کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
804221 | 1467871 | 2014 | 13 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Finite element solution of Fokker–Planck equation of nonlinear oscillators subjected to colored non-Gaussian noise Finite element solution of Fokker–Planck equation of nonlinear oscillators subjected to colored non-Gaussian noise](/preview/png/804221.png)
Nonlinear oscillators subjected to colored Gaussian/non-Gaussian excitations are modelled through a set of three coupled first-order stochastic differential equations by representing the excitation as a first-order filtered white noise. A 3-D finite element (FE) formulation is developed to solve the corresponding 3-D Fokker Planck (FP) equations. The joint probability density functions of the state variables, obtained as a solution of the FP equation, are typically non-Gaussian and are used for computing the crossing statistics of the response – an essential metric for time variant reliability analysis. The method is illustrated through a noisy Lorenz attractor and a Duffing oscillator subjected to additive colored noise. The increase in state-space dimension when the Duffing oscillator is additionally excited with a parametric Gaussian noise is effectively handled by using stochastic averaging to reduce the state-space dimension. Investigations are carried out to examine the accuracy of the FE method vis-a-vis Monte Carlo simulations. The proposed method is observed to be computationally significantly cheaper for these three problems.
Journal: Probabilistic Engineering Mechanics - Volume 38, October 2014, Pages 143–155