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Probabilistic responses of three-dimensional stochastic vibro-impact systems

Author

Listed:
  • Ma, Shichao
  • Wang, Liang
  • Ning, Xin
  • Yue, Xiaole
  • Xu, Wei

Abstract

Chatter between devices becomes a primary concern in actual engineering problems since it may cause the reduction of efficiency. Due to random factors and non-smooth properties, difficulties rest in deriving the analytical results and such systems are generally investigated with simplified approximate methods. In this context, the present paper pioneers the response analysis of three-dimensional hydraulic relief valve impact systems under stochastic excitations. In order to retain the non-smooth characteristics of the systems under consideration, no non-smooth transformation is imposed on the original system. A procedure in which the stochastic trajectories start from the contact surface and return to the contact surface for the next time is constructed. Probability density functions (PDFs) of the random trajectories returning to the contact surface at any time can be obtained, and the proposed procedure is proved accurate and efficient using Monte Carlo (MC) simulations in this paper. Moreover, we find that the flow rate of the systems can lead to the stochastic P-bifurcation on the contact surface. Further discussion indicates that the proposed procedure can substantially reflect the complicated dynamic behaviors of the high-dimensional vibro-impact systems.

Suggested Citation

  • Ma, Shichao & Wang, Liang & Ning, Xin & Yue, Xiaole & Xu, Wei, 2019. "Probabilistic responses of three-dimensional stochastic vibro-impact systems," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 308-314.
    • Handle: RePEc:eee:chsofr:v:126:y:2019:i:c:p:308-314
    DOI: 10.1016/j.chaos.2019.06.023
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    References listed on IDEAS

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    1. Yue, Xiaole & Xu, Wei & Jia, Wantao & Wang, Liang, 2013. "Stochastic response of a ϕ6 oscillator subjected to combined harmonic and Poisson white noise excitations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(14), pages 2988-2998.
    2. Yue, Xiaole & Xu, Wei & Zhang, Ying & Du, Lin, 2018. "Analysis of global properties for dynamical systems by a modified digraph cell mapping method," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 206-212.
    3. Yue, Xiaole & Xu, Yong & Xu, Wei & Sun, Jian-Qiao, 2019. "Probabilistic response of dynamical systems based on the global attractor with the compatible cell mapping method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 509-519.
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    Cited by:

    1. Han, Ping & Wang, Liang & Xu, Wei & Zhang, Hongxia & Ren, Zhicong, 2021. "The stochastic P-bifurcation analysis of the impact system via the most probable response," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

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