Variational formulation of acoustic radiation from submerged spheroidal shells

Abstract

The surface variational principle (SVP) governing acoustic interaction between a vibrating surface and a surrounding fluid is combined with the dynamic equations governing response of a shell of revolution subjected to axisymmetric harmonic excitation. Ritz series representations are used to represent the spatial dependence of the surface pressure and shell displacement components. Two formulations are presented, with the difference being whether an intermediate computation of the in-vacuo modes is performed. The direct approach, in which the Ritz coefficients are determined directly from the coupled formulation, is used to validate the SVP approach for the case of a spherical shell, whose response is known analytically. For the case of a slender spheroidal shell, the direct approach is compared to the results obtained from the modal approach, in which a truncated set of in-vacuo modes forms the basis functions representing displacement. The aspect ratio and shell properties for this evaluation are selected to be in a range in which eigenvalue veering phenomena between two modes are encountered in the absence of fluid loading. The excitation is taken to be a uniform internal pressure having harmonic temporal variation. It is shown that truncations should include the modes involved in the eigenvalue veering process, even when the excitation frequency is sufficiently low to expect modal truncation to be reasonably accurate for predicting in-vacuo response.