Stationary response of stochastically excited nonlinear systems with continuous-time Markov jump |
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| Authors: | Shan-shan Pan Wei-qiu Zhu Rong-chun Hu Rong-hua Huan |
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| Institution: | 1.Department of Mechanics,Zhejiang University,Hangzhou,China;2.State Key Laboratory of Fluid Power and Mechatronic Systems,Zhejiang University,Hangzhou,China;3.Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province,Zhejiang University,Hangzhou,China |
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| Abstract: | 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. |
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