doi:10.3850/978-981-08-7619-7_P025

ABSTRACT

In this paper, a finite element procedure is developed to solve the generalized Fokker- Planck equation for the probability density function of the stationary responses of the non-linear stochastic oscillator subjected to external Poisson white noise excitation. As the domain of the probability density function of system responses is usually infinite, equivalent statistical linearization is adopted to estimate the finite range of finite element mesh. The elements with nonlinear shape functions are employed. With this method, the PDF is expressed as the product of shape functions and the node values of the probability density function. The shape function of C¹ is constructed for the elements in local coordinates. And then 3 × 3 Gaussian-Legendre integration rule is used for the numerical calculation. At last a set of algebraic equations are obtained and the constraint that the integral of the probabilities over the whole domain equals 1 is considered for numerical analysis. Examples are given to illustrate the validity of the solution procedure. Results obtained from the finite element procedure are also compared with those obtained from Monte Carlo Simulation.

Keywords: Finite-element-method, Fokker-Planck equation, Shape function, Poisson white noise.

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