Stationary response analysis for a stochastic Duffing oscillator comprising fractional derivative element

Chun Yan Sun, Wei Xu

科研成果: 期刊稿件文章同行评审

10 引用 (Scopus)

摘要

Stationary response is investigated for a Duffing oscillator comprising fractional derivative elements excited by Gaussian white noise in the present paper. Firstly, harmonic balance technique is adopted to form a statistically equivalent linear system. Then, stochastic averaging is applied to the system to obtain a Markovian approximation of the response amplitude, and the associated Fokker-Planck equation and its stationary solution are derived. Furthermore, in virtue of Laplace transform, the transfer function of the equivalent linear system with amplitude-dependent coefficients is derived and it gives the conditional power spectral density, after weighted by the stationary probability density function, estimations of the power spectral density for the response and related statistics are derived. Numerical simulations verify the reliability of the proposed procedure, even for strongly nonlinear oscillators with properties like spectrum broadening and multimodal pattern.

源语言英语
页(从-至)374-380
页数7
期刊Zhendong Gongcheng Xuebao/Journal of Vibration Engineering
28
3
DOI
出版状态已出版 - 1 6月 2015

指纹

探究 'Stationary response analysis for a stochastic Duffing oscillator comprising fractional derivative element' 的科研主题。它们共同构成独一无二的指纹。

引用此