A joint wavenumber-time domain technique to determine the transient acoustic radiation loading on planar vibrators

Abstract

A new method is presented to determine the transient radiation loading on planar vibrators mounted on rigid infinite baffles by using a wave-vector-time domain technique. The specified non-uniform velocity of the vibrator is expressed as a time-dependent modal expansion where the modes are solutions to the homogeneous problem. The time-dependent acoustic modal forces can then be expressed as a sum of the modal radiation impulse responses convolved with the modal velocities. In order to evaluate the radiation impulse responses, the relationship between the Fourier and Hankel transforms of circular symmetric functions is first used to express the Green's function for the problem as an integral over wave-vector space. The integral form of the Green's function is then used to reduce the expression for the radiation impulse responses from a double surface integral over the vibrator to an integral over the wave-vector space. In contrast to the double surface integral, which is difficult to evaluate, the integral over the wave-vector space can be evaluated easily. Numerical results are presented for clamped circular plates and simply supported square plates.