Response and stability of SDOF viscoelastic system under wideband noise excitations

Ling, Quan; Jin, Xiaoling; Huang, Zhongdong

doi:10.1016/j.jfranklin.2011.05.019

Cited by 31 publications

(12 citation statements)

References 26 publications

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“…The phenomenon known as viscoelasticity is defined as a solid material exhibiting viscous and elastic behaviour similar to liquids [1][2][3][4][5][6][7][8]. Over the last few decades, the study of viscoelasticity has widely attracted the interest of physicists, mathematicians and engineers [1,4,[9][10][11][12][13][14][15][16][17][18][19]. For viscoelastic bodies, creep tests and relaxation tests have shown that the stress depends not only on the instantaneous strain but also on the time history of the strain [2,[20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Stationary probability densities of generalized Maxwell-type viscoelastic systems under combined harmonic and Gaussian white noise excitations

Wang

2020

J Braz. Soc. Mech. Sci. Eng.

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Viscoelasticity has been widely studied over the past few decades as a combination of the viscous effects of energy dissipation and the elastic effects of energy storage. As an application, viscoelastic dampers are commonly used to suppress the dynamic behaviour of structures. However, in an actual physical environment, it is difficult to explore the stationary probability densities of random responses for viscoelastic systems. For this purpose, we present a numerical method to investigate the dynamic behaviour of a generalized Maxwell-type viscoelastic system under harmonic and Gaussian white noise excitations. Using approximate equivalent and stochastic averaging, we establish an averaged Itô differential equation for the amplitude of the system. For primary external resonance, we solve the reduced Fokker-Planck-Kolmogorov equation by using the successive over-relaxation technique combined with a finite difference method. Through Monte Carlo simulations, we verify the applicability, accuracy and efficiency of the proposed methodology and demonstrate that viscoelasticity has a significant impact on the dynamic behaviour of the viscoelastic systems. This work reveals the remarkable influences of viscoelasticity, excitation intensities, linear and nonlinear damping and linear and nonlinear stiffness on the probability density functions of system responses, which can guide the selection of materials, stiffnesses and structures in viscoelastic damper design.

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Section: Introductionmentioning

confidence: 99%

Stationary probability densities of generalized Maxwell-type viscoelastic systems under combined harmonic and Gaussian white noise excitations

Wang

2020

J Braz. Soc. Mech. Sci. Eng.

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“…erefore, lots of researchers pay lots of attentions to evaluate the system responses, reliability, and security under broadband noise excitations. Ling et al studied the response and stability of the SDOF viscoelastic system subjected to the wideband noise excitations by using the stochastic averaging [11]. Janevski obtained the Lyapunov exponent and moment Lyapunov exponent of Hill's equation with frequency and damping coefficients fluctuated by correlated wideband random processes by the stochastic averaging, both first order and second order [12].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Responses for the Vibro‐Impact System under the Broadband Noise

Guan

Ling

2019

Shock and Vibration

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The stochastic averaging is applied to derive the random responses of the SDOF vibro-impact system with one-side wall under additive and multiplicative broadband noise, where the impact is described by the modified Hertzian contact model. Compared with the popular simplified “classical model” (i.e., x˙−=rx˙+), the whole impact process is captured by the modified Hertzian contact model without any assumptions. One example is given to illustrate the proposed technique. The comparison between the analytical results and those from Monte Carlo simulations manifests the accuracy of the proposed technique. It should be pointed out that the technique proposed in this paper is powerful for the cases of weak excitation and big enough bandwidth of the broadband noise. Finally, the influences of various parameters are also discussed in detail.

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“…Ling et al [7] discussed the response and almost-sure stability of a 1DOF viscoelastic system with strongly nonlinear stiffness under wideband noise excitations. Moment Lyapunov exponents of a viscoelastic system under the excitation of a wideband noise were investigated by using the averaging method of both first order and second order [8].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Stability of Coupled Viscoelastic Systems Excited by Real Noise

Deng

2018

Mathematical Problems in Engineering

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The moment stochastic stability and almost-sure stochastic stability of two-degree-of-freedom coupled viscoelastic systems, under the parametric excitation of a real noise, are investigated through the moment Lyapunov exponents and the largest Lyapunov exponent, respectively. The real noise is also called the Ornstein-Uhlenbeck stochastic process. For small damping and weak random fluctuation, the moment Lyapunov exponents are determined approximately by using the method of stochastic averaging and a formulated eigenvalue problem. The largest Lyapunov exponent is calculated through its relation with moment Lyapunov exponents. The stability index, the stability boundaries, and the critical excitation are obtained analytically. The effects of various parameters on the stochastic stability of the system are then discussed in detail. Monte Carlo simulation is carried out to verify the approximate results of moment Lyapunov exponents. As an application example, the stochastic stability of a flexural-torsional viscoelastic beam is studied.

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Response and stability of SDOF viscoelastic system under wideband noise excitations

Cited by 31 publications

References 26 publications

Stationary probability densities of generalized Maxwell-type viscoelastic systems under combined harmonic and Gaussian white noise excitations

Stationary probability densities of generalized Maxwell-type viscoelastic systems under combined harmonic and Gaussian white noise excitations

Stochastic Responses for the Vibro‐Impact System under the Broadband Noise

Stochastic Stability of Coupled Viscoelastic Systems Excited by Real Noise

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