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Response analysis for a vibroimpact Duffing system with bilateral barriers under external and parametric Gaussian white noises

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  • Yang, Guidong
  • Xu, Wei
  • Gu, Xudong
  • Huang, Dongmei

Abstract

In this paper, a vibroimpact Duffing oscillator with two barriers that are symmetrical with respect to the equilibrium point of the system is considered for the cases of external and parametric Gaussian white noise random excitations. According to the levels of the system energy, the motions of the unperturbed vibroimpact system are divided into two types: oscillations without impacts and oscillations with alternate impacts on both sides. Then, under the assumption that the vibroimpact Duffing system is quasi-conservative, the stochastic averaging method for energy envelope is applied to obtain the averaged drift and diffusion coefficients for the two types of motions, respectively. The Probability Density Functions (PDFs) of stationary responses are derived by solving the corresponding Fokker-Plank-Kolmogorov (FPK) equation. Lastly, results obtained from the proposed procedure are validated by directly numerical simulation. Meanwhile, effects of the position of bilateral barriers and the random excitations on the PDFs of the stationary responses are also discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:87:y:2016:i:c:p:125-135
    DOI: 10.1016/j.chaos.2016.03.017
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    References listed on IDEAS

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    1. Luo, Albert C.J. & Chen, Lidi, 2005. "Periodic motions and grazing in a harmonically forced, piecewise, linear oscillator with impacts," Chaos, Solitons & Fractals, Elsevier, vol. 24(2), pages 567-578.
    2. R. A. Ibrahim & I. M. Grace, 2010. "Modeling of Ship Roll Dynamics and Its Coupling with Heave and Pitch," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-32, September.
    3. 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.

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