FE based solution of FPK equations for nonlinear oscillators driven by colored gaussian noise

The focus of this study is on estimating the stationary probability density function of the response of nonlinear oscillators subjected to colored Gaussian noise excitations.The governing equations of motion of the dynamical system are written in the form of coupled first order stochastic differential equations by expressing the colored noise as filtered Gaussian white noise processes. This results in an increase in the state space dimension. The stationary probability density function of the response is obtained by the numerical solution of the corresponding Fokker-Planck (FP) equation using the finite element method. The developed numerical method is first applied to a Lorenz attractor under white noise excitations and subsequently applied to a Duffing oscillator excited by colored Gaussian noise. The numerical predictions are compared with those obtained from full scale Monte Carlo simulations. © 2013 Taylor & Francis Group, London.