Free and forced vibration analysis of moderately thick plates with uncertain material properties using the Chaotic Radial Basis Function

Abstract

The Chaotic Radial Basis Function, which is a recently developed method [1,2], is used for free and forced vibration analysis of moderately thick plates with random material properties and considering random dynamic loading. The element free Galerkin method, which is one of the most popular mesh free method, is employed for obtaining the deterministic models of the free and forced vibration of the moderately thick plates. The random input of the system including the plate module of elasticity, material density, natural frequency and the dynamic loading are expressed by the Karhunen Loeve (KL) expansion. Accordingly, by inserting the KL expansions of the random input and the Chaotic Radial Basis Function expansion of the dynamic response in the deterministic models, and then applying a Galerkin projection, the governing equations for the stochastic free and forced vibration are obtained. The accuracy of the method is investigated by a comparison with the Monte Carlo simulation. It is seen that the method gives both accurate results and a considerable reduction in the computational cost. Further, the applicability of the method is shown through studying the stochastic dynamic behavior of plates for several values of the statistical parameters of the random input.