| Stochastic responses of Duffing–Van der Pol vibro-impact system under additive colored noise excitation |
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| 引用本文： | 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, 0(11): 159-165 |
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| 作者姓名： | 李超 徐伟 王亮 李东喜 |
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| 基金项目： | 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）. |
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| 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.
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| 关 键 词： | 碰撞振动系统 噪声激励 随机响应 PDF格式 波尔 马尔可夫过程 概率密度函数 PDF文件 |
Stochastic responses of Duffing-Van der Pol vibro-impact system under additive colored noise excitation |
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| Li Chao,Xu Wei,Wang Liang,Li Dong-Xi. Stochastic responses of Duffing-Van der Pol vibro-impact system under additive colored noise excitation[J]. Chinese Physics B, 2013, 0(11): 159-165 |
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| Authors: | Li Chao Xu Wei Wang Liang Li Dong-Xi |
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| Affiliation: | [1]Department of Applied Mathematics, Northwestern Polytechnical University, Xi＇an 710072, China [2]School of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China |
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| 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. |
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| Keywords: | vibro-impact system colored noise non-smooth transformation stochastic bifurcation |
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