Dynamic instability of damped composite skew plates under non-uniform in-plane periodic loading

Abstract

In this paper, the non-linear dynamic instability of damped composite skew plates under non-uniform in-plane periodic loadings is studied using analytical methods. The structural model for composite skew plate is based on first order shear deformation theory considering von-Kármán geometric nonlinearity. The analytical expressions for stress distributions within the composite skew plate subjected to three different types of non-uniform in-plane loadings are developed by solving, plane elasticity problem. Subsequently, using these stress distributions and via Hamilton principle, the equations governing the dynamic instability of composite skew plates are derived in terms of displacement (u–v–w) and rotation (φx,φy) variables. The generalized differential quadrature method is used to reduce the governing partial differential equations into a set of ordinary differential (Mathieu type) equations. The dynamic instability regions are traced by the periodic solutions (with period T and 2T) to Mathieu-type differential equations. Numerical results are presented to demonstrate the influence of skew angles, boundary conditions, non-uniform loadings and damping on the dynamic instability regions. Furthermore, the characteristic features of linear and nonlinear response in stable and unstable regions are studied. This brings out various features of instability problem such as existence of beats, effect of non-linearity and damping on response and its dependence on forcing frequency.