linear VCC equations which can in some cases be hard to converge depending on the molecule, the basis set, and the vibrational state in question. We present and compare a range of different algorithms for solving the VCC equations ranging from a full Newton-Raphson method to approximate quasi-Newton models using an array of different convergence-acceleration schemes. The convergence properties and computational cost of the algorithms are compared for the optimization of VCC states. This includes both simple ground-state problems and difficult excited states with strong non-linearities. Furthermore, the effects of using tensor-decomposed solution vectors and residuals are investigated and discussed. The results show that for standard ground-state calculations, the conjugate residual with optimal trial vectors algorithm has the shortest time-to-solution although the full Newton-Raphson method converges in fewer macro-iterations. Using decomposed tensors does not affect the observed convergence rates in our test calculations as long as the tensors are decomposed to sufficient accuracy.
Remick, Kevin; Dane Quinn, D.; Michael McFarland, D.; Bergman, Lawrence; Vakakis, Alexander
2016-05-01
The authors investigate a vibration-based energy harvesting system utilizing essential (nonlinearizable) nonlinearities and electromagnetic coupling elements. The system consists of a grounded, weakly damped linear oscillator (primary system) subjected to a single impulsive load. This primary system is coupled to a lightweight, damped oscillating attachment (denoted as nonlinear energy sink, NES) via a neodymium magnet and an inductance coil, and a piano wire, which generates an essential geometric cubic stiffness nonlinearity. Under impulsive input, the transient damped dynamics of this system exhibit transient resonance captures (TRCs) causing intentional large-amplitude and high-frequency instabilities in the response of the NES. These TRCs result in strong energy transfer from the directly excited primary system to the light-weight attachment. The energy is harvested by the electromagnetic elements in the coupling and, in the present case, dissipated in a resistive element in the electrical circuit. The primary goal of this work is to numerically, analytically, and experimentally demonstrate the efficacy of employing this type of intentional high-frequency dynamic instability to achieve enhanced vibration energy harvesting under impulsive excitation.
Nonlinear Dynamics of a Spring-Supported Piston in a Vibrated Liquid-Filled Housing: II. Experiments
O'Hern, T. J.; Torczynski, J. R.; Clausen, J. R.
2016-11-01
The nonlinear dynamics of a piston supported by a spring in a vibrated liquid-filled housing is investigated experimentally. The housing containing the piston and the liquid is subjected to vibrations along its axis. A post fixed to the housing penetrates a hole through the piston and produces a flow resistance that depends on piston position. Flexible bellows attached to the housing ends enable the piston, liquid, and bellows to execute a collective motion that forces little liquid through the flow resistance. The low damping of this motion leads to a resonance, at which the flow-resistance nonlinearity produces a net force on the piston that can cause it to compress its spring. Experiments are performed to investigate the nonlinear dynamics of this system, and these results are compared to theoretical and numerical results. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
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.
Wang, Yi-Ze; Wang, Yue-Sheng; Ke, Liao-Liang
2016-09-01
In the present work, the nonlinear vibration of a carbon nanotube which is subjected to the external parametric excitation is studied. By the nonlocal continuum theory and nonlinear von Kármán beam theory, the governing equation of the carbon nanotube is derived with the consideration of the large deformation. The principle parametric resonance of the nanotube is discussed and the approximation explicit solution is presented by the multiple scale method. Numerical calculations are performed. It can be observed that when the mode number is 1, the stable region can be significantly changed by the parametric excitation, length-to-diameter ratio and matrix stiffness. This phenomenon becomes different to appear if the mode number increases. Moreover, the small scale effects have great influences on the positive bifurcation point for the short carbon nanotube, and the nonlocal continuum theory can present the proper model.
Directory of Open Access Journals (Sweden)
M. Li
2012-01-01
Full Text Available This paper proposes a mathematical model of the multirotor system with a flexible coupling on spring supports on Lagrange's approach, which has taken into account the effects of dynamic angular misalignment and mass unbalance. Then its nonlinear dynamic behaviors of the system are discussed based on the method of multiple scales and numerical technique, respectively. The results show that the responses of the system in lateral directions contain a similar component to that of the mass unbalanced system on both the vibrating frequency and amplitude and involve the typical nonlinear components such as the ones from some combined frequencies; the results also reveal that the numerical agreements on the above-mentioned methods are perfect for the transient responses.
Cazzulani, Gabriele; Resta, Ferruccio; Ripamonti, Francesco
2012-04-01
Large mechanical structures are often affected by high level vibrations due to their flexibility. These vibrations can reduce the system performances and lifetime and the use of active vibration control strategies becomes very attractive. In this paper a combination of resonant control and a disturbance estimator is proposed. This solution is able to improve the system performances during the transient motion and also to reject the disturbance forces acting on the system. Both control logics are based on a modal approach, since it allows to describe the structure dynamics considering only few degrees of freedom.
Non-linear vibrational response of Ge and SiC membranes
Zhou, L. Q.; Colston, G.; Pearce, M. J.; Prince, R. G.; Myronov, M.; Leadley, D. R.; Trushkevych, O.; Edwards, R. S.
2017-07-01
Characterisation of membranes produced for use as micro-electro-mechanical systems using vibrational techniques can give a measure of their behaviour and suitability for operation in different environments. Two membranes are studied here: germanium (Ge) and cubic silicon carbide (3C-SiC) on a silicon (Si) substrate. When driven at higher displacements, the membranes exhibit self-protecting behaviour. The resonant vibration amplitude is limited to a maximum value of around 10 nm, through dissipation of energy via higher harmonic vibrations. This is observed for both materials, despite their different Young's moduli and defect densities.
Svinkin, Mark R.
2016-12-01
The authors suggested a hybrid method for modeling the time history of structural vibrations triggered by impact dynamic loads from construction equipment and blasting, and they stated, "In this work, a hybrid method has been proposed to calculate the theoretical seismograms of structural vibrations. The word "hybrid" denotes a combination of field measurements and computer simulations. Then, based on nonlinear system theory, a novel method is proposed to predict the signal induced by impact loading".
Bouchard, M
2001-01-01
In recent years, a few articles describing the use of neural networks for nonlinear active control of sound and vibration were published. Using a control structure with two multilayer feedforward neural networks (one as a nonlinear controller and one as a nonlinear plant model), steepest descent algorithms based on two distinct gradient approaches were introduced for the training of the controller network. The two gradient approaches were sometimes called the filtered-x approach and the adjoint approach. Some recursive-least-squares algorithms were also introduced, using the adjoint approach. In this paper, an heuristic procedure is introduced for the development of recursive-least-squares algorithms based on the filtered-x and the adjoint gradient approaches. This leads to the development of new recursive-least-squares algorithms for the training of the controller neural network in the two networks structure. These new algorithms produce a better convergence performance than previously published algorithms. Differences in the performance of algorithms using the filtered-x and the adjoint gradient approaches are discussed in the paper. The computational load of the algorithms discussed in the paper is evaluated for multichannel systems of nonlinear active control. Simulation results are presented to compare the convergence performance of the algorithms, showing the convergence gain provided by the new algorithms.
Rezaee, Mousa; Jahangiri, Reza
2015-05-01
In this study, in the presence of supersonic aerodynamic loading, the nonlinear and chaotic vibrations and stability of a simply supported Functionally Graded Piezoelectric (FGP) rectangular plate with bonded piezoelectric layer have been investigated. It is assumed that the plate is simultaneously exposed to the effects of harmonic uniaxial in-plane force and transverse piezoelectric excitations and aerodynamic loading. It is considered that the potential distribution varies linearly through the piezoelectric layer thickness, and the aerodynamic load is modeled by the first order piston theory. The von-Karman nonlinear strain-displacement relations are used to consider the geometrical nonlinearity. Based on the Classical Plate Theory (CPT) and applying the Hamilton's principle, the nonlinear coupled partial differential equations of motion are derived. The Galerkin's procedure is used to reduce the equations of motion to nonlinear ordinary differential Mathieu equations. The validity of the formulation for analyzing the Limit Cycle Oscillation (LCO), aero-elastic stability boundaries is accomplished by comparing the results with those of the literature, and the convergence study of the FGP plate is performed. By applying the Multiple Scales Method, the case of 1:2 internal resonance and primary parametric resonance are taken into account and the corresponding averaged equations are derived and analyzed numerically. The results are provided to investigate the effects of the forcing/piezoelectric detuning parameter, amplitude of forcing/piezoelectric excitation and dynamic pressure, on the nonlinear dynamics and chaotic behavior of the FGP plate. It is revealed that under the certain conditions, due to the existence of bi-stable region of non-trivial solutions, system shows the hysteretic behavior. Moreover, in absence of airflow, it is observed that variation of control parameters leads to the multi periodic and chaotic motions.
Interferometric star tracker Project
National Aeronautics and Space Administration — Optical Physics Company (OPC) proposes to develop a high accuracy version of its interferometric star tracker capable of meeting the milli-arcsecond-level pointing...
DEFF Research Database (Denmark)
Zhang, Zili; Nielsen, Søren R. K.; Basu, Biswajit
2015-01-01
Tuned liquid dampers (TLDs) utilize the sloshing motion of the fluid to suppress structural vibrations and become a natural candidate for damping vibrations in rotating wind turbine blades. The centrifugal acceleration at the tip of a wind turbine blade can reach a magnitude of 7–8g. This facilit......Tuned liquid dampers (TLDs) utilize the sloshing motion of the fluid to suppress structural vibrations and become a natural candidate for damping vibrations in rotating wind turbine blades. The centrifugal acceleration at the tip of a wind turbine blade can reach a magnitude of 7–8g...... studied in the numerical simulation. It is shown that the one-mode model is able to predict the sloshing force and the damped structural response accurately, since the primary damping effect on the structure is achieved by the first sloshing mode of the fluid. Although it is unable to predict the fluid...
Institute of Scientific and Technical Information of China (English)
郑雨军; 丁世良
2000-01-01
The vibrational excitations of bent triatomic molecules are studied by using Lie algebra. The RMS error of fitting 30 spectroscopic data is 1.66 cm-1 for SO2. The results show that the expansion of a molecular algebraic Hamiltonian can well describe the experimental data. And the total vibrational levels can be calculated using this Hamiltonian. At the same time, the potential energy surface can also be obtained with the algebraic Hamiltonian.
Subrahmanyam, K. B.; Kaza, K. R. V.; Brown, G. V.; Lawrence, C.
1987-01-01
The coupled bending-bending-torsional equations of dynamic motion of rotating, linearly pretwisted blades are derived including large precone, second degree geometric nonlinearities and Coriolis effects. The equations are solved by the Galerkin method and a linear perturbation technique. Accuracy of the present method is verified by conparisons of predicted frequencies and steady state deflections with those from MSC/NASTRAN and from experiments. Parametric results are generated to establish where inclusion of only the second degree geometric nonlinearities is adequate. The nonlinear terms causing torsional divergence in thin blades are identified. The effects of Coriolis terms and several other structurally nonlinear terms are studied, and their relative importance is examined.
Subrahmanyam, K. B.; Kaza, K. R. V.; Brown, G. V.; Lawrence, C.
1986-01-01
The coupled bending-bending-torsional equations of dynamic motion of rotating, linearly pretwisted blades are derived including large precone, second degree geometric nonlinearities and Coriolis effects. The equations are solved by the Galerkin method and a linear perturbation technique. Accuracy of the present method is verified by comparisons of predicted frequencies and steady state deflections with those from MSC/NASTRAN and from experiments. Parametric results are generated to establish where inclusion of only the second degree geometric nonlinearities is adequate. The nonlinear terms causing torsional divergence in thin blades are identified. The effects of Coriolis terms and several other structurally nonlinear terms are studied, and their relative importance is examined.
Energy Technology Data Exchange (ETDEWEB)
Dijkstra, Arend G., E-mail: arend.dijkstra@mpsd.mpg.de, E-mail: tanimura@kuchem.kyoto-u.ac.jp [Max Planck Institute for the Structure and Dynamics of Matter, Hamburg (Germany); Tanimura, Yoshitaka, E-mail: arend.dijkstra@mpsd.mpg.de, E-mail: tanimura@kuchem.kyoto-u.ac.jp [Department of Chemistry, Kyoto University, Kyoto (Japan)
2015-06-07
We study hole, electron, and exciton transports in a charge transfer system in the presence of underdamped vibrational motion. We analyze the signature of these processes in the linear and third-, and fifth-order nonlinear electronic spectra. Calculations are performed with a numerically exact hierarchical equations of motion method for an underdamped Brownian oscillator spectral density. We find that combining electron, hole, and exciton transfers can lead to non-trivial spectra with more structure than with excitonic coupling alone. Traces taken during the waiting time of a two-dimensional (2D) spectrum are dominated by vibrational motion and do not reflect the electron, hole, and exciton dynamics directly. We find that the fifth-order nonlinear response is particularly sensitive to the charge transfer process. While third-order 2D spectroscopy detects the correlation between two coherences, fifth-order 2D spectroscopy (2D population spectroscopy) is here designed to detect correlations between the excited states during two different time periods.
Dijkstra, Arend G; Tanimura, Yoshitaka
2015-06-01
We study hole, electron, and exciton transports in a charge transfer system in the presence of underdamped vibrational motion. We analyze the signature of these processes in the linear and third-, and fifth-order nonlinear electronic spectra. Calculations are performed with a numerically exact hierarchical equations of motion method for an underdamped Brownian oscillator spectral density. We find that combining electron, hole, and exciton transfers can lead to non-trivial spectra with more structure than with excitonic coupling alone. Traces taken during the waiting time of a two-dimensional (2D) spectrum are dominated by vibrational motion and do not reflect the electron, hole, and exciton dynamics directly. We find that the fifth-order nonlinear response is particularly sensitive to the charge transfer process. While third-order 2D spectroscopy detects the correlation between two coherences, fifth-order 2D spectroscopy (2D population spectroscopy) is here designed to detect correlations between the excited states during two different time periods.
John, C Jesintha; Amalanathan, M; Sajan, D; Lakshmi, K Udaya; Joe, I Hubert
2011-01-01
FT-Raman and FT-IR spectra of the nonlinear optical crystal 1-(4-N,N-dimethylaminopyridinium) acetic acid bromide monohydrate have been recorded and analyzed. The equilibrium geometry, vibrational wavenumbers and the first order hyperpolarizability of the crystal have been calculated with the help of density functional theory computations. The assignments of the vibrational spectra have been carried out with the help of Scaled Quantum Mechanic force field theory. Optimized geometry gives the charge transfer interaction of the pyridine ring and the amino group in the electron-donor side of the nonlinear optic chromophore. Electron-phonon coupling and O-H⋯O interactions in making the molecule nonlinear optical active have been analyzed based on the vibrational spectral features. The Natural Bond Orbital analysis confirms the occurrence of strong intermolecular O-H⋯O hydrogen bonding. Copyright © 2010 Elsevier B.V. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Volpe, M.C. [Caen Univ., 14 (France)
1997-12-31
Double Giant Resonances, vibrational states in which a Giant Resonance is excited on top of another Giant Resonance, have been in the last years the object of many theories and studies. Whereas the measured energies and widths of these states agree with a theoretical predictions, the measured excitation cross sections on the other hand are almost always larger than the calculated ones. The standard theoretical approaches are based both on a harmonic approximation for the collective motion on the nucleus and on its linear response to an external field. In this work the influence of anharmonicities and non-linearities in the external field on the excitation of Double Giant Resonances are studied. First, an oscillator model and an extension of the Lipkin-Meshkow-Glick model are used to study the effects of anharmonicities and non-linearities on the excitation probabilities. The results show that these terms can influence the excitation probability of the second excited state in a significant way. Secondly, these exactly soluble schematic models are used to study some of the approximations made in microscopic calculations based on boson expansion methods and also some aspects on the time-dependent mean field approach. Finally, a microscopic calculation of the Coulomb excitation cross sections of Double Giant Resonances is presented for several nuclei. It is found that, for {sup 208} Pb, the inclusion of anharmonicities and non-linearities and the consideration of many states that play a role in the excitation process give a satisfactory agreement between calculated and observed cross sections. (author). 113 refs.
On the vibrations of a simply supported square plate on a weakly nonlinear elastic foundation
Zarubinskaya, M.A.; Van Horssen, W.T.
2003-01-01
In this paper an initial-boundary value problem for a weakly nonlinear plate equation with a quadratic nonlinearity will be studied. This initial-boundary value problem can be regarded as a simple model describing free oscillations of a simply supported square plate on an elastic foundation. It is a
Experimental verification of a bridge-shaped, nonlinear vibration energy harvester
Energy Technology Data Exchange (ETDEWEB)
Gafforelli, Giacomo, E-mail: giacomo.gafforelli@polimi.it; Corigliano, Alberto [Department of Civil and Environmental Engineering, Politecnico di Milano, Milano, 20133 (Italy); Xu, Ruize; Kim, Sang-Gook [Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
2014-11-17
This paper reports a comprehensive modeling and experimental characterization of a bridge shaped nonlinear energy harvester. A doubly clamped beam at large deflection requires stretching strain in addition to the bending strain to be geometrically compatible, which stiffens the beam as the beam deflects and transforms the dynamics to a nonlinear regime. The Duffing mode non-linear resonance widens the frequency bandwidth significantly at higher frequencies than the linear resonant frequency. The modeling includes a nonlinear measure of strain coupled with piezoelectric constitutive equations which end up in nonlinear coupling terms in the equations of motion. The main result supports that the power generation is bounded by the mechanical damping for both linear and nonlinear harvesters. Modeling also shows the power generation is over a wider bandwidth in the nonlinear case. A prototype is manufactured and tested to measure the power generation at different load resistances and acceleration amplitudes. The prototype shows a nonlinear behavior with well-matched experimental data to the modeling.
Samareh, Hossein; Khoshrou, Seyed Hassan; Shahriar, Kourosh; Ebadzadeh, Mohammad Mehdi; Eslami, Mohammad
2017-09-01
When particle's wave velocity resulting from mining blasts exceeds a certain level, then the intensity of produced vibrations incur damages to the structures around the blasting regions. Development of mathematical models for predicting the peak particle velocity (PPV) based on the properties of the wave emission environment is an appropriate method for better designing of blasting parameters, since the probability of incurred damages can considerably be mitigated by controlling the intensity of vibrations at the building sites. In this research, first out of 11 blasting and geo-mechanical parameters of rock masses, four parameters which had the greatest influence on the vibrational wave velocities were specified using regression analysis. Thereafter, some models were developed for predicting the PPV by nonlinear regression analysis (NLRA) and artificial neural network (ANN) with correlation coefficients of 0.854 and 0.662, respectively. Afterward, the coefficients associated with the parameters in the NLRA model were optimized using optimization particle swarm-genetic algorithm. The values of PPV were estimated for 18 testing dataset in order to evaluate the accuracy of the prediction and performance of the developed models. By calculating statistical indices for the test recorded maps, it was found that the optimized model can predict the PPV with a lower error than the other two models. Furthermore, considering the correlation coefficient (0.75) between the values of the PPV measured and predicted by the optimized nonlinear model, it was found that this model possesses a more desirable performance for predicting the PPV than the other two models.
Nonlinear Vibration Induced by the Water-film Whirl and Whip in a Sliding Bearing Rotor System
Institute of Scientific and Technical Information of China (English)
ZHAI Liming; LUO Yongyao; WANG Zhengwei; KITAUCHI Seishiro; MIYAGAWA Kazuyoshi
2016-01-01
Many industrial applications and experiments have shown that sliding bearings often experience fluid film whip due to nonlinear fluid film forces which can cause rotor-stator rub-impact failures. The oil-film whips have attracted many studies while the water-film whips in the water lubricated sliding bearing have been little researched with the mechanism still an open problem. The dynamic fluid film forces in a water sliding bearing are investigated numerically with rotational, whirling and squeezing motions of the journal using a nonlinear model to identify the relationships between the three motions. Rotor speed-up and slow-down experiments are then conducted with the rotor system supported by a water lubricated sliding bearing to induce the water-film whirl/whip and verify the relationship. The experimental results show that the vibrations of the journal alternated between increasing and decreasing rather than continuously increasing as the rotational speed increased to twice the first critical speed, which can be explained well by the nonlinear model. The radial growth rate of the whirl motion greatly affects the whirl frequency of the journal and is responsible for the frequency lock in the water-film whip. Further analysis shows that increasing the lubricating water flow rate changes the water-film whirl/whip characteristics, reduces the first critical speed, advances the time when significant water-film whirling motion occurs, and also increases the vibration amplitude at the bearing center which may lead to the rotor-stator rub-impact. The study gives the insight into the water-film whirl and whip in the water lubricated sliding bearing.
Nonlinear vibration induced by the water-film whirl and whip in a sliding bearing rotor system
Zhai, Liming; Luo, Yongyao; Wang, Zhengwei; Kitauchi, Seishiro; Miyagawa, Kazuyoshi
2016-03-01
Many industrial applications and experiments have shown that sliding bearings often experience fluid film whip due to nonlinear fluid film forces which can cause rotor-stator rub-impact failures. The oil-film whips have attracted many studies while the water-film whips in the water lubricated sliding bearing have been little researched with the mechanism still an open problem. The dynamic fluid film forces in a water sliding bearing are investigated numerically with rotational, whirling and squeezing motions of the journal using a nonlinear model to identify the relationships between the three motions. Rotor speed-up and slow-down experiments are then conducted with the rotor system supported by a water lubricated sliding bearing to induce the water-film whirl/whip and verify the relationship. The experimental results show that the vibrations of the journal alternated between increasing and decreasing rather than continuously increasing as the rotational speed increased to twice the first critical speed, which can be explained well by the nonlinear model. The radial growth rate of the whirl motion greatly affects the whirl frequency of the journal and is responsible for the frequency lock in the water-film whip. Further analysis shows that increasing the lubricating water flow rate changes the water-film whirl/whip characteristics, reduces the first critical speed, advances the time when significant water-film whirling motion occurs, and also increases the vibration amplitude at the bearing center which may lead to the rotor-stator rub-impact. The study gives the insight into the water-film whirl and whip in the water lubricated sliding bearing.
DEFF Research Database (Denmark)
Lazarov, Boyan Stefanov; Thomsen, Jon Juel; Snaeland, Sveinn Orri
2008-01-01
The aim of this article is to investigate how highfrequency (HF) excitation, combined with strong nonlinear elastic material behavior, influences the effective material or structural properties for low-frequency excitation and wave propagation. The HF effects are demonstrated on discrete linear s...... spring-mass chains with non-linear inclusions. The presented analytical and numerical results suggest that the effective material properties can easily be altered by establishing finite amplitude HF standing waves in the non-linear regions of the chain....
Akbari, M. R.; Ganji, D. D.; Ahmadi, A. R.; Kachapi, Sayyid H. Hashemi
2014-03-01
In the current paper, a simplified model of Tower Cranes has been presented in order to investigate and analyze the nonlinear differential equation governing on the presented system in three different cases by Algebraic Method (AGM). Comparisons have been made between AGM and Numerical Solution, and these results have been indicated that this approach is very efficient and easy so it can be applied for other nonlinear equations. It is citable that there are some valuable advantages in this way of solving differential equations and also the answer of various sets of complicated differential equations can be achieved in this manner which in the other methods, so far, they have not had acceptable solutions. The simplification of the solution procedure in Algebraic Method and its application for solving a wide variety of differential equations not only in Vibrations but also in different fields of study such as fluid mechanics, chemical engineering, etc. make AGM be a powerful and useful role model for researchers in order to solve complicated nonlinear differential equations.
Nonlinear Dynamics of a Spring-Supported Piston in a Vibrated Liquid-Filled Housing: I. Analysis
Torczynski, J. R.; O'Hern, T. J.; Clausen, J. R.
2016-11-01
The nonlinear dynamics of a piston supported by a spring in a vibrated liquid-filled housing is analyzed. The liquid is viscous, and the flow passages are narrow and depend on piston position. Ordinarily, the piston motion is highly damped. However, if bellows are added to both ends of the housing, then the piston, liquid, and bellows can execute a collective motion that forces relatively little liquid through the flow passages and thus has low damping and a strong resonance. At this frequency, the motion is large, and the nonlinearity from the flow passages produces a net force on the piston that can cause it to compress its spring. This nonlinear dynamical system is analyzed using a perturbation expansion of the Navier-Stokes equations, and the perturbation results are compared to corresponding ALE Navier-Stokes simulations. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Jazar, Reza
2015-01-01
This book focuses on the latest applications of nonlinear approaches in different disciplines of engineering. For each selected topic, detailed concept development, derivations, and relevant knowledge are provided for the convenience of the readers. The topics range from dynamic systems and control to optimal approaches in nonlinear dynamics. The volume includes invited chapters from world class experts in the field. The selected topics are of great interest in the fields of engineering and physics and this book is ideal for engineers and researchers working in a broad range of practical topics and approaches. This book also: · Explores the most up-to-date applications and underlying principles of nonlinear approaches to problems in engineering and physics, including sections on analytic nonlinearity and practical nonlinearity · Enlightens readers to the conceptual significance of nonlinear approaches with examples of applications in scientific and engineering problems from v...
Subrahmanyam, K. B.; Kaza, K. R. V.
1985-01-01
The effects of pretwist, precone, setting angle, Coriolis forces and second degree geometric nonlinearities on the natural frequencies, steady state deflections and mode shapes of rotating, torsionally rigid, cantilevered beams were studied. The governing coupled equations of flap lag extensional motion are derived including the effects of large precone and retaining geometric nonlinearities up to second degree. The Galerkin method, with nonrotating normal modes, is used for the solution of both steady state nonlinear equations and linear perturbation equations. Parametric indicating the individual and collective effects of pretwist, precone, Coriolis forces and second degree geometric nonlinearities on the steady state deflection, natural frequencies and mode shapes of rotating blades are presented. It is indicated that the second degree geometric nonlinear terms, which vanish for zero precone, can produce frequency changes of engineering significance. Further confirmation of the validity of including those generated by MSC NASTRAN. It is indicated that the linear and nonlinear Coriolis effects must be included in analyzing thick blades. The Coriolis effects are significant on the first flatwise and the first edgewise modes.
Nonlinear Steady-State Vibration Analysis of a Beam with Breathing Cracks
Kamiya, Keisuke; Yoshinaga, Terumitsu
This paper presents a method for analysis of steady-state vibration of a beam with breathing cracks, which open and close during vibration. There are several papers treating problems of vibration analysis of a beam with breathing cracks. However, due to their treatments of the condition which determines the switch between the open and closed states of the crack, it is difficult for one to obtain steady-state vibration efficiently by methods such as the incremental harmonic balance method. Since opening and closing of a breathing crack depends on the sign of the bending moment, or the curvature, of the beam, the key point to this problem is explicit treatment of the bending moment. The mixed variational principle allows one to use deflection as well as bending moment as primary variables in the governing equation. In this paper a governing equation of a beam with breathing cracks is derived by a finite element procedure based on the mixed variational principle. Then, the derived governing equations are solved by combining the iteration method and the harmonic balance method. Finally, examples of analysis by the presented method are given.
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.
Gonçalves, P. B.; Silva, F. M. A.; Del Prado, Z. J. G. N.
2008-08-01
In formulating mathematical models for dynamical systems, obtaining a high degree of qualitative correctness (i.e. predictive capability) may not be the only objective. The model must be useful for its intended application, and models of reduced complexity are attractive in many cases where time-consuming numerical procedures are required. This paper discusses the derivation of discrete low-dimensional models for the nonlinear vibration analysis of thin cylindrical shells. In order to understand the peculiarities inherent to this class of structural problems, the nonlinear vibrations and dynamic stability of a circular cylindrical shell subjected to static and dynamic loads are analyzed. This choice is based on the fact that cylindrical shells exhibit a highly nonlinear behavior under both static and dynamic loads. Geometric nonlinearities due to finite-amplitude shell motions are considered by using Donnell's nonlinear shallow-shell theory. A perturbation procedure, validated in previous studies, is used to derive a general expression for the nonlinear vibration modes and the discretized equations of motion are obtained by the Galerkin method using modal expansions for the displacements that satisfy all the relevant boundary and symmetry conditions. Next, the model is analyzed via the Karhunen-Loève expansion to investigate the relative importance of each mode obtained by the perturbation solution on the nonlinear response and total energy of the system. The responses of several low-dimensional models are compared. It is shown that rather low-dimensional but properly selected models can describe with good accuracy the response of the shell up to very large vibration amplitudes.
