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

作　　者：李超 徐伟 王亮 李东喜 

机构地区：[1]Department of Applied Mathematics, Northwestern Polytechnical University [2]School of Mathematics, Taiyuan University of Technology

出　　处：《Chinese Physics B》2013年第11期159-165,共7页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Grant Nos.11172233,10932009,and 11202160);the Natural Science Foundation of Shaanxi Province,China(Grant No.2012JQ1004)

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.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 

分 类 号：O313.4[理学—一般力学与力学基础]