Stationary response of stochastically excited nonlinear systems with continuous-time Markov jump

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• 作者：Shan-shan Pan ; Wei-qiu Zhu ; Rong-chun Hu…
• 关键词：Key wordsNonlinear system ; Continuous ; time Markov jump ; Stochastic excitation ; Stochastic averaging
• 刊名：Journal of Zhejiang University-SCIENCE A
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：18
• 期：2
• 页码：83-91
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Mechanical Engineering; Civil Engineering; Classical and Continuum Physics; Industrial Chemistry/Chemical Engineering;
• 出版者：Zhejiang University Press
• ISSN：1862-1775
• 卷排序：18

文摘

An approximate method for predicting the stationary response of stochastically excited nonlinear systems with continuous-time Markov jump is proposed. By using the stochastic averaging method, the original system is reduced to one governed by a 1D averaged Itô equation for the total energy with the Markov jump process as parameter. A Fokker-Planck- Kolmogorov (FPK) equation is then deduced, from which the approximate stationary probability density of the response of the original system is obtained for different jump rules. To illustrate the effectiveness of the proposed method, a stochastically excited Markov jump Duffing system is worked out in detail.