Free Vibrations of Thin Orthotropic Oblate Spheroidal Shells

Abstract

The problem of the free vibrations of a thin orthotropic, oblate spheroidal shell has been solved by making the assumptions of orthotropic membrane theory and harmonic axisymmetric motion. The theory has reduced the differential equations of motion to a single ordinary second-order differential equation with variable coefficients. The resulting eigenvalue problem is solved by Galerkin's method. The principal directions of the elastic compliances are assumed to be along parallels of latititude and along meridians. Both the oblate spheroidal and spherical shells were studied with various orthotropic constants. The existence of finite bounds for the corresponding mode shapes has been shown. Special consideration is given to the isotropic shell as a limiting case of the orthotropic problem. The present theory in the isotropic case yields the author's previously published results for the isotropic oblate spheroidal shell, as well as the known exact solution of the isotropic spherical shell.