Directory of Open Access Journals (Sweden)
Tamer Ömer
2016-03-01
Full Text Available The molecular modeling of p-nitroanilinium perchlorate molecule was carried out by using B3LYP and HSEH1PBE levels of density functional theory (DFT. The IR and Raman spectra were simulated and the assignments of vibrational modes were performed on the basis of relative contribution of various internal co-ordinates. NBO analysis was performed to demonstrate charge transfer, conjugative interactions and the formation of intramolecular hydrogen bonding interactions within PNAPC. Obtained large dipole moment values showed that PNAPC is a highly polarizable complex, and the charge transfer occurs within PNAPC. Hydrogen bonding and charge transfer interactions were also displayed by small HOMO-LUMO gap and molecular electrostatic potential (MEP surface. The strong evidences that the material can be used as an efficient nonlinear optical (NLO material of PNAPC were demonstrated by considerable polarizability and hyperpolarizability values obtained at DFT levels.
Bao, Bin; Guyomar, Daniel; Lallart, Mickaël
2016-09-01
This article proposes a nonlinear tri-interleaved piezoelectric topology based on the synchronized switch damping on inductor (SSDI) technique, which can be applied to phononic metamaterials for elastic wave control and effective low-frequency vibration reduction. A comparison of the attenuation performance is made between piezoelectric phononic metamaterial with distributed SSDI topology (each SSDI shunt being independently connected to a single piezoelectric element) and piezoelectric phononic metamaterial with the proposed electronic topology. Theoretical results show excellent band gap hybridization (near-coupling between Bragg scattering mechanism and wideband resonance mechanism induced by synchronized switch damping networks in piezoelectric phononic metamaterials) with the proposed electronic topology over the investigated frequency domain. Furthermore, piezoelectric phononic metamaterials with proposed electronic topology generated a better low-frequency broadband gap, which is experimentally validated by measuring the harmonic response of a piezoelectric phononic metamaterial beam under clamped-clamped boundary conditions.
Lu, Y.; Cottone, F.; Boisseau, S.; Galayko, D.; Marty, F.; Basset, P.
2015-12-01
This paper reports for the first time a MEMS electrostatic vibration energy harvester (e-VEH) with corona-charged vertical electrets on its electrodes. The bandwidth of the 1-cm2 device is extended in low and high frequencies by nonlinear elastic stoppers. With a bias voltage of 46 V (electret@21 V + DC external source@25 V) between the electrodes, the RMS power of the device reaches 0.89 μW at 33 Hz and 6.6 μW at 428 Hz. The -3dB frequency band including the hysteresis is 223∼432 Hz, the one excluding the hysteresis 88∼166 Hz. We also demonstrate the charging of a 47 μF capacitor used for powering a wireless and autonomous temperature sensor node with a data transmission beyond 10 m at 868 MHz.
Free and Forced Vibrations of the Strongly Nonlinear Cubic-Quintic Duffing Oscillators
Karahan, M. M. Fatih; Pakdemirli, Mehmet
2017-01-01
Strongly nonlinear cubic-quintic Duffing oscillatoris considered. Approximate solutions are derived using the multiple scales Lindstedt Poincare method (MSLP), a relatively new method developed for strongly nonlinear oscillators. The free undamped oscillator is considered first. Approximate analytical solutions of the MSLP are contrasted with the classical multiple scales (MS) method and numerical simulations. It is found that contrary to the classical MS method, the MSLP can provide acceptable solutions for the case of strong nonlinearities. Next, the forced and damped case is treated. Frequency response curves of both the MS and MSLP methods are obtained and contrasted with the numerical solutions. The MSLP method and numerical simulations are in good agreement while there are discrepancies between the MS and numerical solutions.
Active suppression of nonlinear composite beam vibrations by selected control algorithms
Warminski, Jerzy; Bochenski, Marcin; Jarzyna, Wojciech; Filipek, Piotr; Augustyniak, Michal
2011-05-01
This paper is focused on application of different control algorithms for a flexible, geometrically nonlinear beam-like structure with Macro Fiber Composite (MFC) actuator. Based on the mathematical model of a geometrically nonlinear beam, analytical solutions for Nonlinear Saturation Controller (NSC) are obtained using Multiple Scale Method. Effectiveness of different control strategies is evaluated by numerical simulations in Matlab-Simulink software. Then, the Digital Signal Processing (DSP) controller and selected control algorithms are implemented to the physical system to compare numerical and experimental results. Detailed analysis for the NSC system is carried out, especially for high level of amplitude and wide range of frequencies of excitation. Finally, the efficiency of the considered controllers is tested experimentally for a more complex autoparametric " L-shape" beam system.
Institute of Scientific and Technical Information of China (English)
张文娟; 俞建宁; 张建刚; 杨留猛
2013-01-01
The complex dynamic behavior of the autoparametric system with an attached damped pendulum is studied. The dynamical equation of the system is established using Lagrangian and Newton's second law. The chaotic behavior of the system is analyzed by means of Lyapunov exponent spectrum and the bifurcation diagrams. Nonlinear feedback control method is used to control the chaotic motion state of this vibration system, and then Matlab numerical simulation can prove that nonlinear feedback control method can realize the control of chaotic system, and the method is effective as well.%研究一类带有黏性阻尼摆的振动系统的复杂动力学行为.通过拉格朗日方程和牛顿第二定律,建立此振动系统的动力学方程.借助相图、Lyapunov指数谱和分岔图研究系统的混沌行为,用非线性反馈控制方法对此类振动系统的运动状态进行控制,利用Matlab进行数值仿真.通过受控参数证明利用非线性反馈方法可以实现系统的混沌控制,系统的混沌行为得到了有效控制.
Xiong, Huai; Kong, Xianren; Li, Haiqin; Yang, Zhenguo
2017-01-01
This paper considers dynamics of bilinear hysteretic systems, which are widely used for vibration control and vibration absorption such as magneto-rheological damper, metal-rubber. The method of incremental harmonic balance (IHB) technique that hysteresis is considered in the corrective term is improved in order to determine periodic solutions of bilinear hysteretic systems. The improved continuation method called two points tracing algorithm which is stable to the turning point makes the calculation more efficient for tracing amplitude-frequency response. Precise Hsu's method for analysing the stability of periodic solutions is introduced. The effects of different parameters of bilinear hysteretic oscillator on the response are discussed numerically. Some numerical simulations of considered bilinear hysteretic systems, including a single DOF and a 2DOF system, are effectively obtained by the modified IHB method and the results compare very well with the 4-oder Runge-Kutta method.
El-Mansy, M. A. M.
2017-08-01
Structural and vibrational spectroscopic studies were performed on indigo carmine (IC) isomers using FT-IR spectral analysis along with DFT/B3LYP method utilizing Gaussian 09 software. GaussView 5 program has been employed to perform a detailed interpretation of vibrational spectra. Simulation of infrared spectra has led to an excellent overall agreement with the observed spectral patterns. Mulliken population analyses on atomic charges, MEP, HOMO-LUMO, NLO, first order hyperpolarizability and thermodynamic properties have been examined by (DFT/B3LYP) method with the SDD basis set level. Density of state spectra (DOS) were calculated using GaussSum 3 at the same level of theory. Molecular modeling approved that DOS Spectra are the most significant tools for differentiating between two IC isomers so far. Moreover, The IC isomers (cis-isomer) have shown an extended applicability for manufacturing both NLO and photovoltaic devices such as solar cells.
Directory of Open Access Journals (Sweden)
Zahra Etesami
2017-05-01
Full Text Available We investigate harvesting electrical energy from Gaussian white, Gaussian colored, telegraph and random phase-random amplitude (RARP noises, using linear and nonlinear electromechanical systems. We show that the output power of the linear system with one or two degrees of freedom, is maximum for the Gaussian white noise. The response of the system with two degrees of freedom is widened in a larger frequency domain compared to that of a single degree of freedom system. A nonlinear system generates more power than a linear one.
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.
Asath, R. Mohamed; Premkumar, S.; Rekha, T. N.; Jawahar, A.; Mathavan, T.; Benial, A. Milton Franklin
2016-05-01
The conformational analysis was carried out for 2-amino-3-chloro-5-trifluoromethylpyridine using potential energy surface (PES) scan and the most stable optimized conformer was predicted. The theoretical vibrational frequencies were calculated for the optimized geometry using DFT/B3LYP cc-pVQZ basis set by Gaussian 09 Program. The vibrational frequencies were assigned on the basis of potential energy distribution calculation using VEDA 4.0 program package. The Mulliken atomic charge values were calculated. In the Frontier molecular orbitals analysis, the molecular reactivity, kinetic stability, intermolecular charge transfer studies and the calculation of ionization energy, electron affinity, global hardness, chemical potential, electrophilicity index and softness of the molecule were carried out. The nonlinear optical (NLO) activity was studied and the first order hyperpolarizability value was computed, which was 3.48 times greater than the urea. The natural bond orbital analysis was also performed to confirm the NLO activity of the molecule. Hence, the ACTP molecule is a promising candidate for NLO materials.
NON-LINEAR VIBRATION MODELING WITH THE HELP OF FUNCTIONAL SERIES
Directory of Open Access Journals (Sweden)
Z. M. Ghasanov
2010-06-01
Full Text Available The algorithm of modeling the significantly nonlinear processes – «black boxes» – is offered. It uses functional series. The algorithm is described on the example of modeling of complex oscillations, which occur in acoustic flaw detection.
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.
Assessment of nonlinear distortions in modal testing and analysis of vibrating automotive structures
Verboven, P.; Guillaume, P.; Vanlanduit, S.; Cauberghe, B.
2006-05-01
In this paper, new developments for the nonparametric processing of modal test data are presented. Classically, random noise signals are applied to deal with possible nonlinear distortions during frequency response function measurements of linear dynamic systems. However, the use of multisine excitation signals allows the engineer to control much more his experiments. First of all, the nonparametric estimation of multivariable frequency response functions can be more easily based on an "errors-in-variables" stochastic framework. In addition, the application of a well-chosen multisine excitation permits improvement of the data quality, as well as the detection, qualification and quantification of nonlinear distortions during FRF measurements. To make the presented techniques available for multi-input modal testing, attention is paid to the design of optimal multi-input excitations by maximizing the Fisher information matrix as well as minimizing the crest factor of the applied excitation.
Kougioumtzoglou, I. A.; Fragkoulis, V. C.; Pantelous, A. A.; Pirrotta, A.
2017-09-01
A frequency domain methodology is developed for stochastic response determination of multi-degree-of-freedom (MDOF) linear and nonlinear structural systems with singular matrices. This system modeling can arise when a greater than the minimum number of coordinates/DOFs is utilized, and can be advantageous, for instance, in cases of complex multibody systems where the explicit formulation of the equations of motion can be a nontrivial task. In such cases, the introduction of additional/redundant DOFs can facilitate the formulation of the equations of motion in a less labor intensive manner. Specifically, relying on the generalized matrix inverse theory, a Moore-Penrose (M-P) based frequency response function (FRF) is determined for a linear structural system with singular matrices. Next, relying on the M-P FRF a spectral input-output (excitation-response) relationship is derived in the frequency domain for determining the linear system response power spectrum. Further, the above methodology is extended via statistical linearization to account for nonlinear systems. This leads to an iterative determination of the system response mean vector and covariance matrix. Furthermore, to account for singular matrices, the generalization of a widely utilized formula that facilitates the application of statistical linearization is proved as well. The formula relates to the expectation of the derivatives of the system nonlinear function and is based on a Gaussian response assumption. Several linear and nonlinear MDOF structural systems with singular matrices are considered as numerical examples for demonstrating the validity and applicability of the developed frequency domain methodology.
Nonlinear Vibrations of FGM Cylindrical Panel with Simply Supported Edges in Air Flow
Directory of Open Access Journals (Sweden)
Y. X. Hao
2015-01-01
Full Text Available Chaotic and periodic motions of an FGM cylindrical panel in hypersonic flow are investigated. The cylindrical panel is also subjected to in-plane external loads and a linear temperature variation in the thickness direction. The temperature dependent material properties of panel which are assumed to be changed through the thickness direction only can be determined by a simple power distribution in terms of the volume fractions. With Hamilton’s principle for an elastic body, a nonlinear dynamical model based on Reddy’s first-order shear deformation shell theory and von Karman type geometric nonlinear relationship is derived in the form of partial equations. A third-order piston theory is adopted to evaluate the hypersonic aerodynamic load. Here, Galerkin’s method is employed to discretize this continuous nonlinear dynamic system to ordinary differential governing equations involving two degrees of freedom. The chaotic and periodic response are studied by the direct numerical simulation method for influences of different Mach number and the value of in-plane load. The bifurcations, Poincare section, waveform, and phase plots are presented.
Yan, Guiyun; Chen, Fuquan; Wu, Yingxiong
2016-01-01
Different from previous researches which mostly focused on linear response control of seismically excited high-rise buildings, this study aims to control nonlinear seismic response of high-rise buildings. To this end, a semi-active control strategy, in which H∞ control algorithm is used and magneto-rheological dampers are employed for an actuator, is presented to suppress the nonlinear vibration. In this strategy, a modified Kalman-Bucy observer which is suitable for the proposed semi-active strategy is developed to obtain the state vector from the measured semi-active control force and acceleration feedback, taking into account of the effects of nonlinearity, disturbance and uncertainty of controlled system parameters by the observed nonlinear accelerations. Then, the proposed semi-active H∞ control strategy is applied to the ASCE 20-story benchmark building when subjected to earthquake excitation and compared with the other control approaches by some control criteria. It is indicated that the proposed semi-active H∞ control strategy provides much better control performances by comparison with the semi-active MPC and Clipped-LQG control approaches, and can reduce nonlinear seismic response and minimize the damage in the buildings. Besides, it enhances the reliability of the control performance when compared with the active control strategy. Thus, the proposed semi-active H∞ control strategy is suitable for suppressing the nonlinear vibration of high-rise buildings.
Hydrogen Bonding in Ionic Liquids Probed by Linear and Nonlinear Vibrational Spectroscopy
Roth, C; Kerlé, D; Friedriszik, F; Lütgens, M; Lochbrunner, S; Kühn, O; Ludwig, R
2012-01-01
Three imidazolium-based ionic liquids of the type [Cnmim][NTf2] with varying alkyl chain lengths (n = 1, 2 and 8) at the 1 position of the imidazolium ring were studied applying IR, linear Raman, and multiplex CARS spectroscopy. The focus has been on the CH-stretching region of the imidazolium ring, which is supposed to carry information about a possible hydrogen bonding network in the ionic liquid. The measurements are compared to calculations of the corresponding anharmonic vibrational spectra for a cluster of [C2mim][NTf2] consisting of four ion pairs. The results support the hypothesis of moderate hydrogen bonding involving the C(4)-H and C(5)-H groups and somewhat stronger hydrogen bonds of the C(2)-H groups.
Nonlinear Dynamical Analysis on Four Semi-Active Dynamic Vibration Absorbers with Time Delay
Directory of Open Access Journals (Sweden)
Yongjun Shen
2013-01-01
Full Text Available In this paper four semi-active dynamic vibration absorbers (DVAs are analytically studied, where the time delay induced by measurement and execution in control procedure is included in the system. The first-order approximate analytical solutions of the four semi-active DVAs are established by the averaging method, based on the illustrated phase difference of the motion parameters. The comparisons between the analytical and the numerical solutions are carried out, which verify the correctness and satisfactory precision of the approximate analytical solutions. Then the effects of the time delay on the dynamical responses are analyzed, and it is found that the stability conditions for the steady-state responses of the primary systems are all periodic functions of time delay, with the same period as the excitation one. At last the effects of time delay on control performance are discussed.
Research on modeling of nonlinear vibration isolation system based on BouceWen model
Institute of Scientific and Technical Information of China (English)
Zhi-ling PENG; Chun-gui ZHOU
2014-01-01
A feedforword neural network of multi-layer topologies for systems with hysteretic nonlinearity is constructed based on BouceWen dif-ferential model. It not only reflects the hysteresis force characteristics of the BouceWen model, but also determines its corresponding pa-rameters. The simulation results show that restoring forceedisplacement curve hysteresis loop is very close to the real curve. The model trained can accurately predict the time response of system. The model is checked under the noise level. The result shows that the model has higher modeling precision, good generalization capability and a certain anti-interference ability.
Using strong nonlinearity and high-frequency vibrations to control effective mechanical stiffness
DEFF Research Database (Denmark)
Thomsen, Jon Juel
2008-01-01
High-frequency excitation (HFE) can be used to change the effective stiffness of an elastic structure, and related quanti-ties such as resonance frequencies, wave speed, buckling loads, and equilibrium states. There are basically two ways to do this: By using parametrical HFE (with or without non...... the method of direct separation of motions with results of a modified multiple scales ap-proach, valid also for strong nonlinearity, the stiffening ef-fect is predicted for a generic 1-dof system, and results are tested against numerical simulation and ((it is planned)) laboratory experiments....
Non-Linear Vibrations, Stability, and Dynamics of Structures and Mechanisms
1989-08-01
particle of matter can occupy only one position in space. On the basis of this law, it is not difficult to show that a rigid body can assume only one...Em+n) is desired, with m > 0, then all terms of O(em +n) must be retained in the expanded equations. With this in mind , we address some other...concerning the 3 nonlinear non-planar response of inextensional beams and of beam-like structures. These include modal interactins both in the
Faster Simulation Methods for the Non-Stationary Random Vibrations of Non-Linear MDOF Systems
DEFF Research Database (Denmark)
Askar, A.; Köylüoglu, H. U.; Nielsen, Søren R. K.;
In this paper semi-analytical forward-difference Monte Carlo simulation procedures are proposed for the determination of the lower order statistics and the Joint Probability Density Function (JPDF) of the stochastic response of geometrically nonlinear multi-degree-of-freedom structural systems....... Such a treatment offers higher rates of convergence, faster speed and higher accuracy. These procedures are compared to the direct Monte Carlo simulation procedure, which uses a fourth order Runge-Kutta scheme with the white noise process approximated by a broad band Ruiz-Penzien broken line process...
Using strong nonlinearity and high-frequency vibrations to control effective mechanical stiffness
DEFF Research Database (Denmark)
Thomsen, Jon Juel
2008-01-01
High-frequency excitation (HFE) can be used to change the effective stiffness of an elastic structure, and related quanti-ties such as resonance frequencies, wave speed, buckling loads, and equilibrium states. There are basically two ways to do this: By using parametrical HFE (with or without non...... the method of direct separation of motions with results of a modified multiple scales ap-proach, valid also for strong nonlinearity, the stiffening ef-fect is predicted for a generic 1-dof system, and results are tested against numerical simulation and ((it is planned)) laboratory experiments....
Bifurcation of piecewise-linear nonlinear vibration system of vehicle suspension
Institute of Scientific and Technical Information of China (English)
Shun ZHONG; Yu-shu CHEN
2009-01-01
A kinetic model of the piecewise-linear nonlinear suspension system that consists of a dominant spring and an assistant spring is established.Bifurcation of the resonance solution to a suspension system with two degrees of freedom is investigated with the singularity theory.Transition sets of the system and 40 groups of bifurcation diagrams are obtained.The local bifurcation is found,and shows the overall characteristics of bifurcation.Based on the relationship between parameters and the topological bifurcation solutions,motion characteristics with different parameters are obtained.The results provides a theoretical basis for the optimal control of vehicle suspension system parameters.
Ko, Chang-Yong; Chang, Yunhee; Kim, Sol-Bi; Kim, Shinki; Kim, Gyoosuk; Ryu, Jeicheong; Mun, Musung
2014-01-01
Numerous studies have reported the efficacy of vibration in sensory feedback or substitution devices for users of myoelectric hand prostheses. Although most myoelectric hand prostheses are presently manipulated by a surface electromyogram (sEMG), only a few studies have been conducted on the effect of vibration on an sEMG. This study aimed to determine whether vibration stimulation affects the linear and nonlinear properties of surface electromyography (sEMG) considering the skin properties. The vibration stimuli, with frequencies ranging from 37 to 258 Hz, were applied to the proximal part of the arms of the eight female and seven male subjects. The skinfold thickness, hardness, and vibration threshold at the stimuli loci were measured. The root mean square (rms) and fractal dimension (DF) of the sEMG were measured at a distance of 1 cm in the upward direction from the stimuli loci. Above 223 Hz there were no differences between the rms of the genders in between the vibration stimuli (p > 0.05). Moreover, no differences were observed between the DF of the genders for any frequency (p > 0.05). Above 149 Hz, there were correlations between the rms and the skin hardness in the females. Otherwise, no correlations were observed between the rms and DF and the skin properties in both genders for most of the frequencies (all p > 0.05). These results suggest that vibration stimuli affect the linear properties of the sEMG, but not the nonlinear properties.
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.
Non-Gaussian approach for parametric random vibration of non-linear structures
Ibrahim, R. A.; Soundararajan, A.
1984-01-01
The dynamic response of a nonlinear, single degree of freedom structural system subjected to a physically white noise parametric excitation is investigated. The Ito stochastic calculus is employed to derive a general differential equation for the moments of the response coordinates. The differential equations of moments of any order are found to be coupled with higher order moments. A non-Gaussian closure scheme is developed to truncate the moment equations up to fourth order. The statistical of the stationary response are computed numerically and compared with analytical solutions predicted by a Gaussian closure scheme and the stochastic averaging method. It is found that the computed results exhibit the jump phenomenon which is typical of the characteristics of deterministic nonlinear systems. In addition, the numerical algorithm leads to multiple solutions all of which give positive mean squares. However, two of these solutions are found to violate the properties of high order moments. One solution preserves the moments properties and demonstrates that the system achieves a stationary response.
Directory of Open Access Journals (Sweden)
de Pontes B. R.
2012-07-01
Full Text Available In this paper, we deal with the research of a vibrating model of an energy harvester device, including the nonlinearities in the model of the piezoelectric coupling and the non-ideal excitation. We show, using numerical simulations, in the analysis of the dynamic responses, that the harvested power is influenced by non-linear vibrations of the structure. Chaotic behavior was also observed, causing of the loss of energy throughout the simulation time. Using a perturbation technique, we find an approximate analytical solution for the non-ideal system. Then, we apply both two control techniques, to keep the considered system, into a stable condition. Both the State Dependent Ricatti Equation (SDRE control as the feedback control by changing the energy of the oscillator, were efficient in controlling of the considered non-ideal system.
Sajan, D; Vijayan, N; Safakath, K; Philip, Reji; Joe, I Hubert
2011-07-28
FT-IR and Raman spectra of the nonlinear optical material sodium acid phthalate hemihydrate crystal have been recorded and analyzed. The equilibrium geometry, bonding features, and harmonic vibrational wavenumbers have been investigated with the help of the B3LYP density functional theory method. A detailed interpretation of the vibrational spectra was carried out with the aid of normal coordinate analysis following the scaled quantum mechanical force field methodology. The natural bond orbital analysis confirms the occurrence of strong intermolecular hydrogen bonding in the molecule. Nonlinear optical absorption of the sample has been studied at 532 nm using single 5 ns laser pulses, employing the open-aperture Z-scan technique. It is found that the NaAPH molecule is a potential candidate for optical limiting applications. © 2011 American Chemical Society
非线性部件的轴系动稳态响应研究%RESEARCH ON STEADY VIBRATION RESPONSE OF SHAFTING WITH NONLINEAR COUPLING
Institute of Scientific and Technical Information of China (English)
龚宪生; 谢志江; 唐一科
2001-01-01
对有局部非线性的船舶推进轴系振动稳态响应进行理论和试验研究。在考虑联轴器非线性刚度和阻尼的情况下,以GLM(Galerkin-Levenberg-Marquardt)法为基础,提出一种分离变换法并编制相应计算程序。用此方法及程序对一单圆盘轴系振动稳态响应进行计算并进行试验。结果表明,计算所获振动稳态响应时间历程与试验所获振动稳态响应时间历程吻合好。%Theoretical and experimental research on steady vibration response of shipping propulsion shafting with local nonlinear characteristics are done. Owing to the coupling with the nonlinear characteristics, it is difficult that steady vibration response of the shafting is got fen by regular solutions. On the basis of GLM(Galerkin-Levenberg-Marquardt) method, a new method that is called the separating and transform algorithm is proposed and programmed. It can be used for calculating steady vibration response of the shafting with the coupling. Steady vibration response of a single disk rotor is calculated using the program and is tested. The results show that the method and the program are useful for calculating steady vibration response of the shafting with local nonlinear dynamic stiffness and damping. Theoretical results obtained by calculating are coincident with experimental one.
Institute of Scientific and Technical Information of China (English)
GU Ji-jun; AN Chen; LEVI Carlos; SU Jian
2012-01-01
The Generalized Integral Transform Technique (GITT) was applied to predict dynamic response of Vortex-Induced Vibration (VIV) of a long flexible cylinder.A nonlinear wake oscillator model was used to represent the cross-flow force acting on the cylinder,leading to a coupled system of second-order Partial Differential Equations (PDEs) in temporal variable.The GITT approach was used to transform the system of PDEs to a system of Ordinary Differential Equations (ODEs),which was numerically solved by using the Adams-Moulton and Gear method (DIVPAG) developed by the International Mathematics and Statistics Library (IMSL).Numerical results were presented for comparison to those given by the finite difference method and experimental results,allowing a critical evaluation of the technique performance.The influence of variation of mean axial tension induced by elongation of flexible cylinder was evaluated,which was shown to be not negligible in numerical simulation of VIV of a long flexible cylinder.
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.
Blanchard, Antoine; Bergman, Lawrence A.; Vakakis, Alexander F.
2017-07-01
We computationally investigate the dynamics of a linearly-sprung circular cylinder immersed in an incompressible flow and undergoing transverse vortex-induced vibration (VIV), to which is attached a rotational nonlinear energy sink (NES) consisting of a mass that freely rotates at constant radius about the cylinder axis, and whose motion is restrained by a rotational linear viscous damper. The inertial coupling between the rotational motion of the attached mass and the rectilinear motion of the cylinder is ;essentially nonlinear;, which, in conjunction with dissipation, allows for one-way, nearly irreversible targeted energy transfer (TET) from the oscillating cylinder to the nonlinear dissipative attachment. At the intermediate Reynolds number Re = 100, the NES-equipped sprung cylinder undergoes repetitive cycles of slowly decaying oscillations punctuated by intervals of chaotic instabilities. During the slowly decaying portion of each cycle, the dynamics of the cylinder is regular and, for large enough values of the ratio ε of the NES mass to the total mass (i.e., NES mass plus cylinder mass), can lead to significant vortex street elongation with partial stabilization of the wake. As ε approaches zero, no such vortex elongation is observed and the wake patterns appear similar to that for a sprung cylinder with no NES. We apply proper orthogonal decomposition (POD) to the velocity flow field during a slowly decaying portion of the solution and show that, in situations where vortex elongation occurs, the NES, though not in direct contact with the surrounding fluid, has a drastic effect on the underlying flow structures, imparting significant and continuous passive redistribution of energy among POD modes. We construct a POD-based reduced-order model for the lift coefficient to characterize energy transactions between the fluid and the cylinder throughout the slowly decaying cycle. We introduce a quantitative signed measure of the work done by the fluid on the
Passian, Ali; Tetard, Laurene; Thundat, Thomas
2013-08-01
This comment on the paper "A comprehensive modeling and vibration analysis of AFM microcantilevers subjected to nonlinear tip-sample interaction forces" by Sohrab Eslami and Jalili (2012) [1] aims to: (1) discuss and elucidate the concept of "virtual resonance" and thus (2) avert a misinterpretation of the experimental results and findings reported in the Tetard et al. Physical Review Letters 106, 180801 (2011) [2].
