NONLINEAR VIBRATION AND POSTBUCKLING OF ISOTROPIC THIN CIRCULAR PLATES ON ELASTIC FOUNDATIONS

An approximate solution for the large deflection axisymmetric responses of isotropic thin circular plates resting on Winkler, Pasternak and non-linear Winkler foundations is presented. Plates with edges elastically restrained against rotation and in-plane displacement are considered. Von Karman type equations in terms of transverse deflection and stress function are employed. A one term mode shape is used to approximate the transverse deflection and Galerkin's method is used to obtain an equation for the central deflection which has the form of a Duffing's equation. Non-linear frequencies, postbuckling response to radial load at the edge and the maximum transient response to transverse step load have been obtained. It is shown that sufficiently accurate results are obtained by this method. Numerical results are presented to illustrate the effect of various parameters.