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Stochastic response of a vibro-impact system with variable mass

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  • Li, Chao

Abstract

Vibro-impact machines are found increasingly broad application in various sectors of the world. And the mass disturbance exists in the process of impact, which refers to the variable mass system that is a common phenomenon in life. With the development of micro-electronic and nanotechnology, it is essential to investigate the effect of mass disturbance on this random vibro-impact system response. The stationary system response is the main topic of the manuscript. In the light of the discontinuity of vibro-impact system, the nonsmooth transformation is introduced to overcome the discontinuity. Then the stochastic averaging technique is applied to the transformed stochastic variable mass system. The approximate analytical response can be obtained by solving associated Fokker–Planck–Kolmogorov equation. A Van der Pol variable mass vibro-impact system is given to illustrate the application and availability of this method. Meanwhile, stochastic P-bifurcation is studied, and a reasonable interpretation is given to explain the procedure of stochastic P-bifurcation.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:516:y:2019:i:c:p:151-160
    DOI: 10.1016/j.physa.2018.10.021
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    References listed on IDEAS

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    1. de Souza, Silvio L.T. & Caldas, Iberê L. & Viana, Ricardo L., 2007. "Damping control law for a chaotic impact oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 745-750.
    2. Qiao, Yan & Xu, Wei & Jia, Wantao & Han, Qun, 2017. "Stochastic stationary response of a variable-mass system with mass disturbance described by Poisson white noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 122-134.
    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. 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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