Abstract
The results of the transverse frequency analysis of complete spherical shells by elastic theory and classical, improved, and membrane shell theories are compared. Fundamental frequencies less than the lowest pure shear frequency of a solid sphere are shown to be accurately predicted by classical shell theory. For shells of vanishing thickness, the equations of elasticity are shown to reduce exactly to the membrane shell equations. Evaluation of the distortional energy associated with each transverse frequency allows a classification of the three frequencies of transverse vibration in each mode shape. This classification is based on predictions by improved shell theory as to the dominant character of the behavior associated with extensional, bending or shear distortion.
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