Transient vibratory response of fluid-loaded shells using convolution integral equations

Abstract

A general time-domain approach is presented to address the transient vibratory response of fluid-loaded shells of arbitrary shape when subjected to specified mechanical and/or acoustical excitations. The approach is based on utilizing an in vacuo eigenvector expansion with time-dependent coefficients to describe the velocity field of the shell. Fluid loading on the shells is described via the use of convolution integrals involving the modal velocity coefficients and mode-dependent acoustic radiation impulse responses. Time domain methods are used to develop a set of universal coupled convolution integral equations for the time-dependent modal velocity coefficients of the shell. Special cases which include a finite plate and an arbitrary shell of revolution are then addressed using the general approach. A reduced set of the coupled convolution integral equations for the time-dependent modal velocity coefficients is obtained for the plate and sets of similar equations are also obtained for the shell.