Yildiz, Nihat; Karabacak, Mehmet; Kurt, Mustafa; Akkoyun, Serkan
2012-05-01
Being directly related to the electric charge distributions in a molecule, the vibrational spectra intensities are both experimentally and theoretically important physical quantities. However, these intensities are inherently highly nonlinear and of complex pattern. Therefore, in particular for unknown detailed spatial molecular structures, it is difficult to make ab initio intensity calculations to compare with new experimental data. In this respect, we very recently initiated entirely novel layered feedforward neural network (LFNN) approach to construct empirical physical formulas (EPFs) for density functional theory (DFT) vibrational spectra of some molecules. In this paper, as a new and far improved contribution to our novel molecular vibrational spectra LFNN-EPF approach, we constructed LFFN-EPFs for absorbances and intensities of 6-choloronicotinic acid (6-CNA) molecule. The 6-CNA data, borrowed from our previous study, was entirely different and much larger than the vibrational intensity data of our formerly used LFNN-EPF molecules. In line with our another previous work which theoretically proved the LFNN relevance to EPFs, although the 6-CNA DFT absorbance and intensity were inherently highly nonlinear and sharply fluctuating in character, still the optimally constructed train set LFFN-EPFs very successfully fitted the absorbances and intensities. Moreover, test set (i.e. yet-to-be measured experimental data) LFNN-EPFs consistently and successfully predicted the absorbance and intensity data. This simply means that the physical law embedded in the 6-CNA vibrational data was successfully extracted by the LFNN-EPFs. In conclusion, these vibrational LFNN-EPFs are of explicit form. Therefore, by various suitable operations of mathematical analysis, they can be used to estimate the electronic charge distributions of the unknown molecule of the significant complexity. Additionally, these estimations can be combined with those of theoretical DFT atomic polar
Study on electromechanical coupling nonlinear vibration of flywheel energy storage system
Institute of Scientific and Technical Information of China (English)
JIANG; Shuyun
2006-01-01
The electromechanical coupling dynamics of the flywheel energy storage system (FESS) with a hybrid permanent magnetic-dynamic spiral groove bearing has been studied. The functions of the kinetic energy, the potential energys, the magnetic field energy in air gap of the flywheel motor and the energy dissipation of the whole system were obtained, and the differential equations set with electromagnetic parameters of FESS was established by applying the extended Lagrange-Maxwell equation. The four-order implicit Runge-Kutta formula to the equations was derived, and the nonlinear algebraic equations were solved by using the Gauss-Newton method. The analytical solution of an example shows that the upper damping coefficient, the lower damping coefficient and the residual magnetic induction of the rare earth permanent magnet play an important role in electromechanical resonance of the flywheel rotor system. There is a small change for the electromechanical coupling resonance frequency with the upper damping coefficient increasing, but the resonance amplitude decreases with the upper damping coefficient increasing. With the lower damping coefficient increasing, the resonance frequency increases, and the resonance amplitude decreases. With the residual magnetic induction of the permanent magnet increasing, the resonance frequency decreases, and the resonance amplitude increases.
Review of Response and Damage of Linear and Nonlinear Systems under Multiaxial Vibration
Directory of Open Access Journals (Sweden)
Ed Habtour
2014-01-01
Full Text Available A review of past and recent developments in multiaxial excitation of linear and nonlinear structures is presented. The objective is to review some of the basic approaches used in the analytical and experimental methods for kinematic and dynamic analysis of flexible mechanical systems, and to identify future directions in this research area. In addition, comparison between uniaxial and multiaxial excitations and their impact on a structure’s life-cycles is provided. The importance of understanding failure mechanisms in complex structures has led to the development of a vast range of theoretical, numerical, and experimental techniques to address complex dynamical effects. Therefore, it is imperative to identify the failure mechanisms of structures through experimental and virtual failure assessment based on correctly identified dynamic loads. For that reason, techniques for mapping the dynamic loads to fatigue were provided. Future research areas in structural dynamics due to multiaxial excitation are identified as (i effect of dynamic couplings, (ii modal interaction, (iii modal identification and experimental methods for flexible structures, and (iv computational models for large deformation in response to multiaxial excitation.
Directory of Open Access Journals (Sweden)
Peter W. Tse
2017-02-01
Full Text Available Bearings are widely used in various industries to support rotating shafts. Their failures accelerate failures of other adjacent components and may cause unexpected machine breakdowns. In recent years, nonlinear vibration responses collected from a dynamic rotor-bearing system have been widely analyzed for bearing diagnostics. Numerous methods have been proposed to identify different bearing faults. However, these methods are unable to predict the future health conditions of bearings. To extend bearing diagnostics to bearing prognostics, this paper reports the design of a state space formulation of nonlinear vibration responses collected from a dynamic rotor-bearing system in order to intelligently predict bearing remaining useful life (RUL. Firstly, analyses of nonlinear vibration responses were conducted to construct a bearing health indicator (BHI so as to assess the current bearing health condition. Secondly, a state space model of the BHI was developed to mathematically track the health evolution of the BHI. Thirdly, unscented particle filtering was used to predict bearing RUL. Lastly, a new bearing acceleration life testing setup was designed to collect natural bearing degradation data, which were used to validate the effectiveness of the proposed bearing prognostic method. Results show that the prediction accuracy of the proposed bearing prognostic method is promising and the proposed bearing prognostic method is able to reflect future bearing health conditions.
Zarepour, Misagh; Amirhosein Hosseini, Seyed
2016-08-01
This study presents an examination of nonlinear free vibration of a nanobeam under electro-thermo-mechanical loading with elastic medium and various boundary conditions, especially the elastic boundary condition. The nanobeam is modeled as an Euler-Bernoulli beam. The von Kármán strain-displacement relationship together with Hamilton’s principle and Eringen’s theory are employed to derive equations of motion. The nonlinear free vibration frequency is obtained for simply supported (S-S) and elastic supported (E-E) boundary conditions. E-E boundary condition is a general and actual form of boundary conditions and it is chosen because of more realistic behavior. By applying the differential transform method (DTM), the nanobeam’s natural frequencies can be easily obtained for the two different boundary conditions mentioned above. Performing a precise study led to investigation of the influences of nonlocal parameter, temperature change, spring constants (either for elastic medium or boundary condition) and imposed electric potential on the nonlinear free vibration characteristics of nanobeam. The results for S-S and E-E nanobeams are compared with each other. In order to validate the results, some comparisons are presented between DTM results and open literature to show the accuracy of this new approach. It has been discovered that DTM solves the equations with minimum calculation cost.
The minimization of ac phase noise in interferometric systems
DEFF Research Database (Denmark)
Filinski, Ignacy; Gordon, R A
1994-01-01
A simple step-by-step procedure, including several novel techniques discussed in the Appendices, is given for minimizing ac phase noise in typical interferometric systems such as two-beam interferometers, holographic setups, four-wave mixers, etc. Special attention is given to index of refraction...... fluctuations, direct mechanical coupling, and acoustic coupling, whose importance in determining ac phase noise in interferometric systems has not been adequately treated. The minimization procedure must be carried out while continuously monitoring the phase noise which can be done very simply by using...... with the optical table will also have to be carefully carried out regardless of the type of interferometric system employed.It is recommended that this be followed by a simple, inexpensive change to a novel type of interferometer discussed in Appendix A which is inherently less sensitive to mechanical vibration...
Self Calibrating Interferometric Sensor
DEFF Research Database (Denmark)
Sørensen, Henrik Schiøtt
This thesis deals with the development of an optical sensor based on micro interferometric backscatter detection (MIBD). A price effective, highly sensitive and ready for mass production platform is the goal of this project. The thesis covers three areas. The first part of the thesis deals...... mask. The fabricated micro structures have been electroplated for later injection molding, showing the potential of the MIBD sensor to be mass produced with high reproducibility and sensitivity. In part three MIBD experiments on vital biological systems are described. Label–free binding studies of bio...
Sato, T.; Masuda, A.; Sanada, T.
2015-12-01
This paper presents an experimental verification of a self-excitation control of a resonance- type vibration energy harvester with a Duffing-type nonlinearity which is designed to perform effectively in a wide frequency range. For the conventional linear vibration energy harvester, the performance of the power generation at the resonance frequency and the bandwidth of the resonance peak are trade-off. The resonance frequency band can be expanded by introducing a Duffing-type nonlinear oscillator in order to enable the harvester to generate larger electric power in a wider frequency range. However, since such nonlinear oscillator can have multiple stable steady-state solutions in the resonance band, it is difficult for the nonlinear harvester to maintain the high performance of the power generation constantly. The principle of self-excitation and entrainment has been utilized to provide the global stability to the highest-energy solution by destabilizing other unexpected lower-energy solutions by introducing a switching circuit of the load resistance between positive and the negative values depending on the response amplitude of the oscillator. It has been experimentally validated that this control law imparts the self-excitation capability to the oscillator to show an entrainment into the highest-energy solution.
Interferometric Fiber Optic Sensors
Directory of Open Access Journals (Sweden)
Hae Young Choi
2012-02-01
Full Text Available Fiber optic interferometers to sense various physical parameters including temperature, strain, pressure, and refractive index have been widely investigated. They can be categorized into four types: Fabry-Perot, Mach-Zehnder, Michelson, and Sagnac. In this paper, each type of interferometric sensor is reviewed in terms of operating principles, fabrication methods, and application fields. Some specific examples of recently reported interferometeric sensor technologies are presented in detail to show their large potential in practical applications. Some of the simple to fabricate but exceedingly effective Fabry-Perot interferometers, implemented in both extrinsic and intrinsic structures, are discussed. Also, a wide variety of Mach-Zehnder and Michelson interferometric sensors based on photonic crystal fibers are introduced along with their remarkable sensing performances. Finally, the simultaneous multi-parameter sensing capability of a pair of long period fiber grating (LPG is presented in two types of structures; one is the Mach-Zehnder interferometer formed in a double cladding fiber and the other is the highly sensitive Sagnac interferometer cascaded with an LPG pair.
Interferometric fiber optic sensors.
Lee, Byeong Ha; Kim, Young Ho; Park, Kwan Seob; Eom, Joo Beom; Kim, Myoung Jin; Rho, Byung Sup; Choi, Hae Young
2012-01-01
Fiber optic interferometers to sense various physical parameters including temperature, strain, pressure, and refractive index have been widely investigated. They can be categorized into four types: Fabry-Perot, Mach-Zehnder, Michelson, and Sagnac. In this paper, each type of interferometric sensor is reviewed in terms of operating principles, fabrication methods, and application fields. Some specific examples of recently reported interferometeric sensor technologies are presented in detail to show their large potential in practical applications. Some of the simple to fabricate but exceedingly effective Fabry-Perot interferometers, implemented in both extrinsic and intrinsic structures, are discussed. Also, a wide variety of Mach-Zehnder and Michelson interferometric sensors based on photonic crystal fibers are introduced along with their remarkable sensing performances. Finally, the simultaneous multi-parameter sensing capability of a pair of long period fiber grating (LPG) is presented in two types of structures; one is the Mach-Zehnder interferometer formed in a double cladding fiber and the other is the highly sensitive Sagnac interferometer cascaded with an LPG pair.
Song, Yang; Liu, Zhigang; Wang, Hongrui; Lu, Xiaobing; Zhang, Jing
2016-06-01
The wind-induced vibration of the high-speed catenary and the dynamic behaviour of the pantograph-catenary under stochastic wind field are firstly analysed. The catenary model is established based on nonlinear cable and truss elements, which can fully describe the nonlinearity of each wire and the initial configuration. The model of the aerodynamic forces acting on the messenger/contact wire is deduced by considering the effect of the vertical and horizontal fluctuating winds. The vertical and horizontal fluctuating winds are simulated by employing the Davenport and Panofsky spectrums, respectively. The aerodynamic coefficients of the contact/messenger wire are calculated through computational fluid dynamics. The wind-induced vibration response of catenary is analysed with different wind speeds and angles. Its frequency-domain characteristics are discussed using Auto Regression model. Finally, a pantograph model is introduced and the contact force of the pantograph-catenary under stochastic wind is studied. The results show that both the wind speed and the attack angle exert a significant effect on the wind-induced vibration. The existence of the groove on the contact wire cross-section leads to a significant change of the aerodynamic coefficient, which affects largely the aerodynamic forces applied on the catenary wires, as well as the vibration response. The vibration frequency with high spectral power mainly concentrates on the predominant frequency of the fluctuating wind and the natural frequency of catenary. The increase in the wind speed results in a significant deterioration of the current collection. The numerical example shows that a relatively stable current collection can be ensured when the wind flows at the relatively horizontal direction.
UVMULTIFIT: A versatile tool for fitting astronomical radio interferometric data
Marti-Vidal, I; Muller, S; Casey, S
2014-01-01
The analysis of astronomical interferometric data is often performed on the images obtained after deconvolution of the interferometer's point spread function (PSF). This strategy can be understood (especially for cases of sparse arrays) as fitting models to models, since the deconvolved images are already non-unique model representations of the actual data (i.e., the visibilities). Indeed, the interferometric images may be affected by visibility gridding, weighting schemes (e.g., natural vs. uniform), and the particulars of the (non-linear) deconvolution algorithms. Fitting models to the direct interferometric observables (i.e., the visibilities) is preferable in the cases of simple (analytical) sky intensity distributions. In this paper, we present UVMULTIFIT, a versatile library for fitting visibility data, implemented in a Python-based framework. Our software is currently based on the CASA package, but can be easily adapted to other analysis packages, provided they have a Python API. We have tested the sof...
The fresnel interferometric imager
Koechlin, Laurent; Serre, Denis; Deba, Paul; Pelló, Roser; Peillon, Christelle; Duchon, Paul; Gomez de Castro, Ana Ines; Karovska, Margarita; Désert, Jean-Michel; Ehrenreich, David; Hebrard, Guillaume; Lecavelier Des Etangs, Alain; Ferlet, Roger; Sing, David; Vidal-Madjar, Alfred
2009-03-01
The Fresnel Interferometric Imager has been proposed to the European Space Agency (ESA) Cosmic Vision plan as a class L mission. This mission addresses several themes of the CV Plan: Exoplanet study, Matter in extreme conditions, and The Universe taking shape. This paper is an abridged version of the original ESA proposal. We have removed most of the technical and financial issues, to concentrate on the instrumental design and astrophysical missions. The instrument proposed is an ultra-lightweight telescope, featuring a novel optical concept based on diffraction focussing. It yields high dynamic range images, while releasing constraints on positioning and manufacturing of the main optical elements. This concept should open the way to very large apertures in space. In this two spacecraft formation-flying instrument, one spacecraft holds the focussing element: the Fresnel interferometric array; the other spacecraft holds the field optics, focal instrumentation, and detectors. The Fresnel array proposed here is a 3.6 ×3.6 m square opaque foil punched with 105 to 106 void “subapertures”. Focusing is achieved with no other optical element: the shape and positioning of the subapertures (holes in the foil) is responsible for beam combining by diffraction, and 5% to 10% of the total incident light ends up into a sharp focus. The consequence of this high number of subapertures is high dynamic range images. In addition, as it uses only a combination of vacuum and opaque material, this focussing method is potentially efficient over a very broad wavelength domain. The focal length of such diffractive focussing devices is wavelength dependent. However, this can be corrected. We have tested optically the efficiency of the chromatism correction on artificial sources (500 < λ < 750 nm): the images are diffraction limited, and the dynamic range measured on an artificial double source reaches 6.2 10 - 6. We have also validated numerical simulation algorithms for larger Fresnel
NONLINEAR VIBRATION CHARACTERISTICS OF SHROUDED BLADE FOR CYLINDRICAL PANEL%壳板凸肩叶片的非线性振动特性
Institute of Scientific and Technical Information of China (English)
李红影; 谢里阳; 郭星辉
2013-01-01
A shrouded blade is investigated in this paper. Using Donnell's nonlinear shallow-shell theory, the nonlinear equation of vibration is obtained, in which the geometric nonlinearity, damping, shroud contact normal load and friction between shrouds are taken into account. Discretized by a Galerkin method, the nonlinear mode equations are studied by using numerical and analytical methods, then nonlinear frequency-response curves are obtained. The stability of periodic solutions of the system is also analyzed. The results show that the periodic changes in the direction of the friction force between shrouds cause the discontinuity of vibration characteristics of the system. In order to describe the inherent vibration characteristic of the system, two frequency-response curves are drawn, which respectively adopts the positive and negative directions of the friction force. With the changes of the direction of a friction force in a period of 774, the vibration of the system also jumps between these two curves with a period 774, this effectively suppress the response amplitude of a shrouded blade, and improves its safety.%以凸肩叶片为研究对象,应用Donnell's简化壳理论建立模型的非线性振动方程,考虑了几何非线性、阻尼、凸肩接触面正压力、摩擦力等因素.采用Galerkin法将振动微分方程离散到模态坐标上,分别应用数值法和近似解析法对方程组求解,得到系统的频率响应曲线,并讨论了系统周期解的稳定性.结果表明,由于凸肩接触面之间摩擦力方向周期性改变,导致系统的振动特性产生不连续性,以摩擦力为正、负方向分别绘制一条频率响应曲线.则随着摩擦力方向T/4周期变换一次,系统的振动也以T/4为周期在两条频率响应曲线上来回跳跃,从而有效抑制叶片的振动响应,提高叶片使用的安全性.
Quantum Interferometric Sensors
Kapale, K T; Lee, H; Kok, P; Dowling, J P; Kapale, Kishore T.; Didomenico, Leo D.; Lee, Hwang; Kok, Pieter; Dowling, Jonathan P.
2005-01-01
Quantum entanglement has the potential to revolutionize the entire field of interferometric sensing by providing many orders of magnitude improvement in interferometer sensitivity. The quantum-entangled particle interferometer approach is very general and applies to many types of interferometers. In particular, without nonlocal entanglement, a generic classical interferometer has a statistical-sampling shot-noise limited sensitivity that scales like $1/\\sqrt{N}$, where $N$ is the number of particles passing through the interferometer per unit time. However, if carefully prepared quantum correlations are engineered between the particles, then the interferometer sensitivity improves by a factor of $\\sqrt{N}$ to scale like 1/N, which is the limit imposed by the Heisenberg Uncertainty Principle. For optical interferometers operating at milliwatts of optical power, this quantum sensitivity boost corresponds to an eight-order-of-magnitude improvement of signal to noise. This effect can translate into a tremendous s...
Nyaupane, Parashu R.; Manzanares, Carlos
2016-06-01
The thermal lens technique is applied to vibrational overtone spectroscopy of solutions of benzene. The pump and probe thermal lens technique has been found to be very sensitive for detecting samples of low concentration in transparent solvents. The C-H fifth vibrational (Δυ = 6) overtone spectrum of benzene is detected at room temperature for compositions per volume in the range (1 to 1× 10-4) using n-C_6H14 as the solvent. By detecting the absorption band in a 100 ppm solution, the peak absorption of the signal is approximately (2.2 ± 0.3)× 10-7 cm-1. The parameters that determine the magnitude of the thermal lens signal such as the pump laser power and the thermodynamic properties of the solvent and solute are discussed. A plot of normalized integrated intensity as a function of composition of benzene in solution reveals a non-linear behavior. The non-linearity cannot be explained assuming solvent enhancement at low concentrations. A two color absorption model that includes the simultaneous absorption of the pump and probe lasers could explain the enhanced magnitude and the non-linear behavior of the thermal lens signal for solutions of composition below 0.01.
Gorb, Yuliya
2010-11-01
We model and analyze the response of nonlinear, residually stressed elastic bodies subjected to small amplitude vibrations superimposed upon large deformations. The problem derives from modeling the use of intravascular ultrasound (IVUS) imaging to interrogate atherosclerotic plaques in vivo in large arteries. The goal of this investigation is twofold: (i) introduce a modeling framework for residual stress that unlike traditional Fung type classical opening angle models may be used for a diseased artery, and (ii) investigate the sensitivity of the spectra of small amplitude high frequency time harmonic vibrations superimposed on a large deformation to the details of the residual stress stored in arteries through a numerical simulation using physiologic parameter values under both low and high blood pressure loadings. The modeling framework also points the way towards an inverse problem using IVUS techniques to estimate residual stress in healthy and diseased arteries. © 2010 Elsevier Ltd. All rights reserved.
Sedighi, H. M.; Shirazi, K. H.
2014-11-01
This article attains a new formulation of beam vibrations on an elastic foundation with quintic nonlinearity, including exact expressions for the beam curvature. To achieve a proper design of the beam structures, it is essential to realize how the beam vibrates in its transverse mode, which, in turn, yields the natural frequency of the system. In this direction, a powerful analytical method called the parameter expansion method is employed to obtain the exact solution of the frequency-amplitude relationship. It is clearly shown that the first term in series expansions is sufficient to produce a highly accurate approximation of the above-mentioned system. Finally, the accuracy of the present analytic procedure is evaluated through comparisons with numerical calculations.
Theory, analysis and design of RF interferometric sensors
Nguyen, Cam
2012-01-01
Theory, Analysis and Design of RF Interferometric Sensors presents the theory, analysis and design of RF interferometric sensors. RF interferometric sensors are attractive for various sensing applications that require every fine resolution and accuracy as well as fast speed. The book also presents two millimeter-wave interferometric sensors realized using RF integrated circuits. The developed millimeter-wave homodyne sensor shows sub-millimeter resolution in the order of 0.05 mm without correction for the non-linear phase response of the sensor's quadrature mixer. The designed millimeter-wave double-channel homodyne sensor provides a resolution of only 0.01 mm, or 1/840th of the operating wavelength, and can inherently suppress the non-linearity of the sensor's quadrature mixer. The experimental results of displacement and velocity measurement are presented as a way to demonstrate the sensing ability of the RF interferometry and to illustrate its many possible applications in sensing. The book is succinct, ye...
Terahertz interferometric imaging of RDX
Sinyukov, Alexander M.; Barat, Robert B.; Gary, Dale E.; Michalopoulou, Zoi-Heleni; Zorych, Ivan; Zimdars, David; Federici, John F.
2007-04-01
Experimental results of homodyne terahertz interferometric 2-D imaging of RDX are presented. Continuous waves at 0.25-0.6 THz are used to obtain images of a C-4 sample at several THz frequencies. The performance of an N element detector array is imitated by only one detector placed at N positions. The distance between the C-4 sample and the detector array is ~30 cm. By taking interferometric images at several THz frequencies RDX can be recognized by the spectral peak at 0.82 THz. Simulations of interferometric images of two point sources of spherical waves are presented. The terahertz interferometric imaging method can be used in defense and security applications to detect concealed weapons, explosives as well as chemical and biological agents.
Zheng, Guangtai; Qiu, Yi; Griffin, Michael J.
2012-12-01
The vertical apparent mass of the human body exhibits nonlinearity, with the principal resonance frequency reducing as the vibration magnitude increases. Measures of the transmission of vibration to the spine and the pelvis have suggested complex modes are responsible for the dominant resonance during vertical excitation, but the modes present with dual-axis excitation have not been investigated. This study was designed to examine how the apparent mass and transmissibility of the human body depend on the magnitude of vertical excitation and the addition of fore-and-aft excitation, and the relation between the apparent mass and the transmissibility of the body. The movement of the body (over the first, fifth and twelfth thoracic vertebrae, the third lumbar vertebra, and the pelvis) in the fore-and-aft and vertical directions (and in pitch at the pelvis) was measured in 12 male subjects sitting with their hands on their laps during random vertical vibration excitation (over the range 0.25-20 Hz) at three vibration magnitudes (0.25, 0.5 and 1.0 m s-2 rms). At the highest magnitude of vertical excitation (1.0 m s-2 rms) the effect of adding fore-aft vibration (at 0.25, 0.5, and 1.0 m s-2 rms) was investigated. The forces in the vertical and fore-and-aft directions on the seat surface were also measured so as to calculate apparent masses. Resonances in the apparent mass and transmissibility to the spine and pelvis in the fore-and-aft and vertical directions, and pitch transmissibility to the pelvis, shifted to lower frequencies as the magnitude of vertical excitation increased and as the magnitude of the additional fore-and-aft excitation increased. The nonlinear resonant behaviour of the apparent mass and transmissibility during dual-axis vibration excitation suggests coupling between the principal mode associated with vertical excitation and the cross-axis influence of fore-and-aft excitation. The transmissibility measures are consistent with complex modes
Institute of Scientific and Technical Information of China (English)
李银山; 刘波; 张明路; 段国林
2011-01-01
计及材料的非线性弹性,建立圆板自由振动的非线性动力学方程.采用Galerkin法,将圆板的非线性动力学偏微分方程简化成四种标准类型的二次非线性微分方程.提出一类强非线性动力系统的初值变换法,将描述动力系统的二阶常微分方程,化为以角频率、振幅和偏心距为独立变量的不完备非线性代数方程组,考虑初始条件补充约束方程,构成频率、振幅和偏心距为变量的完备非线性代数方程组.利用Maple程序可以方便地求解.结果表明,初值变换法不仅适合于对称振动问题,而且适合于非对称振动问题.首次给出二次非线性自由振动的偏一频曲线.%The nonlinear dynamic equation of free vibration of a circular plate is derived with nonlinear theory of elasticity. By using Calerkin' g method, the governing partial differential equation was reduced to four standard types of quadratic nonlinear ordinary ones. A method of initial-value transformation is presented for a class strongly nonlinear dynamic system. By using Ritz-Galerkin s method , an oscillation system governed by a set of second order ordinary differential equations, can be transformed into a set of incomplete non-linear algebraic equations with angular frequencies, amplitudes and central offsets as independent variables. Then, by supplement of some initial-value restrictions, the incomplete equations can be made complete, obtaining a set of non-linear algebraic equations with angular frequencies, amplitudes and central offsets, which can be solved conveniently by Maple program. Hie results show that the method of initial-value transformation can solve not only symmetry problems, but also asymmetry problems for free vibration. The offset-angular frequency backbone curves of quadratic nonlinear equations were presented for the first time.
DEFF Research Database (Denmark)
Lazarov, Boyan Stefanov; Thomsen, Jon Juel
2009-01-01
We investigate how high-frequency (HF) excitation combined with strongly non-linear elasticity may influence the effective properties for low-frequency wave propagation. The HF effects are demonstrated for linear spring-mass chains with embedded non-linear parts. The investigated mechanical syste...
Interferometric Plasmonic Lensing with Nanohole Arrays
Energy Technology Data Exchange (ETDEWEB)
Gong, Yu; Joly, Alan G.; El-Khoury, Patrick Z.; Hess, Wayne P.
2014-12-18
Nonlinear photoemission electron microscopy (PEEM) of nanohole arrays in gold films maps propagating surface plasmons (PSPs) launched from lithographically patterned structures. Strong near field photoemission patterns are observed in the PEEM images, recorded following low angle of incidence irradiation of nanohole arrays with sub-15 fs laser pulses centered at 780 nm. The recorded photoemission patterns are attributed to constructive and destructive interferences between PSPs launched from the individual nanoholes which comprise the array. By exploiting the wave nature of PSPs, we demonstrate how varying the array geometry (hole diameter, pitch, and number of rows/columns) ultimately yields intense localized photoemission. Through a combination of PEEM and finite-difference time-domain simulations, we identify the optimal array geometry for efficient light coupling and interferometric plasmonic lensing. We show a preliminary application of inteferometric plasmonic lensing by enhancing the photoemission from the vertex of a gold triangle using nanohole array.
Compression of interferometric radio-astronomical data
Offringa, A R
2016-01-01
The volume of radio-astronomical data is a considerable burden in the processing and storing of radio observations with high time and frequency resolutions and large bandwidths. Lossy compression of interferometric radio-astronomical data is considered to reduce the volume of visibility data and to speed up processing. A new compression technique named "Dysco" is introduced that consists of two steps: a normalization step, in which grouped visibilities are normalized to have a similar distribution; and a quantization and encoding step, which rounds values to a given quantization scheme using a dithering scheme. Several non-linear quantization schemes are tested and combined with different methods for normalizing the data. Four data sets with observations from the LOFAR and MWA telescopes are processed with different processing strategies and different combinations of normalization and quantization. The effects of compression are measured in image plane. The noise added by the lossy compression technique acts ...
