Asymmetric Modes and Associated Eigenvalues for Spherical Shells

Free asymmetric vibration of spherical shells with clamped and hinged boundary conditions are analyzed using the finite element method. Element stiffness and consistent mass matrices are derived using the improved shell theory, which takes into account the effects of shear deformation and rotary inertia. Natural frequencies for a wide spectrum of shell geometry ranging from shallow cap to hemispherical shell have been computed and are found to be in close agreement with the available data in the literature.