Transient sound radiation from impulsively accelerated bodies

Abstract

This paper presents an integral formulation derived from the Kirchhoff integral theorem for predicting transient sound radiation from an impulsively accelerated body. The acoustic pressure is determined in an explicit form in the frequency domain, and subsequently converted to the time domain through Fourier transformations. This integral formulation can be extended to cases in which the body is subjected to an arbitrarily time-dependent excitation. The transient acoustic pressure is shown to be expressible as a convolution integral of the impulse response function to the time history of the surface velocity of the body. Since there is no relationship between the integral formulations for the exterior and interior regions, solutions for the radiated acoustic pressure in the exterior region are uniquem, even at frequencies corresponding to the eigenfrequencies of the related interior boundary value problem. Analytical results based on this integral formulation agree perfectly with those obtained using other methods for transient sound radiation from an explosively expanding sphere, impulsively accelerated rigid sphere, impulsively accelerated baffled, and unbaffled circular disks. Numerical implementations of the present integral formulation are expected to be more amenable to solution than directly solving the classical Kirchhoff integral formulation in which the frequency and time domains are fully coupled.