Elastic buckling and flexural vibration of variable thickness annular plates under nonuniform inplane forces.

Abstract

This paper deals with elastic buckling and flexural vibration of annular plates whose thicknesses vary linearly in the radial direction. The annular plate is subjected to inplane forces along inner and outer edges, which vary in the circumferential direction. These problems are analyzed by the Galerkin method. Eigenfuctions of the natural vibration of a constant thickness annular plate without inplane forces are used as admissible functions. Two types of inplane forces are adopted; one with a sinusoidally varying nonuniformity along the outer edge, and the other is uniform along parts of the outer edge and zero along the remainder of the edge. The influences of the nonuniformity of the inplane forces on the buckling load and natural frequencies are investigated. It is found that the increse of the nonuniformity decreases the buckling load and the fundamental natural frequency. This tendency becomes more evident when the thickness of the plated at the inner edge is thinner.