ACOUSTIC TWO-DIMENSIONAL RADIATION AND SCATTERING FROM CYLINDERS USING SOURCE DENSITY, SVD AND FOURIER METHODS

Acoustic two-dimensional harmonic radiation and rigid body scattering from cylinders of arbitrary shape with a plane of symmetry are addressed using an internal line monopole and dipole source distribution along the plane of symmetry. A previously developed least mean square error method is used to solve the Neumann boundary value problem. In contrast to the earlier method, Singular Value Decomposition (SVD) methods are presented to determine the line source harmonic multipole distributions from the specified normal velocity at the cylindrical surface and pressures are simply expressed here as line integrals of the source distributions which in the far field reduce to Fourier transform relationships. Several special examples are presented to illustrate the general spatial characteristics of the source strength distributions for cylinders with widely varying aspect ratios. Exact source strength distributions for circular cylinders are developed using the Fourier transform relationships. The resulting source strength distributions involve spatial derivatives of Dirac delta functions and thus have a vanishingly small region of support about the center of the cylinder. In contrast, for cylinders with large aspect ratios the spatial characteristics of the source strength distributions are more closely matched to the normal velocity distribution.