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ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2017, Vol. 18 Issue (2): 83-91    DOI: 10.1631/jzus.A1600176
Articles     
Stationary response of stochastically excited nonlinear systems with continuous-time Markov jump
Shan-shan Pan, Wei-qiu Zhu, Rong-chun Hu, Rong-hua Huan
Department of Mechanics, Zhejiang University, Hangzhou 310027, China; State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China; Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou 310027, 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.

Key words： Nonlinear system      Continuous-time Markov jump      Stochastic excitation      Stochastic averaging     
Received: 23 February 2016      Published: 24 January 2017
CLC:  O324  
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Shan-shan Pan
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Rong-hua Huan
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Shan-shan Pan, Wei-qiu Zhu, Rong-chun Hu, Rong-hua Huan. Stationary response of stochastically excited nonlinear systems with continuous-time Markov jump. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2017, 18(2): 83-91.

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http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.A1600176     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2017/V18/I2/83

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