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In this paper we present a detailed study of the theory of free, axisymmetric vibrations of thin elastic spherical shell and demonstrate by experiment that the normal modes of vibration predicted by theory do exist. The theory, which is an expansion of an ancient study by Lamb, predicts the existence of two infinite sets of normal modes, one of which is bounded in frequency and the other unbounded. The first four modes in each set are identified by experiments on a small steel shell.

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In this paper, the theory is developed for the elastic-plastic response of a thin spherical shell to spherically symmetric internal transient pressure loading. Analytic solutions are obtained to the linear, small-deflection equations of motion for shell materials which exhibit various degrees of strain-hardening. Numerical solutions obtained by digital computer are also presented for the equations for large deflections obtained by accounting for shell thinning and increase in radius during deformation. The theory is compared with experiment, and is shown to be in good agreement.