Stochastic averaging of strongly non-linear oscillators under bounded noise excitation

Z. L. Huang, W. Q. Zhu, Yiqing Ni, J. M. Ko

Research output: Journal article publicationJournal articleAcademic researchpeer-review

60 Citations (Scopus)

Abstract

A stochastic averaging method for strongly non-linear oscillators under external and/or parametric excitation of bounded noise is proposed by using the so-called generalized harmonics functions. The method is then applied to study the primary resonance of Duffing oscillator with hardening spring under external excitation of bounded noise. The stochastic jump and its bifurcation of the system are observed and explained by using the stationary probability density of amplitude and phase. Subsequently, the method is applied to study the dynamical instability and parametric resonance of Duffing oscillator with hardening spring under parametric excitation of bounded noise. The primary unstable region is delineated by evaluating the Lyapunov exponent of linearized system, and the response and jump of non-linear system around the unstable region are examined by using the sample functions and stationary probability density of amplitude and phase.
Original languageEnglish
Pages (from-to)245-267
Number of pages23
JournalJournal of Sound and Vibration
Volume254
Issue number2
DOIs
Publication statusPublished - 4 Jul 2003

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Acoustics and Ultrasonics
  • Mechanics of Materials
  • Mechanical Engineering

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