Institute of Scientific and Technical Information of China (English)
姜剑; 王兆清; 庄美玲
2015-01-01
The nonlinear vibration of multi-degree-of-freedom systems can be modeled by initial value problem of nonlinear differential equation,this paper mainly studied the application of barycentric rational interpolation iterative collocation method to solve nonlinear vibration of multi-degree-of-freedom systems. A linear iterative scheme is constructed for approximating nonlinear differential equations. The linear differential equations are discretized into algebraic equations by applying Barycentric rational interpolation differential matrixes. Then, the numerical results of nonlinear vibration problem can be obtained by solving the algebraic equations with iteration method. The examples of nonlinear vibration of coupled systems demonstrated the proposed method is simple, effective and excellent stability and can accurately simulate various physical quantities of the nonlinear vibration.%多自由度非线性振动的数学模型为非线性微分方程组的初值问题。文章运用重心有理插值迭代配点法研究了求解多自由度非线性振动的问题；通过构造一个逼近非线性微分方程组的线性化迭代格式，采用重心有理插值微分矩阵离散线性化微分方程组，由线性化迭代计算最终得到非线性方程组的数值解。结果表明：依据算例的解析解和数值解比较，重心有理插值迭代配点法能够高精度计算模拟多自由度非线性振动的各项物理量，并且简单有效，具有优异的计算稳定性。
Joannin, Colas; Chouvion, Benjamin; Thouverez, Fabrice; Ousty, Jean-Philippe; Mbaye, Moustapha
2017-01-01
This paper presents an extension to classic component mode synthesis methods to compute the steady-state forced response of nonlinear and dissipative structures. The procedure makes use of the nonlinear complex modes of each substructure, computed by means of a modified harmonic balance method, in order to build a reduced-order model easily solved by standard iterative solvers. The proposed method is applied to a mistuned cyclic structure subjected to dry friction forces, and proves particularly suitable for the study of such systems with high modal density and non-conservative nonlinearities.
Common-Path Interferometric Wavefront Sensing for Space Telescopes
Wallace, James Kent
2011-01-01
This paper presents an optical configuration for a common-path phase-shifting interferometric wavefront sensor.1 2 This sensor has a host of attractive features which make it well suited for space-based adaptive optics. First, it is strictly reflective and therefore operates broadband, second it is common mode and therefore does not suffer from systematic errors (like vibration) that are typical in other interferometers, third it is a phase-shifting interferometer and therefore benefits from both the sensitivity of interferometric sensors as well as the noise rejection afforded by synchronous detection. Unlike the Shack-Hartman wavefront sensor, it has nearly uniform sensitivity to all pupil modes. Optical configuration, theory and simulations for such a system will be discussed along with predicted performance.
MEMS Gyroscope with Interferometric Detection Project
National Aeronautics and Space Administration — The proposed innovation is a novel MEMS gyroscope that uses micro-interferometric detection to measure the motion of the proof mass. Using an interferometric...
Institute of Scientific and Technical Information of China (English)
刘浩然; 侯东晓; 时培明; 刘飞
2011-01-01
考虑轧件弹塑性变形的滞后非线性作用,建立一种轧机辊系滞后非线性垂直振动动力学模型.运用奇点稳定性理论分析该滞后非线性系统的稳定性,得到了系统出现各种不同奇点的条件.同时采用渐进法求解系统在主共振情况下的解析近似解,得到了系统的主共振幅频特性方程.最后以实际轧机参数为例,分析轧件的非线性刚度、阻尼等参数对轧机主共振幅频响应的影响,并研究轧机在不同外部扰动下的分岔行为,发现在不同的外部扰动下,轧机表现出周期、倍周期以及混沌等多种动力学行为,这为研究和抑制轧机振动问题提供了理论参考.%A kind of hysteretic nonlinear vertical vibration dynamic model is established which considers hysteresis of strip's plastic deformation. The stability of the hysteretic nonlinear system is analyzed by using stability theory of singularity, and the conditions for the emergence of various singular points are obtained. Then the analytical approximate solution of the system under periodic excitation is accounted, and the primary resonance amplitude-frequency equation of the system is obtained. Finally, according to the actual parameters of rolling mill, the influence of nonlinear stiffness and nonlinear damp of rolled piece on the primary resonance amplitude-frequency response of rolling mill is analyzed, and the bifurcation behaviors of rolling mill under different external disturbances are studied. It is found that the rolling mill exhibits many dynamic behaviors such as periodic, period-doubling motion and chaos. The results provide theoretical reference for researching and suppressing rolling mill vibration.
Energy Technology Data Exchange (ETDEWEB)
El Arem, S.
2006-01-15
The aim of this work is to study the dynamic response of a cracked rotor to establish some possibilities for early on line crack detection. First, a review on experimental, numerical and analytical works on the dynamics of cracked rotors is given. Then, an original method of calculating the behavior of a cracked beam section in bending with shearing effects is presented. The nonlinear behavior relations are derived from a three-dimensional model taking into account the unilateral contact conditions on the crack's lips. Based on an energy formulation, this method could be applied to any geometry of crack. The exploration by different numerical integration methods of the vibratory response of some models of cracked rotors is presented in the third chapter of this thesis. The un-cracked parts of a rotor are represented by elements of bar or beam type, and the cracked section by a nonlinear spring taking into account the breathing mechanism of the cracks. At the end of this part, an original method of construction of a finite element of a cracked beam is presented. The final chapter is devoted to the analytical study of the system with 2 degrees of freedom. The breathing mechanism of the crack is taken into account by considering specific periodic variation of the global stiffness of the system. The differential equations system is solved using the harmonic balance method. The linear stability of the periodic solutions is studied by the Floquet theory. Some vibratory parameters are proposed as crack indicators. (author)
Canopy reconstruction from interferometric SAR
Varekamp, C.
2001-01-01
Interferometric Synthetic Aperture Radar (InSAR) is investigated as a method for 3D tree mapping. When operational, the method may be important for monitoring forests with a persistent cloud cover such as tropical rain forests. The problem of crown displacement due to lay-over in a vegetation with a
Two-Wavelength Interferometric Keratometer
Hochberg, Eric; Page, Norman
1991-01-01
Proposed interferometric keratometer measures shapes of corneas without touching them. Used to test strongly aspherical optics. Resembling present commercial lens-testing interferometers, generates interferograms representative of deviation of surfaces under test from sphericity. Such interferograms used to generate contour maps of surfaces. Measures corneal topography to diameters as large as 12 mm.
Biggs, Jason D
2009-01-01
The preceding paper describes a strategy for externally influencing the course of short-time electronic excitation transfer (EET) in molecular dimers and observing the process by nonlinear wave-packet interferometry (nl-WPI). Within a sample of isotropically oriented dimers having a specified internal geometry, a vibrational mode internal to the acceptor chromophore can be preferentially driven by electronically nonresonant impulsive stimulated Raman (or resonant infrared) excitation with a short polarized control pulse. A subsequent electronically resonant polarized pump then preferentially excites the donor, and EET ensues. Here we test both the control strategy and its spectroscopic investigation-with some sacrifice of amplitude-level detail-by calculating the pump-probe difference signal. That signal is the limiting case of the control-influenced nl-WPI signal in which the two pulses in the pump pulse-pair coincide, as do the two pulses in the probe pulse-pair. We present calculated pump-probe difference ...
Xiao-Hong, Li; Hong-Ling, Cui; Rui-Zhou, Zhang; Xian-Zhou, Zhang
2015-02-01
The vibrational frequencies of (E)-2-cyano-3-(3-hydroxyphenyl)acrylamide (HB-CA) in the ground state have been calculated using density functional method (B3LYP) with B3LYP/6-311++G(d,p) basis set. The analysis of natural bond orbital was also performed. The IR spectra were obtained and interpreted by means of potential energies distributions (PEDs) using MOLVIB program. In addition, the results show that there exists Csbnd H⋯O hydrogen bond in the title compound, which is confirmed by the natural bond orbital analysis. The predicted NLO properties show that the title compound is a good candidate as nonlinear optical material. The analysis of frontier molecular orbitals shows that HB-CA has high excitation energies, good stability and high chemical hardness. The analysis of MEP map shows the negative and the positive potential sites.
Xiao-Hong, Li; Hong-Ling, Cui; Rui-Zhou, Zhang; Xian-Zhou, Zhang
2015-02-25
The vibrational frequencies of (E)-2-cyano-3-(3-hydroxyphenyl)acrylamide (HB-CA) in the ground state have been calculated using density functional method (B3LYP) with B3LYP/6-311++G(d,p) basis set. The analysis of natural bond orbital was also performed. The IR spectra were obtained and interpreted by means of potential energies distributions (PEDs) using MOLVIB program. In addition, the results show that there exists C-H⋯O hydrogen bond in the title compound, which is confirmed by the natural bond orbital analysis. The predicted NLO properties show that the title compound is a good candidate as nonlinear optical material. The analysis of frontier molecular orbitals shows that HB-CA has high excitation energies, good stability and high chemical hardness. The analysis of MEP map shows the negative and the positive potential sites.
Directory of Open Access Journals (Sweden)
X. Gao
2014-01-01
Full Text Available A methodology is presented to study the resonance and stability for a single-degree-of-freedom (SDOF system with a piecewise linear-nonlinear stiffness term (i.e., one piece is linear and the other is weakly nonlinear. Firstly, the exact response of the linear governing equation is obtained, and a modified perturbation method is applied to finding the approximate solution of the weakly nonlinear equation. Then, the primary and 1/2 subharmonic resonances are obtained by imposing continuity conditions and periodicity conditions. Furthermore, Jacobian matrix is derived to investigate the stability of resonance responses. Finally, the results of theoretical study are compared with numerical results, and a good agreement is observed.
Fleming, David P.; Poplawski, J. V.
2002-01-01
Rolling-element bearing forces vary nonlinearly with bearing deflection. Thus an accurate rotordynamic transient analysis requires bearing forces to be determined at each step of the transient solution. Analyses have been carried out to show the effect of accurate bearing transient forces (accounting for non-linear speed and load dependent bearing stiffness) as compared to conventional use of average rolling-element bearing stiffness. Bearing forces were calculated by COBRA-AHS (Computer Optimized Ball and Roller Bearing Analysis - Advanced High Speed) and supplied to the rotordynamics code ARDS (Analysis of Rotor Dynamic Systems) for accurate simulation of rotor transient behavior. COBRA-AHS is a fast-running 5 degree-of-freedom computer code able to calculate high speed rolling-element bearing load-displacement data for radial and angular contact ball bearings and also for cylindrical and tapered roller beatings. Results show that use of nonlinear bearing characteristics is essential for accurate prediction of rotordynamic behavior.
Mohammadimehr, M.; Mohammadi-Dehabadi, A. A.; Maraghi, Z. Khoddami
2017-04-01
In this research, the effect of non-local higher order stress on the nonlinear vibration behavior of carbon nanotube conveying viscous nanoflow resting on elastic foundation is investigated. Physical intuition reveals that increasing nanoscale stress leads to decrease the stiffness of nanostructure which firstly established by Eringen's non-local elasticity theory (previous nonlocal method) while many of papers have concluded otherwise at microscale based on modified couple stress, modified strain gradient theories and surface stress effect. The non-local higher order stress model (new nonlocal method) is used in this article that has been studied by few researchers in other fields and the results from the present study show that the trend of the new nonlocal method and size dependent effect including modified couple stress theory is the same. In this regard, the nonlinear motion equations are derived using a variational principal approach considering essential higher-order non-local terms. The surrounded elastic medium is modeled by Pasternak foundation to increase the stability of system where the fluid flow may cause system instability. Effects of various parameters such as non-local parameter, elastic foundation coefficient, and fluid flow velocity on the stability and dimensionless natural frequency of nanotube are investigated. The results of this research show that the small scale parameter based on higher order stress help to increase the natural frequency which has been approved by other small scale theories such as strain gradient theory, modified couple stress theory and experiments, and vice versa for previous nonlocal method. This study may be useful to measure accurately the vibration characteristics of nanotubes conveying viscous nanoflow and to design nanofluidic devices for detecting blood Glucose.
Energy Technology Data Exchange (ETDEWEB)
Mohammadimehr, M., E-mail: mmohammadimehr@kashanu.ac.ir [Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, P.O. Box: 87317-53153, Kashan (Iran, Islamic Republic of); Mohammadi-Dehabadi, A.A. [Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, P.O. Box: 87317-53153, Kashan (Iran, Islamic Republic of); Department of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of); Maraghi, Z. Khoddami [Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, P.O. Box: 87317-53153, Kashan (Iran, Islamic Republic of)
2017-04-01
In this research, the effect of non-local higher order stress on the nonlinear vibration behavior of carbon nanotube conveying viscous nanoflow resting on elastic foundation is investigated. Physical intuition reveals that increasing nanoscale stress leads to decrease the stiffness of nanostructure which firstly established by Eringen's non-local elasticity theory (previous nonlocal method) while many of papers have concluded otherwise at microscale based on modified couple stress, modified strain gradient theories and surface stress effect. The non-local higher order stress model (new nonlocal method) is used in this article that has been studied by few researchers in other fields and the results from the present study show that the trend of the new nonlocal method and size dependent effect including modified couple stress theory is the same. In this regard, the nonlinear motion equations are derived using a variational principal approach considering essential higher-order non-local terms. The surrounded elastic medium is modeled by Pasternak foundation to increase the stability of system where the fluid flow may cause system instability. Effects of various parameters such as non-local parameter, elastic foundation coefficient, and fluid flow velocity on the stability and dimensionless natural frequency of nanotube are investigated. The results of this research show that the small scale parameter based on higher order stress help to increase the natural frequency which has been approved by other small scale theories such as strain gradient theory, modified couple stress theory and experiments, and vice versa for previous nonlocal method. This study may be useful to measure accurately the vibration characteristics of nanotubes conveying viscous nanoflow and to design nanofluidic devices for detecting blood Glucose.
Kang, Dong-Keun; Kim, Chang-Wan; Yang, Hyun-Ik
2017-01-01
In the present study we carried out a dynamic analysis of a CNT-based mass sensor by using a finite element method (FEM)-based nonlinear analysis model of the CNT resonator to elucidate the combined effects of thermal effects and nonlinear oscillation behavior upon the overall mass detection sensitivity. Mass sensors using carbon nanotube (CNT) resonators provide very high sensing performance. Because CNT-based resonators can have high aspect ratios, they can easily exhibit nonlinear oscillation behavior due to large displacements. Also, CNT-based devices may experience high temperatures during their manufacture and operation. These geometrical nonlinearities and temperature changes affect the sensing performance of CNT-based mass sensors. However, it is very hard to find previous literature addressing the detection sensitivity of CNT-based mass sensors including considerations of both these nonlinear behaviors and thermal effects. We modeled the nonlinear equation of motion by using the von Karman nonlinear strain-displacement relation, taking into account the additional axial force associated with the thermal effect. The FEM was employed to solve the nonlinear equation of motion because it can effortlessly handle the more complex geometries and boundary conditions. A doubly clamped CNT resonator actuated by distributed electrostatic force was the configuration subjected to the numerical experiments. Thermal effects upon the fundamental resonance behavior and the shift of resonance frequency due to attached mass, i.e., the mass detection sensitivity, were examined in environments of both high and low (or room) temperature. The fundamental resonance frequency increased with decreasing temperature in the high temperature environment, and increased with increasing temperature in the low temperature environment. The magnitude of the shift in resonance frequency caused by an attached mass represents the sensing performance of a mass sensor, i.e., its mass detection
Institute of Scientific and Technical Information of China (English)
Jumpei; TAYAMA; Motohiro; BANNO; Kaoru; OHTA; Keisuke; TOMINAGA
2010-01-01
We have studied vibrational dynamics of the T1u mode of the CN stretching mode of [Ru(CN)6 ]4- in D2O by infrared(IR) nonlinear spectroscopy such as an IR three-pulse photon echo experiment and polarization-sensitive IR pump-probe spectroscopy. The isotropic component of the pump-probe signal shows a bi-exponential decay with time constants of 0.8 ps and 20.8 ps. The fast and slow components correspond to the rapid equilibration between the T1u mode and the Raman active modes of the CN stretching mode and the vibrational population relaxation from the v=1 state of the T1u mode,respectively. Anisotropy of the pump-probe signal decays with a time constant of 3.1 ps,which is due to the time evolution of the superposition states of the triply degenerate T1u modes. Three pulse photon echo measurements showed that the time correlation function of the frequency fluctuation decays bi-exponentially with time constants of 80 fs and 1.4 ps. These time constants depend only on the solute and are independent of the solvent,whereas the amplitudes depend on both the solute and solvent.
Wang, Yufeng; Yu, Zongxue; Sun, Yuxi; Wang, Yishi; Lu, Lude
2011-09-01
The study of imine-bridged organics has been the one hot spot of photo-responsive material sciences in recent years. Herein we make a study of the synthesis, characteristics and potential application of N-(4-hydroxy-phenyl)-2-hydroxy-benzaldehyde-imine (HPHBI), C 13H 11NO 2. The studied compound was synthesized in one step by the condensation reaction of salicylaldehyde and 4-aminophenol in methanol solution, and characterized by single crystal X-ray diffraction, FT-IR and FT-Raman techniques with theoretical calculations at B3LYP/6-31G(d) level. The molecule adopts trans configuration about central C dbnd6 N bond with intramolecular hydrogen bonding, and the adjacent molecules form wave-shaped structure linked by strong intermolecular hydrogen bonding mechanism along b axis. The vibrational spectra have been precisely assigned with the aid of theoretical frequencies. Furthermore, the thermodynamic properties have been obtained by the theoretical vibrational analysis for HPHBI. The total linear polarizability and first-order hyperpolarizabilities calculated on the studied compound respectively present 25.378 Å 3 and 1.655 × 10 -29 cm 5/esu, which indicates the compound has relatively good nonlinear optical property.
基于MATLAB的万向联轴器非线性扭振仿真%Simulation of Nonlinear Torsional Vibration of Universal Joint Based on MATLAB
Institute of Scientific and Technical Information of China (English)
徐翔; 周瑞平; 汪萌生; 祁亮
2011-01-01
利用第一类Lagrange方程建立了万向联轴器非线性扭转振动方程,在此基础上得到该系统的仿真模型并通过特例计算和仿真验证了该模型的正确性；然后通过修改参数获得了系统固有频率随夹角增大而逐渐减小的变化关系,得到了在夹角小于20°时的情况下可忽略夹角进行扭振计算的结论,为万向联轴器在船舶推进轴系的设计和应用提供理论支持.%The nonlinear torsional vibration equations of universal joint is derived by the first kind of Lagrange's equations, and the simulation model of this system is obtained, which was proved to be correct through calculation and simulation results in a special case, then the relationship that the natural frequency decreased with the angle increasing is gotten through the modification parameter, and the conclusion that the angle can be omitted in torsional vibration calculation when it is less than 20 ° is drawn, which provide theoretical support for universal joint design and application in ship propulsion shaft.
Ripamonti, Francesco; Orsini, Lorenzo; Resta, Ferruccio
2015-04-01
Non-linear behavior is present in many mechanical system operating conditions. In these cases, a common engineering practice is to linearize the equation of motion around a particular operating point, and to design a linear controller. The main disadvantage is that the stability properties and validity of the controller are local. In order to improve the controller performance, non-linear control techniques represent a very attractive solution for many smart structures. The aim of this paper is to compare non-linear model-based and non-model-based control techniques. In particular the model-based sliding-mode-control (SMC) technique is considered because of its easy implementation and the strong robustness of the controller even under heavy model uncertainties. Among the non-model-based control techniques, the fuzzy control (FC), allowing designing the controller according to if-then rules, has been considered. It defines the controller without a system reference model, offering many advantages such as an intrinsic robustness. These techniques have been tested on the pendulum nonlinear system.
Tanimura, Y; Steffen, T
2000-01-01
The relaxation processes in a quantum system nonlinearly coupled to a harmonic Gaussian-Markovian heat bath are investigated by the quantum Fokker-Planck equation in the hierarchy form. This model describes frequency fluctuations in the quantum system with an arbitrary correlation time and thus
Indian Academy of Sciences (India)
Srinivasan Bikshandarkoil R; Fernandes Royle
2016-03-01
In {\\it Pramana – J. Phys. } 75, 683 (2010), Gunasekaran et al reported that they have grown the nonlinear optical crystals, urea thiourea mercuric chloride (UTHC) and urea thiourea mercuric sulphate (UTHS).We argue that UTHC and UTHS are dubious crystals and are not what the authors propose.
Steffen, T; Tanimura, Y
2000-01-01
The quantum Fokker-Planck equation is derived for a system nonlinearly coupled to a harmonic oscillator bath. The system-bath interaction is assumed to be linear in the bath coordinates but quadratic in the system coordinate. The relaxation induced dynamics of a harmonic system are investigated by s
Institute of Scientific and Technical Information of China (English)
刘灿昌; 李红艳
2011-01-01
提出非线性的分阶最优控制策略,并将其应用于悬臂梁非线性振动的压电减振控制.建立悬臂梁非线性压电减振系统动力学模型,导出减振系统的非线性动力学运动微分方程.将梁振动挠度和压电驱动器的控制电压同时展开为小参数形式,利用摄动法实现非线性压电控制微分方程的线性化.通过空间解耦,得到状态空间方程.设计非线性分阶控制器,对该减振系统进行分阶最优控制.%A non-linear grade optimal control scheme is proposed and used in the piezoelectric vibration reduction control of non-linear cantilever beam. The dynamic model of non-linear vibration reduction beam with piezoelectric damper is built. The non-linear dynamic differential equations of the vibration reduction system are derived. The vibrational deflection and the piezoelectricity driver control voltage of beam are expanded as the small parametric form. The differential equation is linearized into a set of linear equations by means of perturbation. The state space equations are obtained by decoupling in the space coordinates. The vibration reduction system is controlled by the non-linear grade controllers.
2011-07-21
cowork- ers in the Mechanical Systems Lab. Thanks to Mauro, Dino, Clay, Eric, Debbie, Jens, and Marca for their discussions and assistance with...through static equilibrium simultaneously. iii. Displacement of one mass uniquely defines the displacements of all masses. These criteria are analogous to...be greater. Shaw and Pierre [10, 11] present an alternative definition of nonlinear normal modes, defined for both conservative and dissipative systems
Berjamin, Harold; Vergez, Christophe; Cottanceau, Emmanuel
2015-01-01
A time-domain numerical modeling of brass instruments is proposed. On one hand, outgoing and incoming waves in the resonator are described by the Menguy-Gilbert model, which incorporates three key issues: nonlinear wave propagation, viscothermal losses, and a variable section. The non-linear propagation is simulated by a TVD scheme well-suited to non-smooth waves. The fractional derivatives induced by the viscothermal losses are replaced by a set of local-in-time memory variables. A splitting strategy is followed to couple optimally these dedicated methods. On the other hand, the exciter is described by a one-mass model for the lips. The Newmark method is used to integrate the nonlinear ordinary differential equation so-obtained. At each time step, a coupling is performed between the pressure in the tube and the displacement of the lips. Finally, an extensive set of validation tests is successfully completed. In particular, self-sustained oscillations of the lips are simulated by taking into account the nonli...
IRAN: interferometric remapped array nulling
Aristidi, Eric; Vakili, Farrokh; Abe, Lyu; Belu, Adrian; Lopez, Bruno; Lanteri, Henri; Schutz, A.; Menut, Jean-Luc
2004-10-01
This paper describes a method of beam-combination in the so-called hypertelescope imaging technique recently introduced by Labeyrie in optical interferometry. The method we propose is an alternative to the Michelson pupil reconfiguration that suffers from the loss of the classical object-image convolution relation. From elementary theory of Fourier optics we demonstrate that this problem can be solved by observing in a combined pupil plane instead of an image plane. The point-source intensity distribution (PSID) of this interferometric "image" tends towards a psuedo Airy disc (similar to that of a giant monolithic telescope) for a sufficiently large number of telescopes. Our method is applicable to snap-shot imaging of extended sources with a field comparable to the Airy pattern of single telescopes operated in a co-phased multi-aperture interferometric array. It thus allows to apply conveniently pupil plane coronagraphy. Our technique called Interferometric Remapped Array Nulling (IRAN) is particularly suitable for high dynamic imaging of extra-solar planetary companions, circumstellar nebulosities or extra-galactic objects where long baseline interferometry would closely probe the central regions of AGNs for instance.
Wideband Interferometric Sensing and Imaging Polarimetry
Verdi, James Salvatore; Kessler, Otto; Boerner, Wolfgang-Martin
1996-01-01
Wideband Interferometric Sensing and Imaging Polarimetry (WISIP) has become an important, indispensible tool in wide area military surveillance and global environmental monitoring of the terrestrial and planetary covers. It enables dynamic, real time optimal feature extraction of significant characteristics of desirable targets and/or target sections with simultaneous suppression of undesirable background clutter and propagation path speckle at hitherto unknown clarity and never before achieved quality. WISIP may be adopted to the detection, recognition, and identification (DRI) of any stationary, moving or vibrating targets or distributed scatterer segments versus arbitrary stationary, dynamical changing and/or moving geo-physical/ecological environments, provided the instantaneous 2x2 phasor and 4x4 power density matrices for forward propagation/backward scattering, respectively, can be measured with sufficient accuracy. For example, the DRI of stealthy, dynamically moving inhomogeneous volumetric scatter environments such as precipitation scatter, the ocean/sea/lake surface boundary layers, the littoral coastal surf zones, pack ice and snow or vegetative canopies, dry sands and soils, etc. can now be successfully realized. A comprehensive overview is presented on how these modern high resolution/precision, complete polarimetric co-registered signature sensing and imaging techniques, complemented by full integration of novel navigational electronic tools, such as DGPS, will advance electromagnetic vector wave sensing and imaging towards the limits of physical realization. Various examples utilizing the most recent image data take sets of airborne, space shuttle, and satellite imaging systems demonstrate the utility of WISIP.
Institute of Scientific and Technical Information of China (English)
谢建军; 吴晓
2012-01-01
研究碳纤维材料矩形单层索网在基础位移激励下的非线性振动问题,是索网抗震防震设计的基础.在考虑温度变化的基础上,建立了碳纤维矩形索网在基础位移激励下的非线性振动方程,采用Galerkin原理及KBM法求得了碳纤维材料矩形单层索网非线性振动的近似解.在把碳纤维索网与钢丝索网比较的基础上,讨论分析了温度、位移激励、振幅、阻尼等因素对矩形单层索网非线性振动的影响,得到了碳纤维索网振动特性优于钢丝索网振动特性的结论.%It was studied that the nonlinear vibration of rectangular cable net using carbon fiber cables under foundation displacement excitation,and it is the base of earthquake prevention design of cable net. Meanwhile its nonlinear vibration equation was presented on the basis of considering temperature changing. And the approximate solution of nonlinear vibration of rectangular cable mesh was given used Galerkin principle and KBM method. Then something that affects its nonlinear vibration, such as the amount of temperature changing, foundation displacement excitation, amplitude as well as damping was discussed with the comparison between steel cable and carbon fiber cable. At last the conclusions was got that the vibration characteristics of cable net using carbon fiber cables is superior to cable net using steel.
Institute of Scientific and Technical Information of China (English)
刘少斌
2011-01-01
研究碳纤维材料索桁架在主体结构位移激励下的非线性振动问题,是空间索结构抗震防震设计的基础.在考虑温度变化的基础上,建立碳纤维索桁架在主体结构位移激励下的非线性振动方程,采用Galerkin原理及Krylov-Bogo1iulov-Mitropolsky法求得碳纤维材料索桁架非线性振动的近似解.在将碳纤维索网与钢丝索网比较的基础上,讨论分析温度、位移激励、振幅、阻尼等因素对索桁架非线性振动的影响,得到碳纤维索桁架振动特性优于钢丝索桁架振动特性的结论.%It was studied that the nonlinear vibration of cable truss using carbon fiber cables under main structure displacement excitation, and it is the base of earthquake prevention design of cable net.Meanwhile its nonlinear vibration equation was presented on the basis of considering temperature changing.And the approximate solution of nonlinear vibration of cable truss was given used Galerkin principle and Krylov-Bogoliulov-Mitropolsky method.Then something that affects its nonlinear vibration, such as the amount of temperature changing, main structure displacement excitation, amplitude as well as damping was discussed with the comparison between steel cable and carbon fiber cable.At last the conclusions was got that the vibration characteristics of cable net using carbon fiber cables is superior to cable net using steel.
