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Response probability density functions of Duffing–Van der Pol vibro-impact system under correlated Gaussian white noise excitations

Author

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  • Li, Chao
  • Xu, Wei
  • Feng, Jinqian
  • Wang, Liang

Abstract

This paper aims to investigate the stationary probability density functions (PDFs) of a Duffing–Van der Pol vibro-impact system excited by correlated Gaussian white noise. With the help of non-smooth transformation, the stationary PDFs are formulated analytically by the stochastic averaging of energy envelope. The analytical results are verified by numerical simulation results. Stochastic bifurcations for different parameters are considered, and several special PDF forms are observed in this paper. The first form is the shape of the PDF of total energy can be similar to a crater, which has a minimum and a maximum. The second one is the shape of the joint PDF with three peaks, that is to say, the section of joint PDF has three maximum and two minimum. In addition, the influence of the degree of the correlation of Gaussian white noises is explored.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:6:p:1269-1279
    DOI: 10.1016/j.physa.2012.11.053
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    References listed on IDEAS

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    1. Zhang, Huiqing & Xu, Wei & Xu, Yong & Li, Dongxi, 2009. "Stochastic time-delayed systems driven by correlated noises: Steady-state analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(15), pages 3017-3023.
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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. 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.
    3. 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.
    4. 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.

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