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Stochastic responses of a vibro-impact system with additive and multiplicative colored noise excitations

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Abstract

By the aid of nonsmooth transformation, the stochastic averaging method is extended to solve the stationary response of a vibro-impact system with additive and multiplicative colored noise excitations. The stationary responses are obtained by using the concepts of total phase and residual phase. A Duffing–Van der Pol vibro-impact system is given to illustrate the application of the method. And stochastic P-bifurcation is also investigated.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11172233, 11472212, 11302170 and 11202160) and the Natural Science Foundation of Guangdong Province (Grant No. 2013KJCX0189).

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Authors and Affiliations

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, 710072, Shaanxi, China

    Wei Xu, Chao Li & Xiaole Yue

  2. Department of Mathematics, Foshan University, Guangdong, 528000, China

    Haiwu Rong

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  1. Wei Xu
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  2. Chao Li
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  3. Xiaole Yue
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  4. Haiwu Rong
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Correspondence to Wei Xu.

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Xu, W., Li, C., Yue, X. et al. Stochastic responses of a vibro-impact system with additive and multiplicative colored noise excitations. Int. J. Dynam. Control 4, 393–399 (2016). https://doi.org/10.1007/s40435-014-0143-0

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  • DOI: https://doi.org/10.1007/s40435-014-0143-0

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