Study of the Duffing-Rayleigh oscillator subject to harmonic and stochastic excitations by path integration

W. X. Xie, W. Xu, L. Cai

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

In this paper, the Duffing-Rayleigh oscillator subject to harmonic and stochastic excitations is investigated via path integration based on the Gauss-Legendre integration formula. The method can successfully capture the steady state periodic solution of probability density function. This path integration method, using the periodicity of the coefficient of associated Fokker-Planck-Kolmogorov equation, is extended to deal with the averaged stationary probability density, and is efficient to computation. Meanwhile, the changes of probability density caused by the intensities of harmonic and stochastic excitations, are discussed in three cases through the instantaneous probability density and the averaged stationary probability density.

Original languageEnglish
Pages (from-to)1212-1224
Number of pages13
JournalApplied Mathematics and Computation
Volume172
Issue number2 SPEC. ISS.
DOIs
StatePublished - 15 Jan 2006

Keywords

  • Duffing-Rayleigh oscillator
  • Harmonic and stochastic excitations
  • Path integration
  • Probability density

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