Toutounji, Mohamad
2005-03-22
While an optical linear response function of linearly and quadratically coupled mixed quantum-classical condensed-phase systems was derived by Toutounji [J. Chem. Phys. 121, 2228 (2004)], the corresponding analytical optical line shape is derived. The respective nonlinear correlation functions are also derived. Model calculations involving photon-echo, pump-probe, and hole-burning signals of model systems with both linear and quadratic coupling are provided. Hole-burning formula of Hayes-Small is compared to that of Mukamel in mixed quantum-classical systems.
Iterated unscented Kalman filter for phase unwrapping of interferometric fringes.
Xie, Xianming
2016-08-22
A fresh phase unwrapping algorithm based on iterated unscented Kalman filter is proposed to estimate unambiguous unwrapped phase of interferometric fringes. This method is the result of combining an iterated unscented Kalman filter with a robust phase gradient estimator based on amended matrix pencil model, and an efficient quality-guided strategy based on heap sort. The iterated unscented Kalman filter that is one of the most robust methods under the Bayesian theorem frame in non-linear signal processing so far, is applied to perform simultaneously noise suppression and phase unwrapping of interferometric fringes for the first time, which can simplify the complexity and the difficulty of pre-filtering procedure followed by phase unwrapping procedure, and even can remove the pre-filtering procedure. The robust phase gradient estimator is used to efficiently and accurately obtain phase gradient information from interferometric fringes, which is needed for the iterated unscented Kalman filtering phase unwrapping model. The efficient quality-guided strategy is able to ensure that the proposed method fast unwraps wrapped pixels along the path from the high-quality area to the low-quality area of wrapped phase images, which can greatly improve the efficiency of phase unwrapping. Results obtained from synthetic data and real data show that the proposed method can obtain better solutions with an acceptable time consumption, with respect to some of the most used algorithms.
An All Fiber White Light Interferometric Absolute Temperature Measurement System
Directory of Open Access Journals (Sweden)
Jeonggon Harrison Kim
2008-11-01
Full Text Available Recently the author of this article proposed a new signal processing algorithm for an all fiber white light interferometer. In this article, an all fiber white light interferometric absolute temperature measurement system is presented using the previously proposed signal processing algorithm. Stability and absolute temperature measurement were demonstrated. These two tests demonstrated the feasibility of absolute temperature measurement with an accuracy of 0.015 fringe and 0.0005 fringe, respectively. A hysteresis test from 373K to 873K was also presented. Finally, robustness of the sensor system towards laser diode temperature drift, AFMZI temperature drift and PZT non-linearity was demonstrated.
Coupling between plate vibration and acoustic radiation
Frendi, Abdelkader; Maestrello, Lucio; Bayliss, Alvin
1993-01-01
A detailed numerical investigation of the coupling between the vibration of a flexible plate and the acoustic radiation is performed. The nonlinear Euler equations are used to describe the acoustic fluid while the nonlinear plate equation is used to describe the plate vibration. Linear, nonlinear, and quasi-periodic or chaotic vibrations and the resultant acoustic radiation are analyzed. We find that for the linear plate response, acoustic coupling is negligible. However, for the nonlinear and chaotic responses, acoustic coupling has a significant effect on the vibration level as the loading increases. The radiated pressure from a plate undergoing nonlinear or chaotic vibrations is found to propagate nonlinearly into the far field. However, the nonlinearity due to wave propagation is much weaker than that due to the plate vibrations. As the acoustic wave propagates into the far field, the relative difference in level between the fundamental and its harmonics and subharmonics decreases with distance.
Energy Technology Data Exchange (ETDEWEB)
Sangeetha, K. [Department of Physics, Sri Sarada College for Women, Salem-16 (India); Guru Prasad, L. [Department of Science & Humanities, M. Kumarasamy College of Engineering, Karur (India); Mathammal, R. [Department of Physics, Sri Sarada College for Women, Salem-16 (India)
2016-11-15
Single crystals of 2-methyl 3,5-dinitro benzoic acid with reasonable size have been grown by slow evaporation solution growth method using ethanol as solvent. Quantum chemical calculation of 2-methyl 3,5-Dinitro benzoic acid was carried out by using DFT/B3LYP/6-31+G(d,p) method. The powder X-ray diffraction pattern was recorded and indexed. Both the experimental and theoretical vibrational spectrum validates the presence of functional groups. Polarizability, first order hyperpolarizability and the electric dipole moment values have been computed theoretically. The {sup 1}H and {sup 13}C NMR chemical shift of the molecule was calculated and compared with experimental results. TG/DSC analysis has been employed to understand the thermal and physio-chemical stability of the title compound. Frequency conversion property of the crystal was tested by Kurtz and Perry method. Optical absorption behavior of the grown crystal was examined by recording the optical spectrum and band gap energy was also estimated. The calculated HOMO and LUMO energy shows the charge transfer nature of the molecule.
Sangeetha, K.; Guru Prasad, L.; Mathammal, R.
2016-11-01
Single crystals of 2-methyl 3,5-dinitro benzoic acid with reasonable size have been grown by slow evaporation solution growth method using ethanol as solvent. Quantum chemical calculation of 2-methyl 3,5-Dinitro benzoic acid was carried out by using DFT/B3LYP/6-31+G(d,p) method. The powder X-ray diffraction pattern was recorded and indexed. Both the experimental and theoretical vibrational spectrum validates the presence of functional groups. Polarizability, first order hyperpolarizability and the electric dipole moment values have been computed theoretically. The 1H and 13C NMR chemical shift of the molecule was calculated and compared with experimental results. TG/DSC analysis has been employed to understand the thermal and physio-chemical stability of the title compound. Frequency conversion property of the crystal was tested by Kurtz and Perry method. Optical absorption behavior of the grown crystal was examined by recording the optical spectrum and band gap energy was also estimated. The calculated HOMO and LUMO energy shows the charge transfer nature of the molecule.
Directory of Open Access Journals (Sweden)
L. S. Konev
2015-09-01
Full Text Available Numerical method for calculation of forward and backward waves of intense few-cycle laser pulses propagating in an optical waveguide with dispersion and cubic nonlinearity of electronic and electronic-vibration nature is described. Simulations made with the implemented algorithm show that accounting for Raman nonlinearity does not lead to qualitative changes in behavior of the backward wave. Speaking about quantitative changes, the increase of efficiency of energy transfer from the forward wave to the backward wave is observed. Presented method can be also used to simulate interaction of counterpropagating pulses.
UVMULTIFIT: A versatile tool for fitting astronomical radio interferometric data
Martí-Vidal, I.; Vlemmings, W. H. T.; Muller, S.; Casey, S.
2014-03-01
Context. The analysis of astronomical interferometric data is often performed on the images obtained after deconvolving the interferometer's point spread function. This strategy can be understood (especially for cases of sparse arrays) as fitting models to models, since the deconvolved images are already non-unique model representations of the actual data (i.e., the visibilities). Indeed, the interferometric images may be affected by visibility gridding, weighting schemes (e.g., natural vs. uniform), and the particulars of the (non-linear) deconvolution algorithms. Fitting models to the direct interferometric observables (i.e., the visibilities) is preferable in the cases of simple (analytical) sky intensity distributions. Aims: We present UVMULTIFIT, a versatile library for fitting visibility data, implemented in a Python-based framework. Our software is currently based on the CASA package, but can be easily adapted to other analysis packages, provided they have a Python API. Methods: The user can simultaneously fit an indefinite number of source components to the data, each of which depend on any algebraic combination of fitting parameters. Fits to individual spectral-line channels or simultaneous fits to all frequency channels are allowed. Results: We have tested the software with synthetic data and with real observations. In some cases (e.g., sources with sizes smaller than the diffraction limit of the interferometer), the results from the fit to the visibilities (e.g., spectra of close by sources) are far superior to the output obtained from the mere analysis of the deconvolved images. Conclusions: UVMULTIFIT is a powerful improvement of existing tasks to extract the maximum amount of information from visibility data, especially in cases close to the sensitivity/resolution limits of interferometric observations.
Interferometric Measurement Of Residual Stress
Danyluk, Steven; Andonian, A. T.
1990-01-01
Stress averaged through thickness of plate measured nondestructively. Theory of elasticity combined with laser interferometric technique into technique for measurement of residual stresses in solid objects - usually in thin, nominally-flat plates. Measurements particularly useful in inspection of wafers of single-crystal silicon for making solar cells or integrated circuits, because stresses remaining after crystal-growing process cause buckling or fracture. Used to predict deflections of plates caused by known applied loads under specified boundary condition, or to infer applied loads that cause known deflections. Also used to relate known deflections to residual stresses equivalent to stresses produced by fictitious applied loads.
DEFF Research Database (Denmark)
Thomsen, Jon Juel
dynamical phenomena that can be encountered in engineering and scientific practice. It progresses steadily from linear vibration theory over various levels of nonlinearity to bifurcation analysis, global dynamics and chaotic vibrations. It trains the student to analyze simple models, recognize nonlinear...... phenomena and work with advanced tools such as perturbation analysis and bifurcation analysis. Explaining theory in terms of relevant examples from real systems, this book is user-friendly and meets the increasing interest in non-linear dynamics in mechanical/structural engineering and applied mathematics...
Ben Hassen, Chaouki; Dammak, Thameur; Chniba-Boudjada, Nassira; Mhiri, Tahar; Boujelbene, Mohamed
2017-01-01
Single crystals of a new organic inorganic hybrid compound "bis (2,6-diaminopyridinium) sulfate monohydrate [C5H8N3]2SO4·H2O ([2,6-HDAP]2SO4·H2O)" was synthesized by slow evaporation method at room temperature and characterized by X-ray single crystal diffraction, infrared spectroscopy and DFT calculation. The new hybrid compound crystallizes in the orthorhombic system with the non-centro symmetric space group Pna21 and the following parameters a = 14.759(2) Å, b = 7.076 (2) Å and c = 28.159 (2) Å. The atomic arrangement can be described as inorganic chains following the b axis connected with the organic groups by means of Nsbnd H⋯O hydrogen bonds to form 3D network. Antiparallelly π-π stacked 2,6-HDAP cations form molecular columns in the spaces between the chains. The optimized molecular structure, vibrational spectra and the optical properties were calculated by the density functional theory (DFT) method using the B3LYP function with the LanL2DV basis set. The wavenumber calculated are in good agreement with the observed frequency values. The calculated hyperpolarizability βtot is about 4.5 times more than that of the reference crystal KDP. Hence, the large β value shows that the title compound is an attractive object for future studies of nonlinear optical properties.
Jasensky, Joshua; Boughton, Andrew P; Khmaladze, Alexander; Ding, Jun; Zhang, Chi; Swain, Jason E; Smith, George W; Chen, Zhan; Smith, Gary D
2016-08-01
Cytosolic lipids participate in the growth, development, and overall health of mammalian oocytes including many roles in cellular homeostasis. Significant emphasis has been placed on the study of lipids as a dynamic organelle, which in turn requires the development of tools and techniques to quantitate and compare how lipid content relates to cellular structure, function, and normalcy. Objectives of this study were to determine if nonlinear vibrational microscopy (e.g., coherent anti-Stokes Raman scattering or CARS microscopy) could be used for live-cell imaging to quantify and compare lipid content in mammalian oocytes during development and in relation to body composition; and compare its efficacy to methods involving cellular fixation and staining protocols. Results of this study demonstrate that CARS is able to identify lipids in live mammalian oocytes, and there exists quantifiable and consistent differences in percent lipid composition across ooctyes of different species, developmental stages, and in relation to body composition. Such a method of live-cell lipid quantification has (i) experimental power in basic cell biology, (ii) practical utility for identifying developmental predictive biomarkers while advancing biology-based oocyte/embryo selection, and (iii) ability to yield rationally supporting technology for decision-making in rodents, domestic species, and human assisted reproduction and/or fertility preservation.
Strong nonlinear oscillators analytical solutions
Cveticanin, Livija
2017-01-01
This book outlines an analytical solution procedure of the pure nonlinear oscillator system, offering a solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter. Includes exercises.
Institute of Scientific and Technical Information of China (English)
王光庆; 张伟; 刘创; 杨斌强; 廖维新
2015-01-01
In order to improve the output performances of the linear piezoelectric vibration energy harvester (PVEH),a bistable nonlinear PVEH was developed by adding a Duffing nonlinear magnetic force to a tip end of the linear PVEH. The governing motion of the nonlinear electromechanical lumped parameter of the bistable PVEH was derived with considering the dynamic shape and the axial strain of the cantilevered beam of the linear PVEH ,a four or five order Runge-Kutta algorithm was used to analyze the dynamic behaviors. The frequency responding function was derived with the resonant balance method;the effects of the exciting frequency,the exciting amplitude and the distance between the two magnets were numerically studied. The research results have shown that the bistable mo-tion can not only improve the operating frequency wideband and the energy harvesting efficiency,but also easily make it move in a periodic large-amplitude orbit under a low exciting frequency and amplitude. At last,some experi-ments are carried out to testify the validity of the numerical results.%为了提高线性压电振动能量采集器的输出特性,在线性压电振动能量采集器悬臂梁末端引入Duffing非线性磁力,构造了一种双稳态非线性压电振动能量采集器;综合考虑能量采集器的动态振型与轴向应变分布情况,建立了系统非线性机电耦合集总参数运动控制模型,并利用4阶、5阶Runge-Kutta算法对能量采集器的非线性振动特性进行了数值模拟;利用谐波平衡法计算获得了能量采集器的幅频响应方程,数值分析了激励频率、激励幅值以及磁铁间距等对系统非线性振动特性的影响,发现双稳态运动可以极大地提高能量采集器的频率响应范围和能量采集效率,并且能量采集器在低频、低幅值激励情况下可以产生大幅值周期运动;最后,通过实验对数值计算结果进行了验证.
Rýc, Jan
2011-01-01
Diplomová práce se zabývá bezkontaktními optickými metodami měření vzdálenosti a rychlosti (vibrací). Je zde uveden základní přehled a teoretická rešerže těchto metod. Podrobně je zde rozebrána zejména problematika interferometrických metod pro měření vibrací. Obsahuje rozdělení interferometrů, popis principu jejich funkce a rovněž obsahuje kapitoly zabývající se prvky, které se v interferometrech používají, jako lasery, fotodetektory a prvky v optické trase paprsku (polarizátory, retardéry a...
分子高激发振动态的经典非线性性质%The classical nonlinear properties of molecular highly excited vibration
Institute of Scientific and Technical Information of China (English)
吴国祯
2011-01-01
The concepts of classical nonlinear dynamics are employed to interpret the spectroscopic properties of the molecular highly excited vibration. These concepts include the Morse oscillator, the pendulum dynamics, chaos and the overlapping of resonances leading to chaos. The relations of resonance, constant of motion and the basic dynamical unit to the pendulum dynamics are stressed. An algebraic Hamiltonian in the coset space is employed for the dynamical analysis from which the dynamical potential can be easily obtained. The dynamical potential is closely related to the classical fixed points in which the quantized levels are embedded in various quantal environments.Localized modes are easily identified in various systems which share similar dynamical potentials. The dissociation of DCO radical is finally interpreted by these concepts from the classical nonlinear dynamics.%该文阐述如何运用经典非线性力学的概念,来理解分子高激发振动态的谱学性质.内容包括:莫尔斯振子,单摆的动力学和共振的关系,力学体系的构成单元是单摆,一个共振对应于一个守恒量,混沌,共振的重叠导致混沌的产生等.我们的出发点是运用二次量子化算子构成的代数哈密顿量,经由海森伯对应而得到的陪集空间上的动力学体系.从此哈密顿量,可以得到动力学势.而动力学势和经典的不动点关系密切,并且量子态就处在由动力学势所包围,分成的几个量子环境中.从动力学势,可以依据它的对称性,方便推得局域模式的存在,最后我们利用这些非线性力学的概念,来分析DCO分子高激发振动态的解离问题.
摩擦对齿轮系统非线性振动及稳定性影响研究%Effect of Friction on the Nonlinear Vibration and Stability of Gear System
Institute of Scientific and Technical Information of China (English)
卫一多; 刘凯; 马朝锋; 赵常青; 原园
2012-01-01
To eluicdatie the mechanism effect of friction on the nonlinear vibration and stability of gear system,a nonlinear vibration of torsional model with time-varying stiffness and friction was established,numerical method and analytical expression were given to solve the problem,study the non-linear response and parametric stability of gear system with double periodic parametrically.Effects of the system parameters,such as friction coefficient,mesh stiffneee factor and load sharing coefficient,on the nonlinear vibration response and parametric stability of gear system were investigated.Simulation results demonstrated that rational dynamics parameters can efficiently control the response peak of friction and reduce instability domain.%为研究摩擦对齿轮系统非线性振动的响应和稳定性的影响机理,建立考虑轮齿时变刚度和齿间摩擦的扭转非线性振动模型,用理论解析和数值计算结合的方法,研究周期双参变激励齿轮系统,在摩擦力作用下非线性振动响应和系统参数稳定性问题。研究了摩擦系数、啮合刚度因子及齿间载荷分配系数等参数,对齿轮系统非线性振动响应和参数稳定性的影响。仿真结果证明：合理设计齿轮系统的动力学参数,可有效抑制由摩擦引起的响应峰值和减小系统参数的不稳定性区域。
Cross-calibration of interferometric SAR data
DEFF Research Database (Denmark)
Dall, Jørgen
2003-01-01
Generation of digital elevation models from interferometric synthetic aperture radar (SAR) data is a well established technique. Achieving a high geometric fidelity calls for a calibration accounting for inaccurate navigation data and system parameters as well as system imperfections. Fully...
Improving the performance of interferometric imaging through the use of disturbance feedforward.
Böhm, Michael; Glück, Martin; Keck, Alexander; Pott, Jörg-Uwe; Sawodny, Oliver
2017-05-01
In this paper, we present a disturbance compensation technique to improve the performance of interferometric imaging for extremely large ground-based telescopes, e.g., the Large Binocular Telescope (LBT), which serves as the application example in this contribution. The most significant disturbance sources at ground-based telescopes are wind-induced mechanical vibrations in the range of 8-60 Hz. Traditionally, their optical effect is eliminated by feedback systems, such as the adaptive optics control loop combined with a fringe tracking system within the interferometric instrument. In this paper, accelerometers are used to measure the vibrations. These measurements are used to estimate the motion of the mirrors, i.e., tip, tilt and piston, with a dynamic estimator. Additional delay compensation methods are presented to cancel sensor network delays and actuator input delays, improving the estimation result even more, particularly at higher frequencies. Because various instruments benefit from the implementation of telescope vibration mitigation, the estimator is implemented as a separate, independent software on the telescope, publishing the estimated values via multicast on the telescope's ethernet. Every client capable of using and correcting the estimated disturbances can subscribe and use these values in a feedforward for its compensation device, e.g., the deformable mirror, the piston mirror of LINC-NIRVANA, or the fast path length corrector of the Large Binocular Telescope Interferometer. This easy-to-use approach eventually leveraged the presented technology for interferometric use at the LBT and now significantly improves the sky coverage, performance, and operational robustness of interferometric imaging on a regular basis.
Institute of Scientific and Technical Information of China (English)
钟艳春; 杨庆俊; 包钢
2011-01-01
The nonlinear dynamics characteristic of pneumatic vibration isolation system with a multi-frequency excitation was studied with the method of nonlinear dynamics. First, relative load curve of an air spring under a certain initial pressure was obtained by test, and based on the test data, a cube polynomial equation was obtained by means of nonlinear polynomial curve fitting according to the equilibrium heights of the air spring. Then, the nonlinear model of pneumatic vibration isolation system with a multi-frequency excitation was built and nonlinear dynamics equation was obtained according to nonlinear restoring force of the air spring. Next, the method of multiple scales was used to solve the nonlinear dynamics equation. Finally, combination resonance of pneumatic vibration isolation system with a multi-frequency excitation was analyzed and influences of the nonlinear parameter to the system were discussed. The results show that when combination frequencies are near the linearized natural frequency, combination resonance becomes strong. Cube nonlinear parameter directly influences nonlinear characteristic of the system, the greater the excitation amplitude, the more obvious of the nonlinear characteristic.%运用非线性动力学的方法研究气动隔振系统在多个频率激励下的非线性动力学特性.通过试验的方法得到空气弹簧在一定初始压力下的相对载荷曲线,以空气弹簧工作高度为自变量,用三次多项式对该曲线进行非线性拟合,得到弹簧非线性恢复力与工作高度的三次多项式表达式.建立气动隔振系统在3个激励频率下的非线性模型,根据弹簧的非线性恢复力,得到系统的非线性动力学方程.运用多尺度法对该非线性动力学方程进行求解,分析3个频率共同作用下的组合共振,讨论各非线性参数对系统的影响.研究结果表明:当组合频率接近系统线性化固有频率时,系统具有很强的组合共振;三次非线性
Vibrational Spectroscopy of Biomembranes
Schultz, Zachary D.; Levin, Ira W.
2011-07-01
Vibrational spectroscopy, commonly associated with IR absorption and Raman scattering, has provided a powerful approach for investigating interactions between biomolecules that make up cellular membranes. Because the IR and Raman signals arise from the intrinsic properties of these molecules, vibrational spectroscopy probes the delicate interactions that regulate biomembranes with minimal perturbation. Numerous innovative measurements, including nonlinear optical processes and confined bilayer assemblies, have provided new insights into membrane behavior. In this review, we highlight the use of vibrational spectroscopy to study lipid-lipid interactions. We also examine recent work in which vibrational measurements have been used to investigate the incorporation of peptides and proteins into lipid bilayers, and we discuss the interactions of small molecules and drugs with membrane structures. Emerging techniques and measurements on intact cellular membranes provide a prospective on the future of vibrational spectroscopic studies of biomembranes.
INTERFEROMETRIC VIEWS ON THE CEPHEIDS
Directory of Open Access Journals (Sweden)
A. Mérand
2010-01-01
Full Text Available El método de paralaje de pulsación, o método de Baade-Wesselink (BW, es una poderosa manera de medir distancias a Cefeidas en una manera pseudo-geométrica. En la búsqueda para obtener la más precisa distancia usando interferometría de gran línea de base (alcanzamos 1.5%, nosotros obtuvimos dos resultados quizás no tan insospechados. En primer lugar, nuestros estudios demuestran que alcanzamos un punto donde la suposición que la fotósfera que pulsa se puede aproximar usando modelos estáticos no es válida en el contexto del método BW. En segundo lugar, revelamos la presencia sistemática de envolturas circunestelares (CSE en escala de algunos diámetros estelares, como un leve exceso del infrarrojo cercano, que podría ser una indicación de que está ocurriendo una pérdida de masa. No sólo estos dos resultados representan un sesgo al método BW, y merece ser estudiado observacionalmente, sino también vierten nuevas luces a nuestro conocimiento de las cefeidas y requieren un extenso modelamiento.
Stefanov, Ivan L.; Hadjichristov, Georgi B.
2012-03-01
Optical interferometric technique is applied to characterize the nonlocal response of optically transparent ion implanted polymers. The thermal nonlinearity of the ion-modified material in the near-surface region is induced by continuous wave (cw) laser irradiation at a relatively low intensity. The interferometry approach is demonstrated for a subsurface layer of a thickness of about 100 nm formed in bulk polymethylmethacrylate (PMMA) by implantation with silicon ions at an energy of 50 keV and fluence in the range 1014-1017 cm-2. The laser-induced thermooptic effect in this layer is finely probed by interferometric imaging. The interference phase distribution in the plane of the ion implanted layer is indicative for the thermal nonlinearity of the near-surface region of ion implanted optically transparent polymeric materials.
NON-LINEAR FREE VIBRATION OF FINITE-LENGTH BEAMS ON THE WINKLER FOUNDATION%Winkler地基上有限长梁非线性自由振动
Institute of Scientific and Technical Information of China (English)
马建军; 刘齐建; 王连华; 赵跃宇
2012-01-01
基于经典Winkler地基模型及Euler—Bernoulli梁理论，考虑梁的几何非线性效应，运用Newton第二定律建立了弹性地基上有限长梁的非线性运动方程。采用Galerkin方法对运动方程进行一阶模态截断，进而利用多尺度法求得了该系统自由振动的一阶近似解。揭示了两端简支梁的非线性自由振动特性，分析了弹性模量、长细比及地基刚度系数等参数对系统固有频率的影响。并通过该系统的位移时程曲线，分析了阻尼对弹性地基上梁运动特性的影响。%The non-linear free vibration of a finite-length beam on the elastic foundation is investigated. Based on the Winkler foundation model and Euler-Bernoulli beam theory, the nonlinear motion equation of the finite-length beam on an elastic foundation with geometric nonlinearity is deduced based on the Newton＇s Second Law. The first-order mode truncation of the vibration function is obtained using the Galerkin method. The approximate solution of the free vibration of the finite-length beam is derived utilizing the multi-scale method to illustrate the behaviour of the non-linear free vibration. The effects of the slenderness ratio of beam, the modulus of elastic system and the stiffness of foundation on the natural frequency of the hinged-hinged beam on the Winkler foundation are analyzed. The influence of damping of the soil-beam system on the motion of the beam is also discussed.
Nonlinear Approaches in Engineering Applications
Jazar, Reza
2012-01-01
Nonlinear Approaches in Engineering Applications focuses on nonlinear phenomena that are common in the engineering field. The nonlinear approaches described in this book provide a sound theoretical base and practical tools to design and analyze engineering systems with high efficiency and accuracy and with less energy and downtime. Presented here are nonlinear approaches in areas such as dynamic systems, optimal control and approaches in nonlinear dynamics and acoustics. Coverage encompasses a wide range of applications and fields including mathematical modeling and nonlinear behavior as applied to microresonators, nanotechnologies, nonlinear behavior in soil erosion,nonlinear population dynamics, and optimization in reducing vibration and noise as well as vibration in triple-walled carbon nanotubes. This book also: Provides a complete introduction to nonlinear behavior of systems and the advantages of nonlinearity as a tool for solving engineering problems Includes applications and examples drawn from the el...
Geometrical model fitting for interferometric data: GEM-FIND
Klotz, D; Paladini, C; Hron, J; Wachter, G
2012-01-01
We developed the tool GEM-FIND that allows to constrain the morphology and brightness distribution of objects. The software fits geometrical models to spectrally dispersed interferometric visibility measurements in the N-band using the Levenberg-Marquardt minimization method. Each geometrical model describes the brightness distribution of the object in the Fourier space using a set of wavelength-independent and/or wavelength-dependent parameters. In this contribution we numerically analyze the stability of our nonlinear fitting approach by applying it to sets of synthetic visibilities with statistically applied errors, answering the following questions: How stable is the parameter determination with respect to (i) the number of uv-points, (ii) the distribution of points in the uv-plane, (iii) the noise level of the observations?
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.
Dynamics of laser interferometric gravitational wave detectors
Rakhmanov, Malik
2000-11-01
Dynamics of fields and mirrors in the new laser interferometric gravitational wave detectors is described. The dynamics of fields is formulated in terms of difference equations, which take into account the large delay due to the light transit time in the interferometer arm cavities. Solutions of these field equations are found in both transient and steady-state regimes. The solutions for fields in the transient regime can be used for the measurement of the parameters of Fabry-Perot cavities. The solutions for fields in the steady-state regime can be used for the analysis of noise performance of Fabry-Perot cavities. The dynamics of the mirrors is described in terms of two normal coordinates: the cavity length and its center of mass. Such dynamics is strongly affected by the radiation pressure of light circulating in the cavity. The forces of radiation pressure are nonlinear and nonconservative. These two effects introduce instabilities and give rise to a violation of conservation of energy for the motion of the suspended mirrors. Analytical calculations and numerical simulations of the dynamics are done with applications to the Laser Interferometer Gravitational-Wave Observatory (LIGO). The dynamics of signal recycling and power recycling interferometers is analyzed using the field equations. The response of the interferometers to the input laser field and motion of its mirrors is calculated. Several basic transfer functions are found. These correspond to either a single or a nested cavity. A nested cavity appears either in the dynamics of the differential mode in signal recycling interferometers or in the dynamics of the common mode of power recycling interferometers. The poles of transfer functions of these nested cavities are found. The response of the interferometers to gravitational waves is described: the analysis is done in the rest frame of a local observer which is a natural coordinate system of the detector. This response is given by the interferometer
Compression of interferometric radio-astronomical data
Offringa, A. R.
