Largest Lyapunov exponent for second-order linear systems under combined harmonic and random parametric excitations

H. W. Rong, G. Meng, X. D. Wang, W. Xu, T. Fang

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

The principal resonance of a second-order linear stochastic oscillator to combined harmonic and random parametric excitations is investigated. The method of multiple scales is used to determine the equations of modulation of amplitude and phase. The effects of damping, detuning, bandwidth, and magnitudes of random excitation are analyzed. The method of path integration is used to obtain the steady state probability density function of the system, and then the largest Lyapunov exponent is calculated. The almost-sure stability or instability of the stochastic system depends on the sign of the largest Lyapunov exponent. The theoretical analyses are verified by numerical results.

Original languageEnglish
Pages (from-to)1250-1256
Number of pages7
JournalJournal of Sound and Vibration
Volume283
Issue number3-5
DOIs
StatePublished - 20 May 2005

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