Stochastic stability of viscoelastic systems under Gaussian and Poisson white noise excitations

Xiuchun Li, Jianhua Gu, Wei Xu, Fai Ma

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

As the use of viscoelastic materials becomes increasingly popular, stability of viscoelastic structures under random loads becomes increasingly important. This paper aims at studying the asymptotic stability of viscoelastic systems under Gaussian and Poisson white noise excitations with Lyapunov functions. The viscoelastic force is approximated as equivalent stiffness and damping terms. A stochastic differential equation is set up to represent randomly excited viscoelastic systems, from which a Lyapunov function is determined by intuition. The time derivative of this Lyapunov function is then obtained by stochastic averaging. Approximate conditions are derived for asymptotic Lyapunov stability with probability one of the viscoelastic system. Validity and utility of this approach are illustrated by a Duffing-type oscillator possessing viscoelastic forces, and the influence of different parameters on the stability region is delineated.

Original languageEnglish
Pages (from-to)1579-1588
Number of pages10
JournalNonlinear Dynamics
Volume93
Issue number3
DOIs
StatePublished - 1 Aug 2018

Keywords

  • Gaussian and Poisson noise
  • Lyapunov function
  • Stochastic averaging
  • Stochastic stability
  • Viscoelastic system

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