Elastic Buckling and Flexural Vibration of Annular Plates under Axisymmetric In-plane Forces

Abstract

The problems of elastic buckling and flexural vibration of annular plates under axisymmetric in-plane forces have been analyzed by the Galerkin method. By adopting natural vibration modes of an annular plate without an in-plane force as admissible functions, these problems have been dealt with under various combinations of boundary conditions at the outer and inner edges. Two cases, one the case with uniform in-plane forces along the inner and/or outer edges and the other with steady state thermal stress caused by the temperature difference between inner and outer edges, have been analyzed as examples of axisymmetric in-plane force distributions. The relation of the buckling load parameter with the hole size and the relation of the natural frequency parameters with the magnitude of the in-plane force have been evaluated. It has been found that there is possibility of buckling even in the case of tensile in-plane force or cooling, when the distributed in-plane stress has compressive components.