Stochastic responses of Duffing–Van der Pol vibro-impact system under additive colored noise excitation

doi:10.1088/1674-1056/22/11/110205

中国物理B ›› 2013, Vol. 22 ›› Issue (11): 110205-110205.doi: 10.1088/1674-1056/22/11/110205

Stochastic responses of Duffing–Van der Pol vibro-impact system under additive colored noise excitation

李超^a, 徐伟^a, 王亮^a, 李东喜^b

a Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, China;
b School of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China

收稿日期:2013-03-07 修回日期:2013-04-27 出版日期:2013-09-28 发布日期:2013-09-28
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11172233, 10932009, and 11202160) and the Natural Science Foundation of Shaanxi Province, China (Grant No. 2012JQ1004).

Stochastic responses of Duffing–Van der Pol vibro-impact system under additive colored noise excitation

Li Chao (李超)^a, Xu Wei (徐伟)^a, Wang Liang (王亮)^a, Li Dong-Xi (李东喜)^b

a Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, China;
b School of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China

Received:2013-03-07 Revised:2013-04-27 Online:2013-09-28 Published:2013-09-28
Contact: Li Chao E-mail:xgdlc2011@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11172233, 10932009, and 11202160) and the Natural Science Foundation of Shaanxi Province, China (Grant No. 2012JQ1004).

摘要/Abstract

摘要： A response analysis procedure is developed for a vibro-impact system excited by colored noise. The non-smooth transformation is used to convert the vibro-impact system into a new system without impact term. With the help of the modified quasi-conservative averaging, the total energy of the new system can be approximated as a Markov process, and the stationary probability density function (PDF) of the total energy is derived. The response PDFs of the original system are obtained using the analytical solution of the stationary PDF of the total energy. The validity of the theoretical results is tested through comparison with the corresponding simulation results. Moreover, stochastic bifurcations are also explored.

关键词: vibro-impact system, colored noise, non-smooth transformation, stochastic bifurcation

Abstract: A response analysis procedure is developed for a vibro-impact system excited by colored noise. The non-smooth transformation is used to convert the vibro-impact system into a new system without impact term. With the help of the modified quasi-conservative averaging, the total energy of the new system can be approximated as a Markov process, and the stationary probability density function (PDF) of the total energy is derived. The response PDFs of the original system are obtained using the analytical solution of the stationary PDF of the total energy. The validity of the theoretical results is tested through comparison with the corresponding simulation results. Moreover, stochastic bifurcations are also explored.

Key words: vibro-impact system, colored noise, non-smooth transformation, stochastic bifurcation

中图分类号: (Probability theory, stochastic processes, and statistics)

02.50.-r

05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion) 05.40.Ca (Noise)

李超, 徐伟, 王亮, 李东喜. Stochastic responses of Duffing–Van der Pol vibro-impact system under additive colored noise excitation[J]. 中国物理B, 2013, 22(11): 110205-110205.

Li Chao (李超), Xu Wei (徐伟), Wang Liang (王亮), Li Dong-Xi (李东喜). Stochastic responses of Duffing–Van der Pol vibro-impact system under additive colored noise excitation[J]. Chin. Phys. B, 2013, 22(11): 110205-110205.

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Stochastic responses of Duffing–Van der Pol vibro-impact system under additive colored noise excitation

Stochastic responses of Duffing–Van der Pol vibro-impact system under additive colored noise excitation

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