Vibration of an Aelotropic Spherical Shell

In this paper, a separable homogeneous solution for the displacements and stresses in a freely vibrating deep spherical shell exhibiting spherical isotropy is derived. A six-mode shell theory is proposed that includes the effects of shear deformation, rotary inertia, and transverse normal strain. The frequency spectra, corresponding to three different materials with varying degrees of anisotropy, are analyzed for two values of thickness-to-mean-radius ratios. Also, open spherical shells under various boundary conditions are investigated and mode shapes are studied.