Acoustic axisymmetric radiation and scattering from bodies of revolution using the internal source density and Fourier methods

摘要

A brief review is presented of a previously developed mean-square error method to solve the Neumann boundary-value problem corresponding to acoustic axisymmetric harmonic radiation and rigid body scattering from bodies of revolution of arbitrary shape. The method is based on the use of an internal line monopole source distribution along the axis. In contrast to earlier work, the pressures are simply expressed as line integrals of the source distributions which in the far field reduce to Fourier transform relationships. Exact expressions for the source strength distributions for a sphere are developed using the Fourier transform relationships. The source strength distributions involve spatial derivatives of Dirac delta functions and thus have a vanishingly small region of support about the center of the sphere. For cylindrically shaped bodies with large aspect ratios the spatial characteristics of the source strength distributions are shown to be more closely matched to the normal velocity distribution. The use of a discrete series of Dirac delta functions to represent the continuous line source distributions is presented for spherical radiation and scattering problems.