Effect of Boundary Conditions on Free Vibration of Thick Isotropic Spherical Shells

Abstract

A nine-node Lagrangian finite element is formulated in spherical coordinates and used to study the vibration of thick isotropic spherical shells. The accuracy of the proposed analysis is verified by way of comparison with existing solutions. A comparative study of frequencies of vibration for thick spherical shells for several definitions of a simple support is presented in both tabular and graphical format. The analysis is expanded by including additional results for both free and fixed boundary conditions. An important conclusion is that the manner in which the boundary condition is defined can modify and possibly control the frequency of free vibration.