TY - JOUR
T1 - Study of the Duffing-Rayleigh oscillator subject to harmonic and stochastic excitations by path integration
AU - Xie, W. X.
AU - Xu, W.
AU - Cai, L.
PY - 2006/1/15
Y1 - 2006/1/15
N2 - 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.
AB - 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.
KW - Duffing-Rayleigh oscillator
KW - Harmonic and stochastic excitations
KW - Path integration
KW - Probability density
UR - http://www.scopus.com/inward/record.url?scp=31644434084&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2005.03.018
DO - 10.1016/j.amc.2005.03.018
M3 - 文章
AN - SCOPUS:31644434084
SN - 0096-3003
VL - 172
SP - 1212
EP - 1224
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
IS - 2 SPEC. ISS.
ER -