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

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

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.

Keywords: response Duffing-Rayleigh fractional derivative stochastic averaging method

Received: 14 May 2014
Revised: 18 August 2014
Accepted manuscript online:

PACS:	02.50.-r	(Probability theory, stochastic processes, and statistics)
	05.40.-a	(Fluctuation phenomena, random processes, noise, and Brownian motion)
	05.40.Ca	(Noise)

Fund: 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).

Corresponding Authors: Xu Wei
E-mail: weixu@nwpu.edu.cn

Cite this article:

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 2015 Chin. Phys. B 24 020204

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

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