Nonlinear vibration and postbuckling of orthotropic thin annular plates

Abstract

This paper presents an approximate analytical solution of the geometrically nonlinear elastic axisymmetric response of polar orthotropic thin annular plates. Plates with outer edges elastically restrained against rotation and inplane displacement and with unsupported inner edges are considered. Von Kármán type equations are employed. The deflection is approximated by a one term mode shape satisfying the boundary conditions. Galerkin's method is used to obtain Duffing's equation for the deflection at the inner edge. Nonlinear frequencies, postbuckling response, static response and maximum deflection response under a step load are obtained. It is shown that good engineering accuracy is achieved by the approximate method.