On Free Vibrations of an Embedded Anisotropic Spherical Shell

Abstract

In this paper, free vibrations of a spherically isotropic spherical shell embedded in an elastic medium of Pasternak type are studied by using a six-mode shell theory that includes effects of shear deformation, rotary inertia, and transverse normal strain. The separable homogeneous solution for displacements and stresses in a deep spherical shell is derived and two classes of vibrations are obtained by the introduction of five auxiliary variables. Numerical results are compared with those predicted by two simpler shell theories mentioned in the paper and those by three-dimensional elastic theory.