Response of a Duffing—Rayleigh system with a fractional derivative under Gaussian white noise excitation

doi:10.1088/1674-1056/24/2/020204

›› 2015, Vol. 24 ›› Issue (2): 20204-020204.doi: 10.1088/1674-1056/24/2/020204

Response of a Duffing—Rayleigh system with a fractional derivative under Gaussian white noise excitation

张冉冉, 徐伟, 杨贵东, 韩群

Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China

收稿日期:2014-05-14 修回日期:2014-08-18 出版日期:2015-02-05 发布日期:2015-02-05
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11172233, 11302170, and 11302171) and the Natural Science Foundation of Shaanxi Province, China (Grant Nos. 2014JQ1001).

Response of a Duffing—Rayleigh system with a fractional derivative under Gaussian white noise excitation

Zhang Ran-Ran (张冉冉), Xu Wei (徐伟), Yang Gui-Dong (杨贵东), Han Qun (韩群)

Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China

Received:2014-05-14 Revised:2014-08-18 Online:2015-02-05 Published:2015-02-05
Contact: Xu Wei E-mail:weixu@nwpu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11172233, 11302170, and 11302171) and the Natural Science Foundation of Shaanxi Province, China (Grant Nos. 2014JQ1001).

摘要/Abstract

摘要： In this paper, we consider the response analysis of a Duffing-Rayleigh system with fractional derivative under Gaussian white noise excitation. A stochastic averaging procedure for this system is developed by using the generalized harmonic functions. First, the system state is approximated by a diffusive Markov process. Then, the stationary probability densities are derived from the averaged Itô stochastic differential equation of the system. The accuracy of the analytical results is validated by the results from the Monte Carlo simulation of the original system. Moreover, the effects of different system parameters and noise intensity on the response of the system are also discussed.

关键词: response, Duffing-Rayleigh, fractional derivative, stochastic averaging method

Abstract: In this paper, we consider the response analysis of a Duffing-Rayleigh system with fractional derivative under Gaussian white noise excitation. A stochastic averaging procedure for this system is developed by using the generalized harmonic functions. First, the system state is approximated by a diffusive Markov process. Then, the stationary probability densities are derived from the averaged Itô stochastic differential equation of the system. The accuracy of the analytical results is validated by the results from the Monte Carlo simulation of the original system. Moreover, the effects of different system parameters and noise intensity on the response of the system are also discussed.

Key words: response, Duffing-Rayleigh, fractional derivative, stochastic averaging method

中图分类号: (Probability theory, stochastic processes, and statistics)

02.50.-r

05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion) 05.40.Ca (Noise)

张冉冉, 徐伟, 杨贵东, 韩群. Response of a Duffing—Rayleigh system with a fractional derivative under Gaussian white noise excitation[J]. , 2015, 24(2): 20204-020204.

Zhang Ran-Ran (张冉冉), Xu Wei (徐伟), Yang Gui-Dong (杨贵东), Han Qun (韩群). Response of a Duffing—Rayleigh system with a fractional derivative under Gaussian white noise excitation[J]. Chin. Phys. B, 2015, 24(2): 20204-020204.

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Response of a Duffing—Rayleigh system with a fractional derivative under Gaussian white noise excitation

Response of a Duffing—Rayleigh system with a fractional derivative under Gaussian white noise excitation

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