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Stochastic stationary responses of a viscoelastic system with impacts under additive Gaussian white noise excitation

Author

Listed:
  • Zhao, Xiangrong
  • Xu, Wei
  • Gu, Xudong
  • Yang, Yongge

Abstract

This paper is devoted to investigate the stochastic stationary responses of a viscoelastic system with impacts under additive Gaussian white noise excitation. First, the viscoelastic force is approximated as equivalent stiffness and damping terms, and the original system is replaced by a system without viscoelasticity. Then, the stationary responses of the system are obtained analytically by using non-smooth transformation and stochastic averaging method. The theoretical analyses are verified by numerical results from Monte Carlo simulations. Effects of the noise intensity and the nonlinear damping coefficient on the system responses are investigated. At last, it is worthy noting that the restitution coefficient, the linear damping coefficient and the viscoelastic parameters can induce the occurrence of stochastic P-bifurcation.

Suggested Citation

  • Zhao, Xiangrong & Xu, Wei & Gu, Xudong & Yang, Yongge, 2015. "Stochastic stationary responses of a viscoelastic system with impacts under additive Gaussian white noise excitation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 431(C), pages 128-139.
    • Handle: RePEc:eee:phsmap:v:431:y:2015:i:c:p:128-139
    DOI: 10.1016/j.physa.2015.03.013
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    References listed on IDEAS

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    1. Li, Chao & Xu, Wei & Feng, Jinqian & Wang, Liang, 2013. "Response probability density functions of Duffing–Van der Pol vibro-impact system under correlated Gaussian white noise excitations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1269-1279.
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    Cited by:

    1. Liu, Di & Li, Junlin & Meng, Yu, 2019. "Probabilistic response analysis for a class of nonlinear vibro-impact oscillator with bilateral constraints under colored noise excitation," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 179-188.
    2. Guo, Shu-Ling & Yang, Yong-Ge & Sun, Ya-Hui, 2021. "Stochastic response of an energy harvesting system with viscoelastic element under Gaussian white noise excitation," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    3. Li, Chao, 2019. "Stochastic response of a vibro-impact system with variable mass," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 151-160.

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    1. Li, Chao, 2019. "Stochastic response of a vibro-impact system with variable mass," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 151-160.
    2. Yang, Guidong & Xu, Wei & Gu, Xudong & Huang, Dongmei, 2016. "Response analysis for a vibroimpact Duffing system with bilateral barriers under external and parametric Gaussian white noises," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 125-135.
    3. Liu, Di & Li, Junlin & Meng, Yu, 2019. "Probabilistic response analysis for a class of nonlinear vibro-impact oscillator with bilateral constraints under colored noise excitation," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 179-188.

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