Systems whose specifications change abruptly and statistically, referred to as Markovian-jump systems, are considered in this paper. An approximate method is presented to assess the stationary response of multidegree, nonlinear, Markovian-jump, quasi-nonintegrable Hamiltonian systems subjected to stochastic excitation. Using stochastic averaging, the quasi-nonintegrable Hamiltonian equations are first reduced to a one-dimensional Itô equation governing the energy envelope. The associated Fokker–Planck–Kolmogorov equation is then set up, from which approximate stationary probabilities of the original system are obtained for different jump rules. The validity of this technique is demonstrated by using a nonlinear two-degree oscillator that is stochastically driven and capable of Markovian jumps.
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Research-Article
Stationary Response of a Class of Nonlinear Stochastic Systems Undergoing Markovian Jumps
Rong-Hua Huan,
Rong-Hua Huan
Department of Mechanics,
State Key Laboratory of Fluid Power
Transmission and Control,
State Key Laboratory of Fluid Power
Transmission and Control,
Zhejiang University
,Hangzhou 310027
, China
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Wei-qiu Zhu,
Wei-qiu Zhu
1
Department of Mechanics,
State Key Laboratory of Fluid Power
Transmission and Control,
e-mail: wqzhu@zju.edu.cn
State Key Laboratory of Fluid Power
Transmission and Control,
Zhejiang University
,Hangzhou 310027
, China
e-mail: wqzhu@zju.edu.cn
1Corresponding author.
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Fai Ma,
Fai Ma
Department of Mechanical Engineering,
University of California
,Berkeley, CA 94720
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Zu-guang Ying
Zu-guang Ying
Department of Mechanics,
State Key Laboratory of Fluid Power
Transmission and Control,
State Key Laboratory of Fluid Power
Transmission and Control,
Zhejiang University
,Hangzhou 310027
, China
Search for other works by this author on:
Rong-Hua Huan
Department of Mechanics,
State Key Laboratory of Fluid Power
Transmission and Control,
State Key Laboratory of Fluid Power
Transmission and Control,
Zhejiang University
,Hangzhou 310027
, China
Wei-qiu Zhu
Department of Mechanics,
State Key Laboratory of Fluid Power
Transmission and Control,
e-mail: wqzhu@zju.edu.cn
State Key Laboratory of Fluid Power
Transmission and Control,
Zhejiang University
,Hangzhou 310027
, China
e-mail: wqzhu@zju.edu.cn
Fai Ma
Department of Mechanical Engineering,
University of California
,Berkeley, CA 94720
Zu-guang Ying
Department of Mechanics,
State Key Laboratory of Fluid Power
Transmission and Control,
State Key Laboratory of Fluid Power
Transmission and Control,
Zhejiang University
,Hangzhou 310027
, China
Manuscript received January 28, 2015; final manuscript received February 28, 2015; published online March 31, 2015. Editor: Yonggang Huang.
1Corresponding author.
J. Appl. Mech. May 2015, 82(5): 051008 (6 pages)
Published Online: May 1, 2015
Article history
Received:
January 28, 2015
Revision Received:
February 28, 2015
Online:
March 31, 2015
Citation
Huan, R., Zhu, W., Ma, F., and Ying, Z. (May 1, 2015). "Stationary Response of a Class of Nonlinear Stochastic Systems Undergoing Markovian Jumps." ASME. J. Appl. Mech. May 2015; 82(5): 051008. https://doi.org/10.1115/1.4029954
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