Vibration of doubly curved shallow shells with arbitrary boundaries

Abstract The first comprehensive study of shallow shell vibrations subjected to as many as 21 possible boundary conditions is presented. Thin shallow shell theory is used. Relatively accurate results for natural frequencies of doubly-curved shallow shells have been obtained. These can be used for benchmarking by researchers as well as reference data for practicing engineers. The Ritz method is used to solve for natural vibrations of these shells with arbitrary boundary conditions. Natural frequencies are presented for various shell curvatures including spherical, cylindrical and hyperbolic paraboloidal shells.

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