Acoustic time-dependent energy from force excited fluid loaded elastic shell/panel structures via a generalized modal radiation impulse response approach

A generalized modal radiation impulse response approach is presented to evaluate the space-time surface velocity field, time-dependent force, instantaneous power, and energy transfer into a fluid resulting from the space-time force distribution of fluid loaded plate, shell, and panel structures. The basic approach utilizes the in vacuo eigenvectors of the structure to determine the in fluid response of the structure. Self-and mutual modal radiation impulse responses that couple the modal velocities of the fluid loaded structures are used to express the modal time-dependent velocities as a set of coupled convolution integral equations. A canonical fluid loaded single degree of freedom vibrator is addressed to illustrate the basic approach. A fluid loaded admittance impulse response is introduced and plays a central role in the analysis to evaluate the normal velocity resulting from a specified external force. A time-dependent energy equation is also introduced to investigate the temporal evolution of the internal energy loss and the energy transfer to the fluid. Numerical results are presented for an impulsive excitation of the fluid loaded single degree of freedom vibrator which serves as a canonical problem for investigating the response of complex structures.