Hard duffing-type vibration isolator with combined Coulomb and viscous damping
TL;DR: In this article, the steady state, harmonic response of a vibration isolation system with a cubic, hard non-linear restoring force and combined Coulomb and viscous damping is presented by using the method of harmonic balance.
Abstract: The steady-state, harmonic response of a vibration isolation system with a cubic, hard non-linear restoring force and combined Coulomb and viscous damping is presented. The results have been obtained by using the method of harmonic balance. It has been assumed that the motion is continuous without any stop. An anomalous jump in the response, similar to the one obtained in earlier studies on certain soft systems, is observed when the isolation system is subjected to a base excitation. Linear stability analysis is carried out to determine the status of the anomalous jump. The effect of the damping parameters on the jump in the response is investigated. Transmissibility curves are plotted for various parameter values to study the performance characteristics. The obtained results extend the previous works of Den Hartog and Ruzicka who considered a linear restoring element.
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TL;DR: In this paper, the authors investigated the dynamic behavior of a nonlinear isolator supporting a lumped mass by modelling the dynamic system as a single-degree-of-freedom system.
336 citations
TL;DR: In this article, the Harmonic Balance Method (HBM) is applied to investigate the performance of nonlinear passive vibration isolators with cubic nonlinear damping and linear damping.
Abstract: In the present study, Harmonic Balance Method (HBM) is applied to investigate the performance of passive vibration isolators with cubic nonlinear damping. The results reveal that introducing either cubic nonlinear damping or linear damping could significantly reduce both the displacement transmissibility and the force transmissibility of the isolators over the resonance region. However, at the non-resonance region where frequency is lower than the resonant frequency, both the linear damping and the cubic nonlinear damping have almost no effect on the isolators. At the non-resonance region with higher frequency, increasing the linear damping has almost no effects on the displacement transmissibility but could raise the force transmissibility. In addition, the influence of the cubic nonlinear damping on the isolators is dependent on the type of the disturbing force. If the strength of the disturbing force is constant and independent of the excitation frequency, then the effect of cubic nonlinear damping on both the force and displacement transmissibility would be negligible. But, when the strength of the disturbing force is dependent of the excitation frequency, increasing the cubic nonlinear damping could slightly reduce the relative displacement transmissibility and increase the absolute displacement transmissibility but could significantly increase the force transmissibility. These conclusions are of significant importance in the analysis and design of nonlinear passive vibration isolators.
117 citations
TL;DR: In this article, the authors present a nonlinear dynamic model of a rubber vibration isolator, where the quasistatic and dynamic motion influences on the force response are investigated within the time and frequency domain.
Abstract: In presenting a nonlinear dynamic model of a rubber vibration isolator, the quasistatic and dynamic motion influences on the force response are investigated within the time and frequency domain. It is found that the dynamic stiffness at the frequency of a harmonic displacement excitation, superimposed upon the long term isolator response, is strongly dependent on static precompression, dynamic amplitude and frequency. The problems of simultaneously modelling the elastic, viscoelastic and friction forces are removed by additively splitting them, modelling the elastic force response by a nonlinear, shape factor based approach, displaying results that agree with those of a neo-Hookean hyperelastic isolator at a long term precompression. The viscoelastic force is modeled by a fractional derivative element, while the friction force governs from a generalized friction element displaying a smoothed Coulomb force. A harmonic displacement excitation is shown to result in a force response containing the excitation frequency and its every other higher-order harmonic, while using a linearized elastic force response model, whereas all higher-order harmonics are present for the fully nonlinear case. It is furthermore found that the dynamic stiffness magnitude increases with static precompression and frequency, while decreasing with dynamic excitation amplitude-eventually increasing at the highest amplitudes due to nonlinear elastic effects-with its loss angle displaying a maximum at an intermediate amplitude. Finally, the dynamic stiffness at a static precompression, using a linearized elastic force response model, is shown to agree with the fully nonlinear model except at the highest dynamic amplitudes.
81 citations
TL;DR: The present work provides a comprehensive review on the recent advances in nonlinear vibration energy harvesting and vibration suppression technologies and in particular, the latest developments in multifunctional hybrid technologies are proposed.
Abstract: Limited by the structure, the high-efficiency vibration energy harvesting and vibration suppression have always been a theoretical bottleneck and technical challenge in this field. The nonlinear design of the new vibration structure is an indispensable link in the development of vibration energy harvesting and vibration suppression technologies. Nonlinear technologies not only have the potential to improve the efficiency of the energy harvesters by increasing the useful frequency bandwidth and output power but also have the potential to improve the efficiency of vibration suppressors by reducing the transmission rate and transfer energy. Nonlinear vibration energy harvesting and vibration suppression technologies have been salient topics in the literature and have attracted widespread attention from researchers. The present work provides a comprehensive review on the recent advances in nonlinear vibration energy harvesting and vibration suppression technologies. In particular, the latest developments in multifunctional hybrid technologies are proposed. Various key aspects to improve the performance of nonlinear vibration energy harvesting and vibration suppression systems are discussed, including implementations and configuration designs, nonlinear dynamics mechanisms, various optimizations, multifunctional hybrid, application prospects, and future outlooks.
77 citations
TL;DR: In this paper, the primary resonance response of an asymmetric Duffing oscillator with no linear stiffness term and with hardening characteristic is investigated, and an approximate solution corresponding to the steady-state response is sought by applying the harmonic balance method.
Abstract: The primary resonance response of an asymmetric Duffing oscillator with no linear stiffness term and with hardening characteristic is investigated in this paper. An approximate solution corresponding to the steady-state response is sought by applying the harmonic balance method. Its stability is also studied. It is found that different shapes of frequency–response curves can exist. Multiple-valued solutions, indicating the occurrence of jump phenomena, are observed analytically and confirmed numerically. The influence of the system parameters on the primary resonance response is also examined.
65 citations
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Book•
01 Jan 1977
TL;DR: In this article, a new edition has been expanded to contain an introduction to areas of current importance such as bifurcation, structural stability, and chaotic behavior, including linearization, perturbation theory, subharmonics, stability and limit cycles.
Abstract: This new edition has been expanded to contain an introduction to areas of current importance such as bifurcation, structural stability and chaotic behavior Other topics include linearization, perturbation theory, subharmonics, stability, the existence of limit cycles, and Poincare maps The text is concerned with practical applications and includes over 400 examples and exercises"
1,566 citations
TL;DR: In this paper, the method of equivalent linearization of Kryloff and Bogoliubov is generalized to the case of nonlinear dynamic systems with random excitation, applied to a variety of problems, and the results are compared with exact solutions of the Fokker-Planck equation.
Abstract: The method of equivalent linearization of Kryloff and Bogoliubov is generalized to the case of nonlinear dynamic systems with random excitation. The method is applied to a variety of problems, and the results are compared with exact solutions of the Fokker‐Planck equation for those cases where the Fokker‐Planck technique may be applied. Alternate approaches to the problem are discussed, including the characteristic function method of Rice.
600 citations
TL;DR: In this paper, the response of a single degree of freedom system with dry friction is considered and the asymptotic stability of the steady state motions and some transient behaviors are also determined.
262 citations
TL;DR: In this article, the response of a single degree of freedom spring-mass system with viscous and Coulomb friction, with harmonic base excitation, was determined, and closed form analytical solutions of the equation of motion were found for two cases: (a) continuous motion of the mass and (b) motion of mass with two stops per cycle.
123 citations
TL;DR: In this paper, the steady state relative motion of two masses with dry (Coulomb) friction contact is investigated, where the bodies are assumed to have the same mass and stiffness and are subjected to harmonic excitation.
99 citations