Acoustic transients from planar axisymmetric vibrators using the impulse response approach

Abstract

A generalized impulse response approach is developed to evaluate the transient pressures which result from a general time dependent axisymmetric velocity of a planar vibrator, e.g., a membrane, plate, or disk transducer. The approach, which is based on expressing the velocity distribution in terms of a set of radial orthonormal functions, leads to the pressure being expressed as a sum of convolution integrals which involve the time dependent coefficients of the orthonormal functions and generalized impulse responses. As a specific case of interest and importance, the generalized impulse response is developed for a radiator in which the orthonormal functions are zeroth-order Bessel functions of the first kind. A series representation for the impulse response as a function of an arbitrary spatial wavenumber is obtained via the use of the addition theorem for Bessel functions. Finally, some numerical results are presented to illustrate the effect of a nonuniform spatial velocity on the on-axis nearfield pressures of a pulsed radiator.