On Vibrations of Shallow Spherical Shells

Abstract

The vibration analysis of shallow spherical shells is extended to (a) frequencies of the order of magnitude of the first thickness-shear mode in an infinite plate and (b) moderately thick shells. A tenth-order system of three uncoupled differential equations is derived, which govern the nonsymmetric dynamic deformation of a shallow spherical shell subjected to arbitrary time-dependent surface loads, and separable solutions are obtained in terms of Bessel functions. As an example, a frequency equation is deduced for the determination of natural frequencies higher than those accurately predicted by the classical theory for free vibration of a shallow spherical cap with a clamped edge.