Bifurcation Analysis of a Vibro-Impact Viscoelastic Oscillator with Fractional Derivative Element

Yong Ge Yang, Wei Xu, Yang Quan Chen, Bingchang Zhou

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8 引用 (Scopus)

摘要

To the best of authors' knowledge, little work has been focused on the noisy vibro-impact systems with fractional derivative element. In this paper, stochastic bifurcation of a vibro-impact oscillator with fractional derivative element and a viscoelastic term under Gaussian white noise excitation is investigated. First, the viscoelastic force is approximately replaced by damping force and stiffness force. Thus the original oscillator is converted to an equivalent oscillator without a viscoelastic term. Second, the nonsmooth transformation is introduced to remove the discontinuity of the vibro-impact oscillator. Third, the stochastic averaging method is utilized to obtain analytical solutions of which the effectiveness can be verified by numerical solutions. We also find that the viscoelastic parameters, fractional coefficient and fractional derivative order can induce stochastic bifurcation.

源语言英语
文章编号18501705
期刊International Journal of Bifurcation and Chaos
28
14
DOI
出版状态已出版 - 30 12月 2018

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