A new approximate solution technique for randomly excited nonlinear oscillators. II (Q1202879)

The method of weighted residuals is applied to the reduced Fokker-Planck equation associated with a nonlinear oscillator, which is subjected to both additive and multiplicative Gaussian white noise excitations. A set of constraints are deduced for obtaining an approximate stationary probability density for the system response. One of the constraints coincides with the previously proposed [part I: \textit{G. Q. Cai} and \textit{Y. K. Lin}, Int. J. Nonlinear Mech. 23, No. 5/6, 409-420 (1988; Zbl 0667.70036)] criterion of dissipation energy balancing, and the others are useful for calculating the equivalent conservative force. Applications of the scheme are illustrated by examples, and its accuracy is substantiated by Monte Carlo simulation results.