Vibrations of initially stressed thick circular and annular plates based on a high-order plate theory

Abstract

The average stress method is used to derive the governing equations for circular and annular plates in a general state of initial stress based on a high-order plate theory. The initial stress is taken to be a combination of an extensional stress plus a pure bending stress in the plane of the plate. These equations are solved by the Galerkin method. Natural frequencies of various boundary conditions are obtained for axisymmetric circular and annular plates. The effects of some parameters on the natural frequencies are studied. The results are compared with those of the Mindlin theory.