Vibration of a Radially Loaded Spherical Shell

Abstract

A set of linearized equations is developed, based on the theory of finite elasticity consistent with the assumptions of classical shell theory. They are used to predict the effect of radial loading on the frequencies of a complete, thin, spherical shell. Inducing an initial compressive stress in the shell by radial preload decreases the lowest transverse frequency by an amount dependent on the magnitude of the initial stress and the classical buckling load. The higher transverse frequency predicted by classical shell theory as well as the frequencies of the pure radial and torsional modes are virtually independent of radial pre-load.