Free vibration of an inflated oblate spheroidal shell

Abstract

An approximate analytical solution of the subject problem is developed. The vibration of the oblate spheroid is assumed to be governed by the membrane theory of shells. It is also assumed that the square of eccentricity of the oblate spheroid is small and constant during inflation and that the spheroid is composed of a neo-Hookean material. The first step in the solution process concerns an exact solution of the free vibration problem of an inflated spherical shell. The free vibration of the oblate spheroid is then obtained by Galerkin's method with the modal solutions of the inflated spherical shell being used. The frequencies and mode shapes of both types of shell are given and compared to similar linear solutions. Comparisons of the behavior of oblate spheroidal and spherical shells are given. An interesting instability phenomenon of the vibration of inflated spherical shells is discussed and the constant eccentricity assumption is justified by comparisons with test results.