Three-Dimensional and Shell-Theory Analysis of Elastic Waves in a Hollow Sphere: Part 1—Analytical Foundation

Abstract

In Part 1 of this paper an exact analysis of the nonaxisymmetric wave propagation in a hollow elastic sphere is presented. It is found that the characteristic frequency equation is independent of the longitudinal wave number. Approximate equations for thin shells and membranes are derived by way of asymptotic expansions. In general, the vibrations fall into two distinct classes, one of which is equivoluminal. Also included in the paper is a six-mode shell theory in which the effects of transverse normal strain are included. A technique due to van der Neut is used to separate the governing partial differential equations whereby two frequency equations corresponding to the two classes of vibrations are obtained.