Abstract
This paper presents the development of a finite element for the analysis of spherical shells. Twelve degrees of freedom are taken at each node of the element. The derivation of stiffness and consistent mass matrices is based on the improved shell theory which takes into account the effects of rotary inertia and shear deformation terms. Normal modes and the values of the nondimensional frequency parameter for the free axisymmetric vibration of the spherical shell are calculated using an iterative technique and the orthogonality conditions. These results are then compared with those obtained earlier from the closed form solution of the differential equations of motion. As evident, the present method is found extremely simplified compared to the exact solution of the frequency equation which is transcendental in nature and involves Lagendre functions of complex order. The maximum difference in the results is within 3%–4%. The forced motion of spherical shells subjected to impulsive loadings is also studied in this paper. Detailed numerical results are presented and discussed for various cases of loading conditions.
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