2016-11-01
Context. The volume of radio-astronomical data is a considerable burden in the processing and storing of radio observations that have high time and frequency resolutions and large bandwidths. For future telescopes such as the Square Kilometre Array (SKA), the data volume will be even larger. Aims: Lossy compression of interferometric radio-astronomical data is considered to reduce the volume of visibility data and to speed up processing. Methods: A new compression technique named "Dysco" is introduced that consists of two steps: a normalization step, in which grouped visibilities are normalized to have a similar distribution; and a quantization and encoding step, which rounds values to a given quantization scheme using a dithering scheme. Several non-linear quantization schemes are tested and combined with different methods for normalizing the data. Four data sets with observations from the LOFAR and MWA telescopes are processed with different processing strategies and different combinations of normalization and quantization. The effects of compression are measured in image plane. Results: The noise added by the lossy compression technique acts similarly to normal system noise. The accuracy of Dysco is depending on the signal-to-noise ratio (S/N) of the data: noisy data can be compressed with a smaller loss of image quality. Data with typical correlator time and frequency resolutions can be compressed by a factor of 6.4 for LOFAR and 5.3 for MWA observations with less than 1% added system noise. An implementation of the compression technique is released that provides a Casacore storage manager and allows transparent encoding and decoding. Encoding and decoding is faster than the read/write speed of typical disks. Conclusions: The technique can be used for LOFAR and MWA to reduce the archival space requirements for storing observed data. Data from SKA-low will likely be compressible by the same amount as LOFAR. The same technique can be used to compress data from
Werner, Charles L.; Wegmueller, Urs; Small, David L.; Rosen, Paul A.
1994-01-01
Terrain slopes, which can be measured with Synthetic Aperture Radar (SAR) interferometry either from a height map or from the interferometric phase gradient, were used to calculate the local incidence angle and the correct pixel area. Both are required for correct thematic interpretation of SAR data. The interferometric correlation depends on the pixel area projected on a plane perpendicular to the look vector and requires correction for slope effects. Methods for normalization of the backscatter and interferometric correlation for ERS-1 SAR are presented.
Institute of Scientific and Technical Information of China (English)
陈思忠; 卢凡; 吴志成; 杨林; 赵玉壮
2015-01-01
针对悬架系统非线性特性提出反馈线性化卡尔曼滤波算法。基于微分几何理论，通过求解坐标变换，将车辆非线性振动模型变换成可观测标准型，实现系统精确反馈线性化；采用线性卡尔曼滤波算法，针对变换的线性系统设计观测器，通过坐标逆变换获得原非线性系统的状态观测值。仿真结果表明，该算法能提高车辆振动状态观测精度、降低运算量。%Aiming at the nonlinearity of suspension system,a feedback linearization Kalman filter algorithm was proposed.Based on the differential geometry theory,the nonlinear vehicle vibration model was transformed into a certain observable normal form via the change of state coordinates.Based on the obtained linearized system,an observer was designed by using Kalman filter algorithm.Finally the estimated states of the nonlinear system were obtained through inverse transformation.The simulation results show that compared with the extended Kalman observer,the proposed algorithm can improve the observation accuracy of vehicle vibration states and reduce computational complexity.
Institute of Scientific and Technical Information of China (English)
刘志峰; 蒋凤麒; 杨文通; 蔡力钢
2012-01-01
The transmission error is an important factor causing nonlinear vibration of cycloid bevel gear, and the vibration characteristics of gear system can be improved by prediction and calculation of the dynamic transmission error of cycloid bevel gear. The dynamic response characteristics of cycloid bevel gear were discussed under a range of operation speeds and acting torques. A new approach of surface integration and local FEM was proposed to solve the dynamic transmission error. And then, the strong nonlinear vibration characteristics of gear system were analysed. In the approach, it is no longer necessary to consider the nonlinear factors, such as the lime-varied stiffness and meshing frequency variation, as external excitations. However, in every lime step of gear meshing the dynamic mesh force and dynamic transmission error were calculated, and finally the nonlinear vibration characteristics of cycloid bevel gear were achieved. The approach can precisely present the key factors of the gear teeth, including the tooth geometry and tooth contact stress, which influence the dynamic characteristics of cycloid bevel gear significantly and provides an effective method for the analysis of complex vibration characteristics of cycloid bevel gear transmission system.%齿轮重载啮合中发生的轮齿接触损失会引起齿轮传动中的动态传递误差,动态传递误差的存在是等高齿锥齿轮非线性振动的重要原因,准确预测和计算等高齿锥齿轮传动中的动态传递误差是进一步改善这类齿轮系统振动特性的有效手段.针对某重载等高齿锥齿轮,研究其在一定运行速度和扭矩范围内的频率响应特性,运用一种新的曲面积分与局部有限元联合求解方法求解了等高齿锥齿轮传动中的动态传递误差,揭示出此类传动系统振动的强非线性特性.这种方法无需将时变拟合刚度和啮合频率变量等非线性因素作为外部的激励进行求解,而是从齿轮啮
Note: Near infrared interferometric silicon wafer metrology.
Choi, M S; Park, H M; Joo, K N
2016-04-01
In this investigation, two near infrared (NIR) interferometric techniques for silicon wafer metrology are described and verified with experimental results. Based on the transparent characteristic of NIR light to a silicon wafer, the fiber based spectrally resolved interferometry can measure the optical thickness of the wafer and stitching low coherence scanning interferometry can reconstruct entire surfaces of the wafer.
Large amplitude forced vibration analysis of cross-beam system ...
African Journals Online (AJOL)
user
governing nonlinear differential equation of dynamic equilibrium for forced vibration of a ...... ω is the first natural frequency of the corresponding beam. ..... Although a separate free vibration analysis of the system is not carried out in course.
Deconvolution of interferometric data using interior point iterative algorithms
Theys, C.; Lantéri, H.; Aime, C.
2016-09-01
We address the problem of deconvolution of astronomical images that could be obtained with future large interferometers in space. The presentation is made in two complementary parts. The first part gives an introduction to the image deconvolution with linear and nonlinear algorithms. The emphasis is made on nonlinear iterative algorithms that verify the constraints of non-negativity and constant flux. The Richardson-Lucy algorithm appears there as a special case for photon counting conditions. More generally, the algorithm published recently by Lanteri et al. (2015) is based on scale invariant divergences without assumption on the statistic model of the data. The two proposed algorithms are interior-point algorithms, the latter being more efficient in terms of speed of calculation. These algorithms are applied to the deconvolution of simulated images corresponding to an interferometric system of 16 diluted telescopes in space. Two non-redundant configurations, one disposed around a circle and the other on an hexagonal lattice, are compared for their effectiveness on a simple astronomical object. The comparison is made in the direct and Fourier spaces. Raw "dirty" images have many artifacts due to replicas of the original object. Linear methods cannot remove these replicas while iterative methods clearly show their efficacy in these examples.
Kaliski, S
2013-01-01
This book gives a comprehensive overview of wave phenomena in different media with interacting mechanical, electromagnetic and other fields. Equations describing wave propagation in linear and non-linear elastic media are followed by equations of rheological models, models with internal rotational degrees of freedom and non-local interactions. Equations for coupled fields: thermal, elastic, electromagnetic, piezoelectric, and magneto-spin with adequate boundary conditions are also included. Together with its companion volume Vibrations and Waves. Part A: Vibrations this work provides a wealth
Suresh, S; Gunasekaran, S; Srinivasan, S
2014-05-05
The solid phase FT-IR and FT-Raman spectra of 2-[2-[2-[(2,6-dichlorophenyl)amino]phenyl]acetyl] oxyacetic acid (Aceclofenac) have been recorded in the region 4000-400 and 4000-100 cm(-1) respectively. The optimized molecular geometry and fundamental vibrational frequencies are interpreted with the aid of structure optimizations and normal coordinate force field calculations based on density functional theory (DFT) method and a comparative study between Hartree Fork (HF) method 6-311++G(d,p) level basis set. The calculated harmonic vibrational frequencies were scaled and have been compared with experimental by obtained FT-IR and FT-Raman spectra. A detailed interpretation of the vibrational spectra of this compound has been made on the basis of the calculated potential energy distribution (PED). The time dependent DFT method employed to study its absorption energy and oscillator strength. The linear polarizability (α) and the first order hyper polarizability (β) values of the investigated molecule have been computed. The electronic properties, such as HOMO and LUMO energies, molecular electrostatic potential (MESP) were also performed. Stability of the molecule arising from hyper conjugative interaction, charge delocalization has been analyzed using natural bond orbital (NBO) analysis.
Calibration of mixed-polarization interferometric observations
Marti-Vidal, Ivan; Conway, John; Zensus, Anton J
2016-01-01
Heterodyne receivers register the sky signal on either a circular polarization basis (where it is split into left-hand and right-hand circular polarization) or a linear polarization basis (where it is split into horizontal and vertical linear polarization). We study the problem of interferometric observations performed with telescopes that observe on different polarization bases, hence producing visibilities that we call "mixed basis" (i.e., linear in one telescope and circular in the other). We present novel algorithms for the proper calibration and treatment of such interferometric observations and test our algorithms with both simulations and real data. The use of our algorithms will be important for the optimum calibration of forthcoming observations with the Atacama Large mm/submm Array (ALMA) in very-long-baseline interferometry (VLBI) mode. Our algorithms will also allow us to optimally calibrate future VLBI observations at very high data rates (i.e., wide bandwidths), where linear-polarization feeds w...
Nohara, Ben T.; Arimoto, Akio
2007-01-01
Plates are common structural elements of most engineering structures, including aerospace, automotive, and civil engineering structures. The study of plates from theoretical perspective as well as experimental viewpoint is fundamental to understanding of the behavior of such structures. The dynamic characteristics of plates, such as natural vibrations, transient responses for the external forces and so on, are especially of importance in actual environments. In this...
Analysis of the interferometric Ronchi test.
Malacara, D
1990-09-01
It is well known that the Ronchi test has two equivalent interpretations, Physical, as an interferometer, or geometrical, as if the fringes were just shadows from the fringes on the ruling. The second interpretation is nearly always used in practice because it is simpler. However, the disadvantage is that the irradiance profile of the fringes cannot be calculated with this theory. Here, the interferometric interpretation of the test will be used to obtain the irradiance profile and the sharpness of the fringes.
Digital Detection of Exosomes by Interferometric Imaging
2016-01-01
Exosomes, which are membranous nanovesicles, are actively released by cells and have been attributed to roles in cell-cell communication, cancer metastasis, and early disease diagnostics. The small size (30–100 nm) along with low refractive index contrast of exosomes makes direct characterization and phenotypical classification very difficult. In this work we present a method based on Single Particle Interferometric Reflectance Imaging Sensor (SP-IRIS) that allows multiplexed phenotyping and ...
Institute of Scientific and Technical Information of China (English)
何孔德; 李友荣; 方子帆; 杨蔚华
2012-01-01
针对水下系泊监测平台在水流涡激作用下的稳定性问题,考虑了浮体在振动过程中的变形,建立了其流固耦合的非线性动力学方程,利用谐波平衡法进行了非线性特性定性分析,Melnikov方法进行稳定性判据研究及影响因素分析,以系统出现混沌状态为稳定性控制条件,重点研究了系泊缆支撑间距对稳定性的影响,并计算出支撑间距的临界值.结果表明,系统稳定性随支撑间距增加而降低,当支撑间距超过临界值后,稍微增加都可能导致系泊监测平台振动偏离振动轨道而造成局部失稳甚至结构破坏.为保证监测平台的稳定性,应增加支撑数量,且支撑的间距不能超过系统发生失稳的临界值.%Aiming at the problem of stability by flow vertex - induced action for submerged mooring monitoring platform, the fluid-solid coupling nonlinear dynamic equation is set up by taking into account the deformation of floating body under vibration. Nonlinear characteristic qualitative analysis is made by using harmonic wave equilibrium method and the stability criteria and influencing factors are studied by adopting Melnikov method. The influence of mooring cable support distance on stability is analysed and the critical value of support distance is calculated. The results show that the stability of system will decrease along with the increase of support distance. After the support distance passes the critical value, a little increase will make the mooring platform' s vibration deviate the vibration track, cause local instability and even damage the structure. In order to ensure the stability of mooring platform, the number of support should increase, and the support distance should not pass the critical value which will make the system instable.
Institute of Scientific and Technical Information of China (English)
李啸骢; 鹿建成; 韦善革; 梁志坚; 徐俊华
2014-01-01
为减少机电扰动对汽轮发电机组轴系扭振的影响，在单机无穷大系统中，建立了汽轮发电机组轴系、励磁和调速的六阶非线性状态空间数学模型。基于反馈精确线性化理论，设计了发电机组励磁和调速的多指标非线性协调控制(MINC)策略。同时与线性最优控制(LOC)方法做对比，仿真表明：采用MINC方法，当系统受到短路故障，调功和调压扰动时，不仅能更好地抑制汽轮机和发电机之间功角位移偏差的振荡，减少轴系扭振事故的发生，还可以兼顾各状态量的动、静态性能，提高电力系统稳定运行水平。%To reduce the effect of mechanical and electrical disturbance on torsional vibration of steam-turbine generator shafting, in a single machine infinite system, a six order nonlinear state space model is set up for steam turbine generator shafting based on the generator excitation and speed-regulation system. According to the accurate feedback linearization theory, the multi-index nonlinear coordination (MINC) control strategy is designed for suppressing the torsional vibration of shafting. The strategy is compared with linear optimal control (LOC) method. The simulation results show that when the short-circuit fault occurs and the regulating power and voltage are disturbed, the MINC method can restrain oscillation of the angular displacement deviation between turbine and generator, reduce the risk of shaft torsional vibration, give better consideration of both dynamic and static performance of each state quantity, and stabilize the operation of power system.
Institute of Scientific and Technical Information of China (English)
杨金福; 陈策; 刘玉晗; 韩东江
2011-01-01
Based on gas-dynamic bearings and frequency coupled modulation of rotor-bearing system,the characteristics of rotor bearing system＇s nonlinear vibration experimental investigations were applied to high-speed air cycle refrigerator.Furthermore,some nonlinear characteristics,for example,the motion of rotor,bearings instability and rub-impact which always happen on the flexible shaft,were analyzed.The results show that,if the design margin of safe speed is guaranteed,the steady running speed of the rotor-bearings system can be effectively increased from 40 000 r/min to 60 000 r/min above.%基于气动轴承与轴系耦合调频技术,对高速压气机涡轮转子结构的空气循环制冷机轴系进行非线性振动性能的试验研究,进一步分析了柔性轴系存在转子运动、轴承失稳及碰摩故障的一些非线性特征.研究结果表明：在保证转速设计裕度的前提下,工作转速由40 000r/m提高到了60 000r/m.
Jumps and bi-stability in the phase-gain characteristics of a nonlinear parametric amplifier
DEFF Research Database (Denmark)
Neumeyer, Stefan; van de Looij, Ruud; Thomsen, Jon Juel
2014-01-01
This work experimentally investigates the impact of nonlinearity on macromechanical parametric amplification. For a strong cubic stiffness nonlinearity we observe jumps in gain (ratio of steady-state vibration amplitude of the externally and parametrically excited system, to vibration amplitude...
Vibrational spectroscopy at electrified interfaces
Wieckowski, Andrzej; Braunschweig, Björn
2013-01-01
Reviews the latest theory, techniques, and applications Surface vibrational spectroscopy techniques probe the structure and composition of interfaces at the molecular level. Their versatility, coupled with their non-destructive nature, enables in-situ measurements of operating devices and the monitoring of interface-controlled processes under reactive conditions. Vibrational Spectroscopy at Electrified Interfaces explores new and emerging applications of Raman, infrared, and non-linear optical spectroscopy for the study of charged interfaces. The book draws from hu
Institute of Scientific and Technical Information of China (English)
滕青芳; 孙金龙; 范多旺
2012-01-01
The problem of robust H∞ fault-tolerant control for structural nonlinear vibration systems with multi-constraints is investigated. According to structural dynamics theory, a state-space model containing multi-constraints such as input time-varying delay, actuator failure, parameter nonlinear, disturbance, etc is established. Based on state feedback and Lyapunov stability theory, a sufficient condition of the existence of robust H∞, fault-tolerant controller is derived and then transformed to the corresponding Linear Matrix Inequality (LMI). During inferential reasoning, the matrix inequality is only amplified twice and relied on system's delay-time, so that it is possible to sufficently reduce conservative of controller design. The resultant controller enables structural nonlinear vibration systems to retain robust stability and disturbance attenuation as well as to tolerate actuator failure. A building model with four degrees of freedom subjected to the El Centro earthquake wave is simulated and studied to examine the effectiveness of the algorithm provided above, and the results show that the proposed method is feasible.%研究了多约束条件下非线性结构振动系统的鲁棒H∞容错控制问题.根据建筑结构力学原理,建立了包含输入时变时滞、执行器故障、非线性参数摄动以及干扰等多约束条件的结构振动系统状态模型,基于状态反馈和Lyapunov稳定性理论,提出了一个可满足多约束条件的时滞相关鲁棒H∞容错控制算法,该结果以线性矩阵不等式形式给出.在推导过程中只对矩阵不等式进行了两次放大,结果与输入时滞有关,以尽可能降低控制器设计的保守性.该方法设计的控制器能够使得时滞非线性结构振动系统具有指定H∞范数的干扰抑制能力,对执行器故障具有容错性.通过对一个四自由度建筑结构模型在E1 Centro地震波作用下振动的控制仿真,验证了所提方法的可行性和有效性.
Improving terrain height estimates from RADARSAT interferometric measurements
Energy Technology Data Exchange (ETDEWEB)
Thompson, P.A.; Eichel, P.H.; Calloway, T.M.
1998-03-01
The authors describe two methods of combining two-pass RADAR-SAT interferometric phase maps with existing DTED (digital terrain elevation data) to produce improved terrain height estimates. The first is a least-squares estimation procedure that fits the unwrapped phase data to a phase map computed from the DTED. The second is a filtering technique that combines the interferometric height map with the DTED map based on spatial frequency content. Both methods preserve the high fidelity of the interferometric data.
Xie, Fang; Ren, Junyu; Chen, Zhimin; Feng, Qibo
2010-02-01
A highly stabilised vibration-displacement measurement system, which employs fiber Bragg gratings (FBGs) to interleave two fiber Michelson interferometers that share the common-interferometric-optical path, is presented. The phase change in the interferometric signals of the two fiber Michelson interferometers have been tracked, respectively, with two electronic feedback loops. One of the fiber interferometers is used to stabilise the system by the use of an electronic feedback loop to compensate the environmental disturbances. The second fiber interferometer is used to perform the measurement task and employs another electronic feedback loop to track the phase change in the interferometric signal. The measurement system is able to measure vibration-displacement and provide the sense of direction of the displacement. The frequency range of the measured vibration-displacement is from 0.1 to 200 Hz and the measurement resolution is 10 nm.
Directory of Open Access Journals (Sweden)
Daaf Sandkuijl
Full Text Available A new nonlinear microscopy technique based on interference of backward-reflected third harmonic generation (I-THG from multiple interfaces is presented. The technique is used to measure height variations or changes of a layer thickness with an accuracy of up to 5 nm. Height variations of a patterned glass surface and thickness variations of fibroblasts are visualized with the interferometric epi-THG microscope with an accuracy at least two orders of magnitude better than diffraction limit. The microscopy technique can be broadly applied for measuring distance variations between membranes or multilayer structures inside biological tissue and for surface height variation imaging.
Nonlinear Response of Strong Nonlinear System Arisen in Polymer Cushion
Directory of Open Access Journals (Sweden)
Jun Wang
2013-01-01
Full Text Available A dynamic model is proposed for a polymer foam-based nonlinear cushioning system. An accurate analytical solution for the nonlinear free vibration of the system is derived by applying He's variational iteration method, and conditions for resonance are obtained, which should be avoided in the cushioning design.
Directory of Open Access Journals (Sweden)
Lhoucine Boutahar
2016-03-01
Full Text Available Some Functionally Graded Materials contain pores due to the result of processing; this influences their elastic and mechanical properties. Therefore, it may be very useful to examine the vibration behavior of thin Functionally Graded Annular Plates Clamped at both edges including porosities. In the present study, the rule of mixture is modified to take into account the effect of porosity and to approximate the material properties assumed to be graded in the thickness direction of the examined annular plate. A semi-analytical model based on Hamilton’s principle and spectral analysis is adopted using a homogenization procedure to reduce the problem under consideration to that of an equivalent isotropic homogeneous annular plate. The problem is solved by a numerical iterative method. The effects of porosity, material property, and elastic foundations characteristics on the CCFGAP axisymmetric large deflection response are presented and discussed in detail.
Model Order Selection in Multi-baseline Interferometric Radar Systems
Directory of Open Access Journals (Sweden)
Fulvio Gini
2005-12-01
Full Text Available Synthetic aperture radar interferometry (InSAR is a powerful technique to derive three-dimensional terrain images. Interest is growing in exploiting the advanced multi-baseline mode of InSAR to solve layover effects from complex orography, which generate reception of unexpected multicomponent signals that degrade imagery of both terrain radar reflectivity and height. This work addresses a few problems related to the implementation into interferometric processing of nonlinear algorithms for estimating the number of signal components, including a system trade-off analysis. Performance of various eigenvalues-based information-theoretic criteria (ITC algorithms is numerically investigated under some realistic conditions. In particular, speckle effects from surface and volume scattering are taken into account as multiplicative noise in the signal model. Robustness to leakage of signal power into the noise eigenvalues and operation with a small number of looks are investigated. The issue of baseline optimization for detection is also addressed. The use of diagonally loaded ITC methods is then proposed as a tool for robust operation in the presence of speckle decorrelation. Finally, case studies of a nonuniform array are studied and recommendations for a proper combination of ITC methods and system configuration are given.
Nanda, Kirti; Kundu, R. S.; Sharma, Sarita; Mohan, Devendra; Punia, R.; Kishore, N.
2015-07-01
Samarium oxide doped Barium-Zinc-Borate glasses with compositions xSm2O3-(100-x)[0.1BaO-0.4ZnO-0.5B2O3]; x = 0.0, 0.5, 1.0, 1.5 and 2.0 have been prepared by melt quench technique. The amorphous nature of as-prepared glasses has been ascertained by X-ray diffraction patterns. The observed values of density and molar volume of the glass samples are found to increase with the increase in concentration of Sm2O3. Fourier Transform Infrared spectra of the prepared glasses indicate that Sm2O3 acts as glass modifier. With the increase in Sm2O3 content, BO4 structural units start converting into BO3 structural units. The values of optical energy band gap (Eg), estimated from Tauc's plots, are observed to decrease with the increase in Sm2O3 content. The nonlinear optical properties of glass samples have been investigated by Z-scan method with nanosecond pulsed laser at ˜532 nm in both open and close aperture geometries. The values of two photon absorption coefficient (β) and nonlinear refractive index (n2) have been estimated by fitting of experimentally observed data with theoretical models and both are found to increase with the increase in Sm3+ ions concentration in the glass matrix. The total third order nonlinear susceptibility (χ(3)) have been calculated and observed to increase with the increase in Sm3+ ions concentration.
Institute of Scientific and Technical Information of China (English)
时培明; 李纪召; 刘彬; 韩东颖
2012-01-01
Considering the effects caused by the coexisting of two different periodic parametric excitations in rotating machinery driving system, the dynamical equation of a nonlinear torsional vibration system was established based on Lagrange equation. The model contains quasi-periodic parametrically excited stiffness and friction damping. The amplitude-frequency characteristic equation and bifurcation response equation were obtained by solving the torsional vibration system using multi-scale method. On this basis, the periodic bursting of the nonlinear torsional vibration system was studied when large difference gap exists between the frequencies of the two periodic parametrical excitations. The influences of fast-varying parametrical excitation and slow-varying parametrical excitation on the periodic bursting of the torsional vibration system were analyzed. The parameter regions of periodic bursting were obtained with the help of numerical simulation. The mutual transition between quiescent state and spiking state of the system occurs in this region. When the amplitude of the fast-varying excitation reduces, the area of spiking state extends and the time of bursting prolongs. The bursting type and trajectory of the system can be changed by regulating the amplitude of slow-varying parametric excitation.%摘要:考虑旋转机械中两种频率不同的周期参数激励同时存在对其传动系统的影响,基于拉格朗日方程,建立一类含准周期参激刚度和摩擦阻尼的非线性扭振系统的动力学方程.运用多尺度法对该扭振系统进行求解,得到系统在1/2亚谐波主参数共振下的幅频特性方程和分岔响应方程.在此基础上,研究了当两种周期参激的频率相差较大时非线性扭振系统的周期簇发现象,分析了快变参激和慢变参激对扭振系统的周期簇发的影响.通过数值仿真,给出了产生周期簇发的参数取值区域.在该区域内系统发生静息态与激发态的相互转
Speckle interferometric observations of close binary stars
Saha, S K; Yeswanth, L; Anbazhagan, P
2002-01-01
Speckle interferometric technique is employed to record a series of hundreds of short-exposure images of several close binary stars with sub-arcsecond separation through a narrow band filter at the Cassegrain focus of the 2.34 meter (m) Vainu Bappu telescope (VBT), situated at Vainu Bappu Observatory (VBO), Kavalur, India. The data are recorded sequentially by a Peltier-cooled intensified CCD camera with 10 ms exposure. The auto-correlation method is applied to determine the angular separations and position angles of these binary systems.
The response of interferometric gravitational wave detectors
Finn, Lee Samuel
2008-01-01
The standard derivation of the response of interferometric gravitational wave detectors makes a series of erroneous approximations regarding the coordinate trajectory of the light and the parameterization of the null geodesic it travels along. These errors appear to have remained unrecognized for at least thirty five years. We provide, in full detail, a correct derivation of the response of a single-bounce Michelson interferometer to gravitational waves, compare it to the "standard", but incorrect, derivation, and show where the earlier mistakes were made. By a fortuitous set of circumstances, not generally so, the final result is the same.
Interferometric Calibration with Natural Distributed Targets
DEFF Research Database (Denmark)
Dall, Jørgen; Christensen, Erik Lintz
2002-01-01
Cross-calibration is a fully automated algorithm for calibration of interferometric synthetic aperture radar (IFSAR) data. It has been developed for single-pass interferometry, but the principles may be applicable to multi-pass interferometry, too. The algorithm is based on natural distributed...... targets and it excels by neither requiring surveyed ground control points nor dedicated calibration scenes. However, the parameters to be calibrated must be stable during mapping. The algorithm has been applied to data from the Danish airborne SAR, EMISAR, and the performance has been assessed...
Cross-calibration of interferometric SAR data
DEFF Research Database (Denmark)
Dall, Jørgen
2003-01-01
Generation of digital elevation models from interferometric synthetic aperture radar (SAR) data is a well established technique. Achieving a high geometric fidelity calls for a calibration accounting for inaccurate navigation data and system parameters as well as system imperfections. Fully......, but not necessarily from map to map. It is based on natural distributed targets for which no a priori knowledge is needed. In particular, no DEM is required as in calibration techniques based on dedicated calibration scenes. To achieve absolute calibration, i.e. elimination of a constant elevation offset, a single...
Light-pulse atom interferometric device
Biedermann, Grant; McGuinness, Hayden James Evans; Rakholia, Akash; Jau, Yuan-Yu; Schwindt, Peter; Wheeler, David R.
2016-03-22
An atomic interferometric device useful, e.g., for measuring acceleration or rotation is provided. The device comprises at least one vapor cell containing a Raman-active chemical species, an optical system, and at least one detector. The optical system is conformed to implement a Raman pulse interferometer in which Raman transitions are stimulated in a warm vapor of the Raman-active chemical species. The detector is conformed to detect changes in the populations of different internal states of atoms that have been irradiated by the optical system.
