UTILIZING THE PROBABILITY DENSITY FUNCTION FOR ANALYTIC BIFURCATION IDENTIFICATION OF ISOTROPIC FGM PLATES DRIVEN BY LATERALLY STOCHASTIC LOADS

In this paper, an analytic method to evaluate the probability density function of the laterally white noise excitation for nonlinear functionally graded plates and investigate the bifurcation points in their responses is presented. First, the nonlinear governing equation of a typical functionally graded plate is derived, and then by using Fokker Planck Kolmogorov method, an analytic relation for the joint probability density function is obtained. Defining non dimensional parameters in the governing equation, the nonlinear behavior and the bifurcation phenomenon are studied with respect to the joint probability density function and for a vast spectrum of functionally graded plates under laterally white noise excitation but determined constant inplane forces. To validate our results, some of the analytic cases are resolved by direct numerical methods which show also a good agreement.