A WAVE-VECTOR-TIME-DOMAIN TECHNIQUE TO DETERMINE THE TRANSIENT ACOUSTIC RADIATION LOADING ON CYLINDRICAL VIBRATORS IN AN INVISCID FLUID WITH AXIAL-FLOW

A wave-vector-time-domain method that was used to obtain the transient acoustic radiation loading on vibrating finite cylinders is extended to include the effects of the presence of inviscid axial flow. The method is based on the use of a time-dependent modal expansion for the velocity of the vibrator which has infinite rigid extensions. The solution to the boundary value problem for the pressure is first obtained in wave-vector-time space. The time-dependent modal forces are then expressed as a sum of the modal radiation impulse responses of the finite cylinder convolved with the time-dependent modal velocities. The modal radiation impulse responses are obtained by using the impulse responses of an infinite cylinder and the modes in wave-vector space. The approach can thus be easily used to obtain the radiation impulse responses for various boundary conditions, length to radius ratios, and arbitrary space- and time-dependent surface velocities. Numerical results are presented for a wide range of Mach numbers and for length to radius ratios of simple supported cylindrical shells.