The High-Frequency Radiation of Sound from Bodies of Arbitrary Shape

Abstract

In this paper the problem of calculating the sound field in a three-dimensional fluid of infinite extent due to a body of arbitrary shape which is vibrating harmonically is considered. Interest is focused on the case in which the parameter a/λ is large, where a is some characteristic dimension of the radiator. The approach here is to replace the familiar Helmholtz integral formula with an algebraic relationship which is approximately valid on the surface S of the body and to use this relationship to determine the acoustic potential at each point on S, given the normal gradient of the acoustic potential at that point. The acoustic potential exterior to the body is then calculated by numerical evaluation of the Helmholtz formula. By replacing the Helmholtz integral formula on the surface with the algebraic relationship, two troublesome problems associated with integral equation methods are avoided: the need to evaluate singular integrands and the problem of nonuniqueness of the solution at certain frequencies. The approach is evaluated by considering the high-frequency radiation from a finite cylinder up to a value of ka = 15. Comparison data are provided by solving the Helmholtz integral equation using an overdeter-mination method to circumvent nonuniqueness.