Transient structural acoustics: The impact excitation of fluid loaded spherical shells via a generalized modal radiation impulse response approach

Abstract

A generalized modal radiation impulse response approach based on in vacuo eigenfunction expansions was recently developed to evaluate the space-time surface velocity vector field, instantaneous power, and energy transfer into a fluid resulting from the space-time force distribution of fluid loaded shell and panel structures. The impact excitation of a fluid loaded spherical shell is addressed in this paper to illustrate the generalized modal approach for an analytically tractable problem. In vacuo eigenfunctions of spherical shells are presented and a modal based pressure impulse response approach is developed to evaluate the associated transient pressure field. Coupled shell and acoustic field equations for the modal velocities in the time and frequency domains are developed to evaluate the modal velocities via the use of modal radiation impulse responses and impedances. The numerical results are presented to illustrate the characteristics of modal pressure impulse responses and modal radiation impulse responses, which couple the modal velocities, as well as the modal coupling effects of the fluid on the modal velocities, the energy transfer into a fluid, and the far field pressures for the breathing mode, rigid body mode, and higher order shell modes.