Dynamic post-buckling characteristics of circular plates

Abstract

An approximate analytic method is developed herein to study the post-buckling response of a thin elastic circular plate under the action of axisymmetric, time-dependent radial thrusts. The plate response is assumed to be in resonance with the principal mode of vibration of the plate, thereby neglecting effects associated with higher vibrational modes. It is shown that for certain simple cases of loading history and for small penetrations of the post-buckling domain, the above assumption is a valid approximation and leads to a powerful simplification in the governing equations of the problem which then reduce to a single nonlinear differential equation of the cubic order. It is the purpose of this paper to formulate this equation for which an analytical solution is then obtained. The post-buckling response of the plate under a step loading history is presented.