Institute of Scientific and Technical Information of China (English)
周涛; 朱乐东; 郭震山
2011-01-01
利用涡激共振竖向位移响应,基于广义谐波函数KBM法并引入缓变参数的概念,对Scanlan经验非线性模型进行处理,识别其中的气动参数,并得到Seanlan非线性涡激力.对识别得到的Scanlan非线性涡激力,分别通过:用Newmarkβ反求响应与实测响应进行比较;与从大平同步测得的合力中提取出实测的涡激力进行比较,对识别精度做出评价.试验是在同济大学TJ-1号风洞均匀流场中进行的,以象山港大桥初始设计阶段节段模型为例,用激光位移计采集模型的位移响应,并用一维梁式应变测力天平同步采集模型所受的力.%Aerodynamic parameters of Scanlan' s nonlinear empirical model were identified by using the data of vertical vortex response. Based on the generalized harmonic wave functionH KBM method and under the presupposition of slowly varying parameters, the function of Scanlan' s nonlinear empirical model was solved. And then the aerodynamic parameters of the model and the Scanlan' s nonlinear vortex-induced force were identified. The identification precision was evaluated via the following two methods: the response calculated according to the Newmark β method was compared with the field measured response; and the self-excited VIV force extracted from the total force collected by the one-dimensional balances was compared with the field measured exciting force. The experiment was carried out in TJ-1 wind tunnel of Tongji University using the preliminarily designed section model of Xiangshangang bridge. The vertical response of the section model was collected by the laser displacement sensor, and meanwhile the total force was collected by beam-type strain force balances of one-dimension.
Interferometric interpolation of sparse marine data
Hanafy, Sherif M.
2013-10-11
We present the theory and numerical results for interferometrically interpolating 2D and 3D marine surface seismic profiles data. For the interpolation of seismic data we use the combination of a recorded Green\\'s function and a model-based Green\\'s function for a water-layer model. Synthetic (2D and 3D) and field (2D) results show that the seismic data with sparse receiver intervals can be accurately interpolated to smaller intervals using multiples in the data. An up- and downgoing separation of both recorded and model-based Green\\'s functions can help in minimizing artefacts in a virtual shot gather. If the up- and downgoing separation is not possible, noticeable artefacts will be generated in the virtual shot gather. As a partial remedy we iteratively use a non-stationary 1D multi-channel matching filter with the interpolated data. Results suggest that a sparse marine seismic survey can yield more information about reflectors if traces are interpolated by interferometry. Comparing our results to those of f-k interpolation shows that the synthetic example gives comparable results while the field example shows better interpolation quality for the interferometric method. © 2013 European Association of Geoscientists & Engineers.
Digital Detection of Exosomes by Interferometric Imaging
Daaboul, George G.; Gagni, Paola; Benussi, Luisa; Bettotti, Paolo; Ciani, Miriam; Cretich, Marina; Freedman, David S.; Ghidoni, Roberta; Ozkumur, Ayca Yalcin; Piotto, Chiara; Prosperi, Davide; Santini, Benedetta; Ünlü, M. Selim; Chiari, Marcella
2016-01-01
Exosomes, which are membranous nanovesicles, are actively released by cells and have been attributed to roles in cell-cell communication, cancer metastasis, and early disease diagnostics. The small size (30–100 nm) along with low refractive index contrast of exosomes makes direct characterization and phenotypical classification very difficult. In this work we present a method based on Single Particle Interferometric Reflectance Imaging Sensor (SP-IRIS) that allows multiplexed phenotyping and digital counting of various populations of individual exosomes (>50 nm) captured on a microarray-based solid phase chip. We demonstrate these characterization concepts using purified exosomes from a HEK 293 cell culture. As a demonstration of clinical utility, we characterize exosomes directly from human cerebrospinal fluid (hCSF). Our interferometric imaging method could capture, from a very small hCSF volume (20 uL), nanoparticles that have a size compatible with exosomes, using antibodies directed against tetraspanins. With this unprecedented capability, we foresee revolutionary implications in the clinical field with improvements in diagnosis and stratification of patients affected by different disorders. PMID:27853258
Energy Technology Data Exchange (ETDEWEB)
McGuire, John Andrew [Univ. of California, Berkeley, CA (United States)
2004-11-24
The high temporal resolution and broad bandwidth of a femtosecond laser system are exploited in a pair of nonlinear optical studies of surfaces. The dephasing dynamics of resonances associated with the adatom dangling bonds of the Si(111)7 x 7 surface are explored by transient second-harmonic hole burning, a process that can be described as a fourth-order nonlinear optical process. Spectral holes produced by a 100 fs pump pulse at about 800 nm are probed by the second harmonic signal of a 100 fs pulse tunable around 800 nm. The measured spectral holes yield homogeneous dephasing times of a few tens of femtoseconds. Fits with a Lorentzian spectral hole centered at zero probe detuning show a linear dependence of the hole width on pump fluence, which suggests that charge carrier-carrier scattering dominates the dephasing dynamics at the measured excitation densities. Extrapolation of the deduced homogeneous dephasing times to zero excitation density yields an intrinsic dephasing time of {approx} 70 fs. The presence of a secondary spectral hole indicates that scattering of the surface electrons with surface optical phonons at 570 cm^{-1} occurs within the first 200 fs after excitation. The broad bandwidth of femtosecond IR pulses is used to perform IR-visible sum frequency vibrational spectroscopy. By implementing a Fourier-transform technique, we demonstrate the ability to obtain sub-laser-bandwidth spectral resolution. FT-SFG yields a greater signal when implemented with a stretched visible pulse than with a femtosecond visible pulse. However, when compared with multichannel spectroscopy using a femtosecond IR pulse but a narrowband visible pulse, Fourier-transform SFG is found to have an inferior signal-to-noise ratio. A mathematical analysis of the signal-to-noise ratio illustrates the constraints on the Fourier-transform approach.
Issanchou, Clara; Bilbao, Stefan; Le Carrou, Jean-Loïc; Touzé, Cyril; Doaré, Olivier
2017-04-01
This article is concerned with the vibration of a stiff linear string in the presence of a rigid obstacle. A numerical method for unilateral and arbitrary-shaped obstacles is developed, based on a modal approach in order to take into account the frequency dependence of losses in strings. The contact force of the barrier interaction is treated using a penalty approach, while a conservative scheme is derived for time integration, in order to ensure long-term numerical stability. In this way, the linear behaviour of the string when not in contact with the barrier can be controlled via a mode by mode fitting, so that the model is particularly well suited for comparisons with experiments. An experimental configuration is used with a point obstacle either centered or near an extremity of the string. In this latter case, such a pointwise obstruction approximates the end condition found in the tanpura, an Indian stringed instrument. The second polarisation of the string is also analysed and included in the model. Numerical results are compared against experiments, showing good accuracy over a long time scale.
Nicolas, Maxime
2016-01-01
Engineering school; This course is designed for students of Polytech Marseille, engineering school. It covers first the physics of vibration of the harmonic oscillator with damping and forcing, coupled oscillators. After a presentation of the wave equation, the vibration of strings, beams and membranes are studied.
Zarei, Seyed Amir; Khaledian, Donya; Akhtari, Keivan; Hassanzadeh, Keyumars
2015-11-01
The experimental fourier transform infrared (FT-IR) and ultraviolet-visible (UV-Vis) spectra of copper(II) and nickel(II) complexes of the deprotonated tetradentate Schiff base ligand N,N‧-bis(2-hydroxybenzylidene)-2,2-dimethyl-1,3-propanediamine (H2L) are compared with their corresponding theoretical ones. The applied theoretical method is based on the density functional theory and time-dependent density functional theory at the UPBE0/PBE0 levels using Def2-TZVP basis set. The computational optimised geometric parameters of the complexes are in good agreement with their corresponding experimental data. The FT-IR and UV-Vis spectra of the complexes were reproduced on the basis of their optimised structures. The vibrational assignments of some fundamental modes of the complexes are performed. The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energies are calculated. The analyses of the calculated electronic absorption spectra of the complexes are carried out to elucidate the electronic transitions assignments and their characters. Second-order nonlinear optical property of the complexes is evaluated by the above-mentioned theoretical method that implies much greater values for the complexes in comparison with the corresponding value of urea.
Institute of Scientific and Technical Information of China (English)
何其伟; 俞翔; 毛为民
2016-01-01
Cascades of subharmonic waves and their stability for a high-dimensional strongly nonlinear vibration isolation system were studied by combining the harmonic balance method and the predictor-corrector method.The amplitude-frequency curve of every subharmonic wave was plotted.Two routes of bifurcation were analyzed and the boundaries of the period-doubling bifurcations were obtained through the stability analysis,and then the parametric regions of chaos were estimated.The results agreed well with those obtained with numerical simulations.%从次谐波级联角度，利用谐波平衡法与跟踪延拓算法得到了高维强非线性隔振系统各级次谐波的幅频特性曲线，分析了次谐波的稳定性，研究了两条分岔道路，得到了典型的倍周期分岔值，以此估计了混沌参数区域，与数值计算结果吻合较好。
Iwahashi, Takashi; Ishiyama, Tatsuya; Sakai, Yasunari; Morita, Akihiro; Kim, Doseok; Ouchi, Yukio
2015-10-14
IR-visible sum-frequency generation (IV-SFG) vibrational spectroscopy and a molecular dynamics (MD) simulation were used to study the local layering order at the interface of 1-butanol-d9 and 1-butyl-3-methylimidazolium hexafluorophosphate ([bmim]PF6), a room-temperature ionic liquid (RTIL). The presence of a local non-polar layer at the interface of the two polar liquids was successfully demonstrated. In the SFG spectra of 1-butanol-d9, we observed significant reduction and enhancement in the strength of the CD3 symmetric stretching (r(+)) mode and the antisymmetric stretching (r(-)) mode peaks, respectively. The results can be well explained by the presence of an oppositely oriented quasi-bilayer structure of butanol molecules, where the bottom layer is strongly bound by hydrogen-bonding with the PF6(-) anion. MD simulations reveal that the hydrogen-bonding of butanol with the PF6(-) anion causes the preferential orientation of the butanols; the restriction on the rotational distribution of the terminal methyl group along their C3 axis enhances the r(-) mode. As for the [bmim](+) cations, the SFG spectra taken within the CH stretch region indicate that the butyl chain of [bmim](+) points away from the bulk RTIL phase to the butanol phase at the interface. Combining the SFG spectroscopy and MD simulation results, we propose an interfacial model structure of layering, in which the butyl chains of the butanol molecules form a non-polar interfacial layer with the butyl chains of the [bmim](+) cations at the interface.
Research on interferometric photonic crystal fiber hydrophone
Luo, Hong; Zhang, Zhen-hui; Wang, Fu-yin; Xiong, Shui-dong
2013-08-01
Current research on photonic crystal fiber (PCF) for acoustic sensing was focused on the PCF's pressure sensitivity enhancement. However, whether the enhancement of the PCF's pressure sensitivity can be actually realized is still controversial. Practical hydrophone, utilizing PCFs, to manifest its superior sensitivity to normal single mode fibers (SMFs) for acoustic sensing, should be made. Account to this point of view, actual hydrophone was fabricated. Index guiding PCF was used, the fiber core is solid silicon dioxide (SiO2), and the cladding is SiO2 filled with lots of periodical transverse circular air hollows. The PCF, mounted on an air-backed mandrel for structural sensitivity enhancement, was used as a sensing arm of the fiber Michelson interferometer. The other arm, so called reference arm, was made of SMF. Faraday rotator mirrors (FRM) were spliced in the end of each interferometric arm account for polarization induced phase fading, which is a common scheme in fiber interferometric sensing systems. A similar hydrophone, with all the same structure except that the PCF was exchanged into SMF, was also fabrication to make the contrast. The narrowlinewidth and frequency-tunable optical fiber laser was used to achieve high accuracy optical interferometric measurement. Meanwhile, the phase generated carrier (PGC) modulation-demodulation scheme was adopted to interrogate the measurand signal. Experiment was done by using acoustic standing-wave test apparatus. Linearity characteristics of the two hydrophones were measured at frequency 100Hz, 500Hz, and 1000Hz, experimental results showed that the maximum error of the linearity was 10%, a little larger than the theoretical results. Pressure sensitivities of the PCF hydrophone and the SMF hydrophone were measured using a reference standard PZT hydrophone in the frequency range from 20 Hz to 1600 Hz, the measurement data showed that the sensitivity of the PCF hydrophone was about -162.8 dB re. rad/μPa, with a
Institute of Scientific and Technical Information of China (English)
林洪文; 马强; 唐文彦; 王军; 张晓琳
2014-01-01
为减小传统扭摆振动数学模型在大尺寸板状物体转动惯量测量中的误差，建立扭摆振动一般形式的非线性数学模型，利用弱非线性条件下平均值方法将其线性化获得扭摆振动线性化方程。导出转动惯量新的数学表达式并计算转动惯量，其结果的重复性误差减小、精度提高，实现转动惯量的精确测量。%Here,a general nonlinear mathematical model of torsional pendulum vibration was built to reduce the error of the traditional torsional pendulum vibration model in measuring moment of inertia for large scaled plate-like objects.The average value method under a weak nonlinear damping condition was adopted to linearize the nonlinear model to get a linear equation of torsional pendulum vibration.The new mathematical expression for the moment of inertia to be measured was deduced and calculated.The results obtained with the new model showed higher repeatability and accuracy in measurement of moment of inertia of large scaled plate-liked objects.
Magnetically levitated autoparametric broadband vibration energy harvesting
Kurmann, L.; Jia, Y.; Manoli, Y.; Woias, P.
2016-11-01
Some of the lingering challenges within the current paradigm of vibration energy harvesting (VEH) involve narrow operational frequency range and the inevitable non-resonant response from broadband noise excitations. Such VEHs are only suitable for limited applications with fixed sinusoidal vibration, and fail to capture a large spectrum of the real world vibration. Various arraying designs, frequency tuning schemes and nonlinear vibratory approaches have only yielded modest enhancements. To fundamentally address this, the paper proposes and explores the potentials in using highly nonlinear magnetic spring force to activate an autoparametric oscillator, in order to realize an inherently broadband resonant system. Analytical and numerical modelling illustrate that high spring nonlinearity derived from magnetic levitation helps to promote the 2:1 internal frequency matching required to activate parametric resonance. At the right internal parameters, the resulting system can intrinsically exhibit semi-resonant response regardless of the bandwidth of the input vibration, including broadband white noise excitation.
The case for optical interferometric polarimetry
Elias, Nicholas M; Schmitt, Henrique R; Jorgensen, Anders M; Ireland, Michael J; Perraut, Karine
2008-01-01
Within the last 10 years, long-baseline optical interferometry (LBOI) has benefited significantly from increased sensitivity, spatial resolution, and spectral resolution, e.g., measuring the diameters and asymmetries of single stars, imaging/fitting the orbits of multiple stars, modeling Be star disks, and modeling AGN nuclei. Similarly, polarimetry has also yielded excellent astrophysical results, e.g., characterizing the atmospheres and shells of red giants/supergiants, modeling the envelopes of AGB stars, studying the morphology of Be stars, and monitoring the short- and long- term behavior of AGNs. The next logical evolutionary step in instrumentation is to combine LBOI with polarimetry, which is called optical interferometric polarimetry (OIP). In other words, measurements of spatial coherence are performed simultaneously with measurements of coherence between orthogonal polarization states.
The 2010 Interferometric Imaging Beauty Contest
Malbet, Fabien; Duvert, Gilles; Lawson, Peter; Chiavassa, Andrea; Young, John; Baron, Fabien; Buscher, David; Rengaswamy, Sridharan; Kloppenborg, Brian; Vannier, Martin; Mugnier, Laurent
2010-01-01
We present the results of the fourth Optical/IR Interferometry Imaging Beauty Contest. The contest consists of blind imaging of test data sets derived from model sources and distributed in the OI-FITS format. The test data consists of spectral data sets on an object "observed" in the infrared with spectral resolution. There were 4 different algorithms competing this time: BSMEM the Bispectrum Maximum Entropy Method by Young, Baron & Buscher; RPR the Recursive Phase Reconstruction by Rengaswamy; SQUEEZE a Markov Chain Monte Carlo algorithm by Baron, Monnier & Kloppenborg; and, WISARD the Weak-phase Interferometric Sample Alternating Reconstruction Device by Vannier & Mugnier. The contest model image, the data delivered to the contestants and the rules are described as well as the results of the image reconstruction obtained by each method. These results are discussed as well as the strengths and limitations of each algorithm.
uvmcmcfit: Parametric models to interferometric data fitter
Bussmann, Shane; Leung, Tsz Kuk (Daisy); Conley, Alexander
2016-06-01
Uvmcmcfit fits parametric models to interferometric data. It is ideally suited to extract the maximum amount of information from marginally resolved observations with interferometers like the Atacama Large Millimeter Array (ALMA), Submillimeter Array (SMA), and Plateau de Bure Interferometer (PdBI). uvmcmcfit uses emcee (ascl:1303.002) to do Markov Chain Monte Carlo (MCMC) and can measure the goodness of fit from visibilities rather than deconvolved images, an advantage when there is strong gravitational lensing and in other situations. uvmcmcfit includes a pure-Python adaptation of Miriad’s (ascl:1106.007) uvmodel task to generate simulated visibilities given observed visibilities and a model image and a simple ray-tracing routine that allows it to account for both strongly lensed systems (where multiple images of the lensed galaxy are detected) and weakly lensed systems (where only a single image of the lensed galaxy is detected).
An interferometric view of hot star disks
Faes, Daniel Moser
2015-01-01
Optical long baseline interferometry was recently established as a technique capable of resolving stars and their circumstellar environments at the milliarcsecond (mas) resolution level. This high-resolution opens an entire new window to the study of astrophysical systems, providing information inaccessible by other techniques. Astrophysical disks are observed in a wide variety of systems, from galaxies up to planetary rings, commonly sharing similar physical processes. Two particular disk like systems are studied in the thesis: (i) B He-rich stars that exhibits magnetic fields in order of kG and that trap their winds in structures called magnetospheres; and (ii) Be stars, fast rotating stars that create circumstellar viscous disks. This study uses the interferometric technique to investigate both the photosphere proper and the circumstellar environment of these stars. The objective is to combine interferometry with other observational techniques (such as spectroscopy and polarimetry) to perform a complete an...
The 2012 interferometric imaging beauty contest
Baron, Fabien; Cotton, William D.; Lawson, Peter R.; Ridgway, Steve T.; Aarnio, Alicia; Monnier, John D.; Hofmann, Karl-Heinz; Schertl, Dieter; Weigelt, Gerd; Thiébaut, Eric; Soulez, Férréol; Mary, David; Millour, Florentin; Vannier, Martin; Young, John; Elias, Nicholas M.; Schmitt, Henrique R.; Rengaswamy, Sridharan
2012-07-01
We present the results of the fifth Interferometric Imaging Beauty Contest. The contest consists in blind imaging of test data sets derived from model sources and distributed in the OIFITS format. Two scenarios of imaging with CHARA/MIRC-6T were offered for reconstruction: imaging a T Tauri disc and imaging a spotted red supergiant. There were eight different teams competing this time: Monnier with the software package MACIM; Hofmann, Schertl and Weigelt with IRS; Thiebaut and Soulez with MiRA ; Young with BSMEM; Mary and Vannier with MIROIRS; Millour and Vannier with independent BSMEM and MiRA entries; Rengaswamy with an original method; and Elias with the radio-astronomy package CASA. The contest model images, the data delivered to the contestants and the rules are described as well as the results of the image reconstruction obtained by each method. These results are discussed as well as the strengths and limitations of each algorithm.
The 2012 Interferometric Imaging Beauty Contest
Baron, Fabien; Lawson, Peter R; Ridgway, Steve T; Aarnio, Alicia; Monnier, John D; Hofmann, Karl-Heinz; Schertl, Dieter; Weigelt, Gerd; Thiébaut, Eric; Soulez, Férréol; Mary, David; Millour, Florentin; Vannier, Martin; Young, John; Elias, Nicholas M; Schmitt, Henrique R; Rengaswamy, Sridharan
2012-01-01
We present the results of the fifth Interferometric Imaging Beauty Contest. The contest consists in blind imaging of test data sets derived from model sources and distributed in the OIFITS format. Two scenarios of imaging with CHARA/MIRC-6T were offered for reconstruction: imaging a T Tauri disc and imaging a spotted red supergiant. There were eight different teams competing this time: Monnier with the software package MACIM; Hofmann, Schertl and Weigelt with IRS; Thi\\'ebaut and Soulez with MiRA ; Young with BSMEM; Mary and Vannier with MIROIRS; Millour and Vannier with independent BSMEM and MiRA entries; Rengaswamy with an original method; and Elias with the radio-astronomy package CASA. The contest model images, the data delivered to the contestants and the rules are described as well as the results of the image reconstruction obtained by each method. These results are discussed as well as the strengths and limitations of each algorithm.
Fundamentals of interferometric gravitational wave detectors
Saulson, Peter R
2017-01-01
LIGO's recent discovery of gravitational waves was headline news around the world. Many people will want to understand more about what a gravitational wave is, how LIGO works, and how LIGO functions as a detector of gravitational waves.This book aims to communicate the basic logic of interferometric gravitational wave detectors to students who are new to the field. It assumes that the reader has a basic knowledge of physics, but no special familiarity with gravitational waves, with general relativity, or with the special techniques of experimental physics. All of the necessary ideas are developed in the book.The first edition was published in 1994. Since the book is aimed at explaining the physical ideas behind the design of LIGO, it stands the test of time. For the second edition, an Epilogue has been added; it brings the treatment of technical details up to date, and provides references that would allow a student to become proficient with today's designs.
Interferometric Approach to Probing Fast Scrambling
Yao, Norman Y; Swingle, Brian; Lukin, Mikhail D; Stamper-Kurn, Dan M; Moore, Joel E; Demler, Eugene A
2016-01-01
Out-of-time-order correlation functions provide a proxy for diagnosing chaos in quantum systems. We propose and analyze an interferometric scheme for their measurement, using only local quantum control and no reverse time evolution. Our approach utilizes a combination of Ramsey interferometry and the recently demonstrated ability to directly measure Renyi entropies. To implement our scheme, we present a pair of cold-atom-based experimental blueprints; moreover, we demonstrate that within these systems, one can naturally realize the transverse-field Sherrington-Kirkpatrick (TFSK) model, which exhibits certain similarities with fast scrambling black holes. We perform a detailed numerical study of scrambling in the TFSK model, observing an interesting interplay between the fast scrambling bound and the onset of spin-glass order.
Matched filtering with interferometric 21 cm experiments
White, Martin; Padmanabhan, Nikhil
2017-10-01
A new generation of interferometric instruments is emerging, which aims to use intensity mapping of redshifted 21 cm radiation to measure the large-scale structure of the Universe at z ≃ 1-2 over wide areas of the sky. While these instruments typically have limited angular resolution, they cover huge volumes and thus can be used to provide large samples of rare objects. In this paper we study how well such instruments could find spatially extended large-scale structures, such as cosmic voids, using a matched filter formalism. Such a formalism allows us to work in Fourier space, the natural space for interferometers, and to study the impact of finite u - v coverage, noise and foregrounds on our ability to recover voids. We find that in the absence of foregrounds, such instruments would provide enormous catalogs of voids, with high completeness, but that control of foregrounds is key to realizing this goal.
The Space Infrared Interferometric Telescope (SPIRIT)
Leisawitz, David T.
2014-01-01
The far-infrared astrophysics community is eager to follow up Spitzer and Herschel observations with sensitive, high-resolution imaging and spectroscopy, for such measurements are needed to understand merger-driven star formation and chemical enrichment in galaxies, star and planetary system formation, and the development and prevalence of water-bearing planets. The Space Infrared Interferometric Telescope (SPIRIT) is a wide field-of-view space-based spatio-spectral interferometer designed to operate in the 25 to 400 micron wavelength range. This talk will summarize the SPIRIT mission concept, with a focus on the science that motivates it and the technology that enables it. Without mentioning SPIRIT by name, the astrophysics community through the NASA Astrophysics Roadmap Committee recently recommended this mission as the first in a series of space-based interferometers. Data from a laboratory testbed interferometer will be used to illustrate how the spatio-spectral interferometry technique works.
Ruiz Delgado, Mari Carmen; Hernández, Víctor; Casado, Juan; López Navarrete, Juan T; Raimundo, Jean-Manuel; Blanchard, Philippe; Roncali, Jean
2003-08-04
fairly large intramolecular charge transfer both in polar and nonpolar solvents. Density functional theory (DFT) calculations have been carried out to assign the relevant electronic and vibrational features and to derive useful information about the molecular structure of these NLO-phores.
Nonlinear generalization of Den Hartog's equal-peak method
Habib, G.; Detroux, T.; Viguié, R.; Kerschen, G.
2015-02-01
This study addresses the mitigation of a nonlinear resonance of a mechanical system. In view of the narrow bandwidth of the classical linear tuned vibration absorber, a nonlinear absorber, termed the nonlinear tuned vibration absorber (NLTVA), is introduced in this paper. An unconventional aspect of the NLTVA is that the mathematical form of its restoring force is tailored according to the nonlinear restoring force of the primary system. The NLTVA parameters are then determined using a nonlinear generalization of Den Hartog's equal-peak method. The mitigation of the resonant vibrations of a Duffing oscillator is considered to illustrate the proposed developments.
Torsional Vibration Analysis of an FR Driveline System
Institute of Scientific and Technical Information of China (English)
任少云; 朱正礼; 张建武
2004-01-01
Towing tractor drivelines are lightly damped non-linear systems. Interactions between components can cause dynamic behavors such as gear gap impact in gear transmissions, shuffle and clonk phenomena in driveline. The torsional vibration of driveline has an important effect on grand engineering vehicle vibration and noise. Through analyzing torsional vibration equations of driveline, torsional vibration model of driveline is developed by using Matlab/Simulink software, Shuffle and clonk phenomena are observed in torsional vibration. The modeling method of analysizing driveline torsional vibration can be used to research and improve similar engineering vehicle driveline behavors.
Non-Interferometric Tomography of Phase Objects Using Spatial Light Modulators
Directory of Open Access Journals (Sweden)
Thanh Nguyen
2016-10-01
Full Text Available Quantitative 3D phase retrieval techniques are based on either interferometric techniques such as holography or noninterferometric intensity-based techniques such as the transport of intensity equation (TIE. Interferometric techniques are vibration-sensitive and often use a reference beam requiring complicated optical alignment. In this work we develop a simple, fast, and noninterferometric tomographic 3D phase retrieval technique based on the TIE which does not suffer from such drawbacks. The optical setup is a modified 4f TIE system which uses an SLM to replace the slow translation of the CCD required to record several diffraction patterns in a traditional TIE system. This novel TIE setup is suitable for dynamical events such as imaging biological processes. A rotating mechanical stage is constructed to obtain tomographic phase images of the object. The tomographic reconstruction algorithm is based on the Fourier slice theorem (backprojection algorithm which applies to objects with a small refractive index span. Simulation and experimental results are shown as part of this work. A graphical user interface is developed to perform the TIE tomographic reconstruction algorithm and to synchronize the captured intensities by the CCD, the phase patterns displayed on the SLM, and the Arduino controlled rotating stage assembly.
Energy Technology Data Exchange (ETDEWEB)
Fan, K-C [Department of Mechanical Engineering, National Taiwan University, 1, Sec. 4 Roosevelt Rd, Taipei, Taiwan (China); Chen, L-C [Graduate Institute of Automation Technology, National Taipei University of Technology, 1 Sec. 3 Chung-Hsiao East Rd, Taipei, 106, Taiwan (China); Lin, C-D [Department of Mechanical Engineering, National Taiwan University, 1, Sec. 4 Roosevelt Rd, Taipei, Taiwan (China); Chang, Calvin C [Industrial Technology Research Institute, Centre for Measurement Standards, 321 Sec. 2, Kuang Fu Rd, Hsinchu, Taiwan, 300 (China); Kuo, C-F [Industrial Technology Research Institute, Centre for Measurement Standards, 321 Sec. 2, Kuang Fu Rd, Hsinchu, Taiwan, 300 (China); Chou, J-T [Industrial Technology Research Institute, Centre for Measurement Standards, 321 Sec. 2, Kuang Fu Rd, Hsinchu, Taiwan, 300 (China)
2005-01-01
The main objective of this technical advance is to provide a single optical interferometric framework and methodology to be capable of delivering both nano-scale static and dynamic surface profilometry. Microscopic interferometry is a powerful technique for static and dynamic characterization of micro (opto) electromechanical systems (M (O) EMS). In view of this need, a microscopic prototype based on white-light stroboscopic interferometry and the white light vertical scanning principle, was developed to achieve dynamic full-field profilometry and characterization of MEMS devices. The system primarily consists of an optical microscope, on which a Mirau interferometric objective embedded with a piezoelectric vertical translator, a high-power LED light module with dual operation modes and light synchronizing electronics unit are integrated. A micro cantilever beam used in AFM was measured to verify the system capability in accurate characterization of dynamic behaviours of the device. The full-field second-mode vibration at a vibratory frequency of 68.60 kHz can be fully characterized and 3-5 nm of vertical measurement resolution as well as tens of micrometers of vertical measurement range can be easily achieved.
