Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4637591 | Applied Mathematics and Computation | 2006 | 13 Pages |
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
W.X. Xie, W. Xu, L. Cai,