Linear and non-linear dynamic instability of functionally graded plate subjected to non-uniform loading

Abstract

The present paper deals with the linear and non-linear dynamic instability of functionally graded materials (FGMs) plate subjected to non-uniform loading. Due to this loading, the in-plane stress distributions within the FG plate in pre-buckling state are evaluated using plate membrane analysis. The FG plate is modeled using higher order shear deformation theory (HSDT) considering von-Kármán geometric nonlinearity. The Galerkin’s method is used to reduce the non-linear governing partial differential equations into a set of ordinary differential equations describing the plate non-linear dynamic instability. Bolotin’s method is used to obtain the boundaries of dynamic instability regions. These boundaries are traced by the periodic solution of linear ordinary differential equation (Mathieu-Hill equation) with period T and 2T. Effects of power index, span-to-thickness ratio, aspect ratio, static load factor, boundary conditions and various types of linearly varying loadings and parabolically distributed loadings on the linear and nonlinear dynamic instability are studied. The study of linear and non-linear response in stable and unstable regions are carried out to identify the dynamic instability behaviour such as dependence of forcing frequency, existence of beats, effect of nonlinearity on the response and influence of the initial conditions.