Axisymmetric Free Vibration of Orthotropic Complete Spherical Shells

This paper presents studies of the axisymmetric free vibration of moderately thick orthotropic complete spherical shells. The mathematical model is formulated in terms of the mid-surface meridian and radial displacements, and cross-section rotation of the meridians by the improved linear elastic shell theory with the effects of transverse shear strain and rotary inertia included. By the use of the Legendre polynomials, the exact solu tion from a set of three governing partial differential equations for the transversely iso tropic case and the series solution from the Ritz method for the polar orthotropic case are obtained. Natural frequencies and modes are found from the eigenproblems by using orthogonality and some special integrals with reasonable results.