Elastic Buckling and Flexural Vibration of Variable-Thickness Annular Plates Under Nonuniform In-Plane Forces

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 in-plane forces along its inner and outer edges, which vary in the circumferential direction. These problems are analyzed by the Galerkin method. Eigenfunctions of the natural vibration of a constant-thickness annular plate without in-plane forces are used as admissible functions. Two types of in-plane forces are adopted ; one a sinusoidally varying nonuniformity along the outer edge, and the other uniform along parts of the outer edge and zero on the remainder of the edge. The influences of the nonuniformity of the in-plane forces on the buckling load and natural frequencies are investigated. It is found that the increase of the nonuniformity decreases the buckling load and the fundamental natural frequency. This tendency becomes more evident when the thickness of the plate at the inner edge is thinner and the hole larger.