Electronic speckle pattern interferometric testing of JWST primary mirror segment assembly
Smith, Koby Z.; Chaney, David M.; Saif, Babak N.
2011-09-01
The James Webb Space Telescope (JWST) Primary Mirror Segment Assembly (PMSA) was required to meet NASA Technology Readiness Level (TRL) 06 requirements in the summer of 2006. These TRL06 requirements included verifying all mirror technology systems level readiness in simulated end-to-end operating conditions. In order to support the aggressive development and technology readiness schedule for the JWST Primary Mirror Segment Assembly (PMSA), a novel approach was implemented to verify the nanometer surface figure distortion effects on an in-process non-polished beryllium mirror surface. At the time that the TRL06 requirements needed to be met, a polished mirror segment had not yet been produced that could have utilized the baselined interferometric optical test station. The only JWST mirror segment available was a finished machined segment with an acid-etched optical surface. Therefore an Electronic Speckle Pattern Interferometer (ESPI) was used in coordination with additional metrology techniques to perform interferometric level optical testing on a non-optical surface. An accelerated, rigorous certification program was quickly developed for the ESPI to be used with the unfinished optical surface of the primary mirror segment. The ESPI was quickly implemented into the PMSA test program and optical testing was very successful in quantifying the nanometer level surface figure deformation changes in the PMSA due to assembly, thermal cycling, vibration, and acoustic testing. As a result of the successful testing, the PMSA passed all NASA TRL06 readiness requirements.
Panesar, Lucy
2007-01-01
Good Vibrations was a market research exercise conducted by Felicity (my alter-ego) and assistants to help develop marketing and packaging for an electro-therapeutic device (vibrator) used to treat hysteria and other female stress related disorders. It was a live art work commissioned by The Live Art Development Agency for East End Collaborations on 6th May 2007 and the South London Gallery for Bonkersfest on 2nd June 2007.
Gupta, Amita; Singh, Ranvir; Ahmad, Amir; Kumar, Mahesh
2003-10-01
Today, vibration sensors with low and medium sensitivities are in great demand. Their applications include robotics, navigation, machine vibration monitoring, isolation of precision equipment & activation of safety systems e.g. airbags in automobiles. Vibration sensors have been developed at SSPL, using silicon micromachining to sense vibrations in a system in the 30 - 200 Hz frequency band. The sensing element in the silicon vibration sensor is a seismic mass suspended by thin silicon hinges mounted on a metallized glass plate forming a parallel plate capacitor. The movement of the seismic mass along the vertical axis is monitored to sense vibrations. This is obtained by measuring the change in capacitance. The movable plate of the parallel plate capacitor is formed by a block connected to a surrounding frame by four cantilever beams located on sides or corners of the seismic mass. This element is fabricated by silicon micromachining. Several sensors in the chip sizes 1.6 cm x 1.6 cm, 1 cm x 1 cm and 0.7 cm x 0.7 cm have been fabricated. Work done on these sensors, techniques used in processing and silicon to glass bonding are presented in the paper. Performance evaluation of these sensors is also discussed.
Distributed fiber optic interferometric geophone system based on draw tower gratings
Xu, Ruquan; Guo, Huiyong; Liang, Lei
2017-09-01
A distributed fiber optic interferometric geophone array based on draw tower grating (DTG) array is proposed. The DTG geophone array is made by the DTG array fabricated based on a near-contact exposure through a phase mask during the fiber drawing process. A distributed sensing system with 96 identical DTGs in an equal separation of 20 m and an unbalanced Michelson interferometer for vibration measurement has been experimentally validated compared with a moving-coil geophone. The experimental results indicate that the sensing system can linearly demodulate the phase shift. Compared with the moving coil geophone, the fiber optic sensing system based on DTG has higher signal-to-noise ratio at low frequency.
Peña Arellano, Fabián Erasmo; Sekiguchi, Takanori; Fujii, Yoshinori; Takahashi, Ryutaro; Barton, Mark; Hirata, Naoatsu; Shoda, Ayaka; van Heijningen, Joris; Flaminio, Raffaele; DeSalvo, Riccardo; Okutumi, Koki; Akutsu, Tomotada; Aso, Yoichi; Ishizaki, Hideharu; Ohishi, Naoko; Yamamoto, Kazuhiro; Uchiyama, Takashi; Miyakawa, Osamu; Kamiizumi, Masahiro; Takamori, Akiteru; Majorana, Ettore; Agatsuma, Kazuhiro; Hennes, Eric; van den Brand, Jo; Bertolini, Alessandro
2016-03-01
KAGRA is a cryogenic interferometric gravitational wave detector currently under construction in the Kamioka mine in Japan. Besides the cryogenic test masses, KAGRA will also rely on room temperature optics which will hang at the bottom of vibration isolation chains. The payload of each chain comprises an optic, a system to align it, and an active feedback system to damp the resonant motion of the suspension itself. This article describes the performance of a payload prototype that was assembled and tested in vacuum at the TAMA300 site at the NAOJ in Mitaka, Tokyo. We describe the mechanical components of the payload prototype and their functionality. A description of the active components of the feedback system and their capabilities is also given. The performance of the active system is illustrated by measuring the quality factors of some of the resonances of the suspension. Finally, the alignment capabilities offered by the payload are reported.
Weighted-elastic-wave interferometric imaging of microseismic source location
Li, Lei; Chen, Hao; Wang, Xiu-Ming
2015-06-01
Knowledge of the locations of seismic sources is critical for microseismic monitoring. Time-window-based elastic wave interferometric imaging and weighted-elastic-wave (WEW) interferometric imaging are proposed and used to locate modeled microseismic sources. The proposed method improves the precision and eliminates artifacts in location profiles. Numerical experiments based on a horizontally layered isotropic medium have shown that the method offers the following advantages: It can deal with low-SNR microseismic data with velocity perturbations as well as relatively sparse receivers and still maintain relatively high precision despite the errors in the velocity model. Furthermore, it is more efficient than conventional traveltime inversion methods because interferometric imaging does not require traveltime picking. Numerical results using a 2D fault model have also suggested that the weighted-elastic-wave interferometric imaging can locate multiple sources with higher location precision than the time-reverse imaging method.
Benefits and limitations of imaging multiples: Interferometric and resonant migration
Guo, Bowen
2015-07-01
The benefits and limitations of imaging multiples are reviewed for interferometric migration and resonant migration. Synthetic and field data examples are used to characterize the effectiveness of the methods.
Spectroscopic and Interferometric Measurements of Nine K Giant Stars
Baines, Ellyn K; Guenther, Eike W; Hatzes, Artie P; Hrudkovu, Marie; van Belle, Gerard T
2016-01-01
We present spectroscopic and interferometric measurements for a sample of nine K giant stars. These targets are of particular interest because they are slated for stellar oscillation observations. Our improved parameters will directly translate into reduced errors in the final masses for these stars when interferometric radii and asteroseismic densities are combined. Here we determine each star's limb-darkened angular diameter, physical radius, luminosity, bolometric flux, effective temperature, surface gravity, metallicity, and mass. When we compare our interferometric and spectroscopic results, we find no systematic offsets in the diameters and the values generally agree within the errors. Our interferometric temperatures for seven of the nine stars are hotter than those determined from spectroscopy with an average difference of about 380 K.
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.
Strongly nonlinear oscillators analytical solutions
Cveticanin, Livija
2014-01-01
This book provides the presentation of the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. The book presents the original author’s method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter is considered. Special attention is given to the one and two mass oscillatory systems with two-degrees-of-freedom. The criteria for the deterministic chaos in ideal and non-ideal pure nonlinear oscillators are derived analytically. The method for suppressing chaos is developed. Important problems are discussed in didactic exercises. The book is self-consistent and suitable as a textbook for students and also for profess...
Laser frequency stabilization based on Sagnac interferometric spectroscopy
Institute of Scientific and Technical Information of China (English)
Hui Yan; Guoqing Yang; Jin Wang; Mingsheng Zhan
2008-01-01
@@ A simple method based on Sagnac interferometric spectroscopy (SIS) is applied for frequency stabilization of diode lasers. Sagnac interferometric spectra of rubidium vapor are investigated both theoretically and experimentally. The interference signal at the output of the Sagnac interferometer displays a sharp dispersion feature near the atomic resonance. This dispersion curve is used as the feedback error signal to stabilize the laser frequency. Linewidth of a diode laser is stabilized down to 1 MHz by this modulation-free method.
Interferometric SAR imaging by transmitting stepped frequency chaotic noise signals
Zhang, Yunhua; Gu, Xiang; Zhai, Wenshuai; Dong, Xiao; Shi, Xiaojin; Kang, Xueyan
2015-10-01
Noise radar has been applied in many fields since it was proposed more than 50 years ago. However, it has not been applied to interferometric SAR imaging yet as far as we know. This paper introduces our recent work on interferometric noise radar. An interferometric SAR system was developed which can transmit both chirp signal and chaotic noise signal (CNS) at multiple carrier frequencies. An airborne experiment with this system by transmitting both signals was carried out, and the data were processed to show the capability of interferometric SAR imaging with CNS. The results shows that although the interferometric phase quality of CNS is degraded due to the signal to noise ratio (SNR) is lower compared with that of chirp signal, we still can get satisfied DEM after multi-looking processing. Another work of this paper is to apply compressed sensing (CS) theory to the interferometric SAR imaging with CNS. The CS theory states that if a signal is sparse, then it can be accurately reconstructed with much less sampled data than that regularly required according to Nyquist Sampling Theory. To form a structured random matrix, if the transmitted signal is of fixed waveform, then random subsampling is needed. However, if the transmitted signal is of random waveform, then only uniform subsampling is needed. This is another advantage of noise signal. Both the interferometric phase images and the DEMs by regular method and by CS method are processed with results compared. It is shown that the degradation of interferometric phases due to subsampling is larger than that of amplitude image.
Institute of Scientific and Technical Information of China (English)
文成秀; 赵长宽; 闻邦椿
2001-01-01
The characteristics of motion in nonlinear vibration mechanismwith piece-wise linearity were analyzed by means of computer simulation and Poincare method. Bifurcation of periodic motions and chaos in the system were studied when the angular frequencies increase from change 30rad/s to 100rad/s by steps 0.1rad/s. There are sudden changes from P-1 to P-3,inverse bifurcation from P-2 to P-1 and sudden change from P-3 to P-1 except that double-periodic bifurcation exist. The global and part bifurcation figure and Poincare mapping figure of chaos and the time-history curves of 3 periodic motions were given.%利用计算机仿真及Poincare映射方法研究不对称分段线性非线性机械系统的运动学特征.研究了外激振力角频率从30rad/s以步长0.1rad/s增加到100rad/s时,系统的周期运动分岔和混沌运动.发现其中除了存在倍周期分岔外,还存在P-1到P-3的突变、P-2到P-1的倒分岔和P-3到P-1的突变.给出了全局分岔图、局部分岔图、混沌运动的Poincare映射及3种周期运动的时间历程曲线和相平面图.对于设计此类机械系统具有指导意义.
Institute of Scientific and Technical Information of China (English)
丁卫君; 聂国华; 王榕
2012-01-01
This paper deals with non-linear free vibration of a single-layer reticulated imperfect shallow spherical shell formed by beam members placed in two orthogonal directions based on an equivalent continuum model. Using both the dynamic equilibrium equation and the compatibility equation in terms of deflection and force function, a characteristic relation between the amplitude and frequency of a clamped or hinged shell was derived by asymptotic iteration method. Numerical examples were given to illustrate the effects of boundary constraints and impaction factor on the characteristic relation. Meanwhile, the present results for the fundamental frequency were compared with data by finite element method using ANSYS code. The results show that the present continuum model has enough precision in computation.%基于梁元正交布置的单层网壳的等效连续化模型,研究了含几何初始缺陷的网格扁球壳非线性自由振动问题.基于用挠度和力函数表示的非线性动力平衡方程和变形协调方程,针对简支和固支两种约束条件,采用渐近迭代法得到了网格扁球壳自由振动的非线性幅-频特征关系.通过数值计算分析了边界约束和缺陷因子等对网壳幅-频关系的影响.同时,对于结构基频,理论结果与基于ANSYS的有限元数值结果的比较,验证了网壳等效连续化模型的精度.
Naturally stable Sagnac-Michelson nonlinear interferometer
Lukens, Joseph M.; Peters, Nicholas A.; Pooser, Raphael C.
2016-12-01
Interferometers measure a wide variety of dynamic processes by converting a phase change into an intensity change. Nonlinear interferometers, making use of nonlinear media in lieu of beamsplitters, promise substantial improvement in the quest to reach the ultimate sensitivity limits. Here we demonstrate a new nonlinear interferometer utilizing a single parametric amplifier for mode mixing---conceptually, a nonlinear version of the conventional Michelson interferometer with its arms collapsed together. We observe up to 99.9\\% interference visibility and find evidence for noise reduction based on phase-sensitive gain. Our configuration utilizes fewer components than previous demonstrations and requires no active stabilization, offering new capabilities for practical nonlinear interferometric-based sensors.
Distributed Fiber-Optic Sensors for Vibration Detection.
Liu, Xin; Jin, Baoquan; Bai, Qing; Wang, Yu; Wang, Dong; Wang, Yuncai
2016-07-26
Distributed fiber-optic vibration sensors receive extensive investigation and play a significant role in the sensor panorama. Optical parameters such as light intensity, phase, polarization state, or light frequency will change when external vibration is applied on the sensing fiber. In this paper, various technologies of distributed fiber-optic vibration sensing are reviewed, from interferometric sensing technology, such as Sagnac, Mach-Zehnder, and Michelson, to backscattering-based sensing technology, such as phase-sensitive optical time domain reflectometer, polarization-optical time domain reflectometer, optical frequency domain reflectometer, as well as some combinations of interferometric and backscattering-based techniques. Their operation principles are presented and recent research efforts are also included. Finally, the applications of distributed fiber-optic vibration sensors are summarized, which mainly include structural health monitoring and perimeter security, etc. Overall, distributed fiber-optic vibration sensors possess the advantages of large-scale monitoring, good concealment, excellent flexibility, and immunity to electromagnetic interference, and thus show considerable potential for a variety of practical applications.
Zhu, Y; Volkov, V V; De Graef, M
2001-01-01
We present our observations of field- and orientation-dependence of magnetic domains and their reversal nucleation at grain boundaries in polycrystalline Nd2Fe14B, using Fresnel- and Foucault-Lorentz microscopy. The local magnetization associated with the domain and domain-wall in Nd2Fe14B and in precipitated Fe particles was mapped using an interferometric holography as well as a novel non-interferometric method based on the 'transport of intensity' equation.
Institute of Scientific and Technical Information of China (English)
王技德; 张国渊
2012-01-01
Considering the tilt of a seal ring, the transient vibration response analysis model of a non--contact mechanical seal was presented. The model was consisted of transient Reynolds equation, motion equation and equation for solving the second--order nonlinear dynamic coefficients of the seal. With Euler method, the characteristic parameters of the transient vibration response were obtained, which included the axial vibration displacements and the angle--swing of the static ring. 14 nonlinear forces and 14 nonlinear overturning moment dynamic coefficients for the non--contact mechanical seal were calculated. The results show that the influences of the damping effects of the sealed fluid between the seal gaps on the axial vibration displacements and the angle--swing are linear. The film thickness distribution changes with the axial vibration of seal, which will lead to static ring swing, and the swing can also cause the axial vibration of the seal.%建立了考虑倾斜情况的弹性补偿单元支撑的非接触机械密封瞬态振动响应分析模型,该模型包括了瞬态Reynolds方程、运动方程以及二阶非线性动特性系数求解方程等。采用Euler法求解获得了非接触机械密封在轴向振动位移和静环倾角随时间变化时的瞬态振动响应特性。计算得到瞬态油膜力作用下的密封轴向力和倾覆力矩相关的14个动特性系数。结果表明：密封间隙内流体阻尼对密封副和摆动的影响是线性的;密封副瞬态振动影响油膜厚度分布,从而引起油膜压力分布发生变化,结果导致密封环发生摆动;密封副摆动同样也会引起密封轴向振动。
Acoustic vs Interferometric Measurements of Lightning
Arechiga, R. O.; Erives, H.; Sonnenfeld, R. G.; Stanley, M. A.; Rison, W.; Thomas, R. J.; Edens, H. E.; Lapierre, J. L.; Stock, M.; Jensen, D.; Morris, K.
2015-12-01
During the summer of 2015 we acquired acoustic and RF data on severalflashes from thunderstorms over Fort Morgan CO. and Langmuir Laboratoryin the Magdalena mountains of central New Mexico. The acoustic arrayswere located at a distance of roughly 150 m from the interferometers.Lightning mapping array and slow antenna data were also obtained. Theacoustic arrays consist of arrays of five audio-range and six infrasoundmicrophones operating at 50 KHz and 1 KHz respectively. The lightninginterferometer at Fort Morgan CO. consists of three flat-plate, 13" diameterantennas at the vertices of an equilateral 50 m per side triangle. Theinterferometer at Langmuir Laboratory consists of three 13" dishes separatedby about 15 m. Both interferometers, operating at 180 Megasamples persecond, use the analysis software and digitizer hardware pioneered byStanley, Stock et al. The high data rate allows for excellent spatialresolution of high speed (and typically high current) processes such asK-changes, return strokes and dart-leaders. In previous studies, we haveshown the usefulness of acoustic recordings to locate thunder sources aswell as infrasound pulses from lightning. This work will present acomparison of Acoustic and Interferometric measurements from lightning,using some interesting flashes, including a positive cloud to ground,that occurred in these campaigns.
The 2016 interferometric imaging beauty contest
Sanchez-Bermudez, J.; Thiébaut, E.; Hofmann, K.-H.; Heininger, M.; Schertl, D.; Weigelt, G.; Millour, F.; Schutz, A.; Ferrari, A.; Vannier, M.; Mary, D.; Young, J.
2016-08-01
Image reconstruction in optical interferometry has gained considerable importance for astrophysical studies during the last decade. This has been mainly due to improvements in the imaging capabilities of existing interferometers and the expectation of new facilities in the coming years. However, despite the advances made so far, image synthesis in optical interferometry is still an open field of research. Since 2004, the community has organized a biennial contest to formally test the different methods and algorithms for image reconstruction. In 2016, we celebrated the 7th edition of the "Interferometric Imaging Beauty Contest". This initiative represented an open call to participate in the reconstruction of a selected set of simulated targets with a wavelength-dependent morphology as they could be observed by the 2nd generation of VLTI instruments. This contest represents a unique opportunity to benchmark, in a systematic way, the current advances and limitations in the field, as well as to discuss possible future approaches. In this contribution, we summarize: (a) the rules of the 2016 contest; (b) the different data sets used and the selection procedure; (c) the methods and results obtained by each one of the participants; and (d) the metric used to select the best reconstructed images. Finally, we named Karl-Heinz Hofmann and the group of the Max-Planck-Institut f ur Radioastronomie as winners of this edition of the contest.
Airborne Radar Interferometric Repeat-Pass Processing
Hensley, Scott; Michel, Thierry R.; Jones, Cathleen E.; Muellerschoen, Ronald J.; Chapman, Bruce D.; Fore, Alexander; Simard, Marc; Zebker, Howard A.
2011-01-01
Earth science research often requires crustal deformation measurements at a variety of time scales, from seconds to decades. Although satellites have been used for repeat-track interferometric (RTI) synthetic-aperture-radar (SAR) mapping for close to 20 years, RTI is much more difficult to implement from an airborne platform owing to the irregular trajectory of the aircraft compared with microwave imaging radar wavelengths. Two basic requirements for robust airborne repeat-pass radar interferometry include the ability to fly the platform to a desired trajectory within a narrow tube and the ability to have the radar beam pointed in a desired direction to a fraction of a beam width. Uninhabited Aerial Vehicle Synthetic Aperture Radar (UAVSAR) is equipped with a precision auto pilot developed by NASA Dryden that allows the platform, a Gulfstream III, to nominally fly within a 5 m diameter tube and with an electronically scanned antenna to position the radar beam to a fraction of a beam width based on INU (inertial navigation unit) attitude angle measurements.
An interferometric view of binary stars
Boffin, Henri M J
2016-01-01
The study of binary stars is critical to apprehend many of the most interesting classes of stars. Moreover, quite often, the study of stars in binary systems is our only mean to constrain stellar properties, such as masses and radii. Unfortunately, a great fraction of the most interesting binaries are so compact that they can only be apprehended by high-resolution techniques, mostly by interferometry. I present some results highlighting the use of interferometry in the study of binary stars, from finding companions and deriving orbits, determining the mass and radius of stars, to studying mass transfer in symbiotic stars, and tackling luminous blue variables. In particular, I show how interferometric studies using the PIONIER instrument have allowed us to confirm a dichotomy within symbiotic stars, obtain masses of stars with a precision better than 1%, and help us find a new Eta Carinae-like system. I will also illustrate the benefits for the study of binary stars one would get from upgrading the VLT Interfe...
Calibration Errors in Interferometric Radio Polarimetry
Hales, Christopher A.
2017-08-01
Residual calibration errors are difficult to predict in interferometric radio polarimetry because they depend on the observational calibration strategy employed, encompassing the Stokes vector of the calibrator and parallactic angle coverage. This work presents analytic derivations and simulations that enable examination of residual on-axis instrumental leakage and position-angle errors for a suite of calibration strategies. The focus is on arrays comprising alt-azimuth antennas with common feeds over which parallactic angle is approximately uniform. The results indicate that calibration schemes requiring parallactic angle coverage in the linear feed basis (e.g., the Atacama Large Millimeter/submillimeter Array) need only observe over 30°, beyond which no significant improvements in calibration accuracy are obtained. In the circular feed basis (e.g., the Very Large Array above 1 GHz), 30° is also appropriate when the Stokes vector of the leakage calibrator is known a priori, but this rises to 90° when the Stokes vector is unknown. These findings illustrate and quantify concepts that were previously obscure rules of thumb.
Interferometric phase reconstruction using simplified coherence network
Zhang, Kui; Song, Ruiqing; Wang, Hui; Wu, Di; Wang, Hua
2016-09-01
Interferometric time-series analysis techniques, which extend the traditional differential radar interferometry, have demonstrated a strong capability for monitoring ground surface displacement. Such techniques are able to obtain the temporal evolution of ground deformation within millimeter accuracy by using a stack of synthetic aperture radar (SAR) images. In order to minimize decorrelation between stacked SAR images, the phase reconstruction technique has been developed recently. The main idea of this technique is to reform phase observations along a SAR stack by taking advantage of a maximum likelihood estimator which is defined on the coherence matrix estimated from each target. However, the phase value of a coherence matrix element might be considerably biased when its corresponding coherence is low. In this case, it will turn to an outlying sample affecting the corresponding phase reconstruction process. In order to avoid this problem, a new approach is developed in this paper. This approach considers a coherence matrix element to be an arc in a network. A so-called simplified coherence network (SCN) is constructed to decrease the negative impact of outlying samples. Moreover, a pointed iterative strategy is designed to resolve the transformed phase reconstruction problem defined on a SCN. For validation purposes, the proposed method is applied to 29 real SAR images. The results demonstrate that the proposed method has an excellent computational efficiency and could obtain more reliable phase reconstruction solutions compared to the traditional method using phase triangulation algorithm.
Acoustic vibration sensor based on nonadiabatic tapered fibers.
Xu, Ben; Li, Yi; Sun, Miao; Zhang, Zhen-Wei; Dong, Xin-Yong; Zhang, Zai-Xuan; Jin, Shang-Zhong
2012-11-15
A simple and low-cost vibration sensor based on single-mode nonadiabatic fiber tapers is proposed and demonstrated. The environmental vibrations can be detected by demodulating the transmission loss of the nonadiabatic fiber taper. Theoretical simulations show that the transmission loss is related to the microbending of the fiber taper induced by vibrations. Unlike interferometric sensors, this vibration sensor does not need any feedback loop to control the quadrature point to obtain a stable performance. In addition, it has no requirement for the coherence of the light source and is insensitive to temperature changes. Experimental results show that this sensing system has a wide frequency response range from a few hertz to tens of kilohertz with the maximal signal to noise ratio up to 73 dB.
DYNAMIC PARAMETERS ESTIMATION OF INTERFEROMETRIC SIGNALS BASED ON SEQUENTIAL MONTE CARLO METHOD
Directory of Open Access Journals (Sweden)
M. A. Volynsky
2014-05-01
Full Text Available The paper deals with sequential Monte Carlo method applied to problem of interferometric signals parameters estimation. The method is based on the statistical approximation of the posterior probability density distribution of parameters. Detailed description of the algorithm is given. The possibility of using the residual minimum between prediction and observation as a criterion for the selection of multitude elements generated at each algorithm step is shown. Analysis of input parameters influence on performance of the algorithm has been conducted. It was found that the standard deviation of the amplitude estimation error for typical signals is about 10% of the maximum amplitude value. The phase estimation error was shown to have a normal distribution. Analysis of the algorithm characteristics depending on input parameters is done. In particular, the influence analysis for a number of selected vectors of parameters on evaluation results is carried out. On the basis of simulation results for the considered class of signals, it is recommended to select 30% of the generated vectors number. The increase of the generated vectors number over 150 does not give significant improvement of the obtained estimates quality. The sequential Monte Carlo method is recommended for usage in dynamic processing of interferometric signals for the cases when high immunity is required to non-linear changes of signal parameters and influence of random noise.
DEFF Research Database (Denmark)
Morrison, Ann; Knudsen, L.; Andersen, Hans Jørgen
2012-01-01
In this paper we describe a field study conducted with a wearable vibration belt where we test to determine the vibration intensity sensitivity ranges on a large diverse group of participants with evenly distributed ages and...... lab studies in that we found a decreased detection rate in busy environments. Here we test with a much larger sample and age range, and contribute with the first vibration sensitivity testing outside the lab in an urban public...
A magnetically sprung vibration harvester
Constantinou, P.; Mellor, P. H.; Wilcox, P. D.
2010-04-01
The use of energy harvesting systems is becoming a more prominent research topic in supplying energy to wireless sensor nodes. The paper will present an analytical 'toolbox' for designing and modeling a vibration energy harvester where the moving mass is suspended magnetically. Calculations from the presented model and measurements from a prototype are compared, and the presence of system non-linearities is shown and discussed. The use of the magnetic suspension and its equivalent hardening spring suspension leads to the system's non-linearity, demonstrating a broad band response and 'jump' phenomenon characteristic. The benefits of these are discussed and the system's performance is compared with those from literature, showing similarity.
Vibrations and stability of complex beam systems
Stojanović, Vladimir
2015-01-01
This book reports on solved problems concerning vibrations and stability of complex beam systems. The complexity of a system is considered from two points of view: the complexity originating from the nature of the structure, in the case of two or more elastically connected beams; and the complexity derived from the dynamic behavior of the system, in the case of a damaged single beam, resulting from the harm done to its simple structure. Furthermore, the book describes the analytical derivation of equations of two or more elastically connected beams, using four different theories (Euler, Rayleigh, Timoshenko and Reddy-Bickford). It also reports on a new, improved p-version of the finite element method for geometrically nonlinear vibrations. The new method provides more accurate approximations of solutions, while also allowing us to analyze geometrically nonlinear vibrations. The book describes the appearance of longitudinal vibrations of damaged clamped-clamped beams as a result of discontinuity (damage). It...