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

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 syste...

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Bibliographic Details
Published inChinese physics B Vol. 22; no. 11; pp. 159 - 165
Main Author 李超 徐伟 王亮 李东喜
Format Journal Article
LanguageEnglish
Published 01.11.2013
Subjects
Approximation
Excitation
Mathematical analysis
Noise
PDF文件
PDF格式
Probability density functions
Simulation
Stochasticity
Transformations
噪声激励
概率密度函数
波尔
碰撞振动系统
随机响应
马尔可夫过程
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ISSN1674-1056
2058-3834
1741-4199
DOI10.1088/1674-1056/22/11/110205

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Summary: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.
Bibliography:vibro-impact system, colored noise, non-smooth transformation, stochastic bifurcation
Li Chao, Xu Wei, Wang Liang, Li Dong-Xi（a） Department of Applied Mathematics, Northwestern Polytechnical University, Xi＇an 710072, China b ） School of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China
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.
11-5639/O4
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SourceType-Scholarly Journals-1
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ISSN:1674-1056
2058-3834
1741-4199
DOI:10.1088/1674-1056/22/11/110205