Vibrations of Annular Plates of Variable Thickness

Abstract

An exact solution for the circular frequencies of a polar orthotropic annular plate of uniform and parabolic thickness under the action of in-plane forces is presented. The annular plate is reinforced with simply supported edge beams at both the inner and outer boundaries. The edge beams are subjected to uniform, radial compressive loadings. Frequency parameters are determined for both axisymmetric and higher modes and are found to be functions of the in-plane loads, plate dimensions and rigidities, edge beam stiffness and moment of inertia parameters, and the profile of the plate. The use of edge beams in this investigation provides a practical method of simulating various types of edge conditions for the polar orthotropic annular plate — including the limiting cases of the simply supported and clamped edge.