Nonlinear Vibration Analysis of Stochastic Thin Plates Based on Lindstedt-Poincar\'{e} Perturbation Method

Abstract

Nonlinear vibration computational problem of stochastic thin plates in large amplitude was investigated here. Based on the nonlinear theory of large deflection of thin plates, we derived the governing equations of nonlinear free vibration of isotropic thin plates. And solved the governing equations by Lindstedt- Poincare Perturbation Method Presented herein are asymptotic analytical solutions for the frequency function of the thin plates with fixed parameters. Based on the theory of random field, after mathematical treatments of the probability density function of random vector expressions, such as determining the interval of integrating, substituting variable and transforming integral order, then the probability density function of nonlinear vibration frequency of stochastic thin plates can be obtained directly. And combined with Monte Carlo Simulation analysis and our previous work (1), the result of the method in this paper is validated, which testifies that the method in this paper is effective and of preferable precision.