Transient Vibration of Thin Elastic Shells

Abstract

A complete solution for the transient response produced by time-dependent surface loads on a thin elastic shell of arbitrary shape is derived by means of the classical method of spectral representation. The solution is expanded in terms of the normal modes of free vibration, and their orthogonality is proved for an arbitrary shell. This method of solution is applicable to any shell for which the free-vibration characteristics (natural frequencies and mode shapes) are known. For application, the response of a hemispherical and a shallow spherical shell to a suddenly applied uniform pressure is calculated and the convergence of the solution is studied in detail. By introducing mode-participation factors, the contribution of each mode to the solution is determined. It is shown that for the shallow shell about four modes are necessary in the solution, while for the hemispherical shell the number of required modes is about fifteen. In either case, when coupled with some available free-vibration analysis, the calculation of the transient response by the method of this paper is well within the practical range of a digital computer.