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
复制标题
DOI：
10.1088/1674-1056/22/11/110205
复制
发表时间：
2013-11
影响因子：
1.7
通讯作者：
Li-Ming Chao;Xu Wei;Wang Liang;Ling Dong-xi
中科院分区：
文献类型：
--
作者：
Li-Ming Chao;Xu Wei;Wang Liang;Ling Dong-xi
针对有色噪声激发的振动冲击系统开发了响应分析程序。非光滑变换用于将振动冲击系统转换为无冲击项的新系统。借助改进的准保守平均，新系统的总能量可以近似为马尔可夫过程，并推导出总能量的平稳概率密度函数（PDF）。使用总能量的平稳 PDF 的解析解获得原始系统的响应 PDF。通过与相应仿真结果的比较，检验了理论结果的有效性。此外，还探讨了随机分岔。
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.