Scattering of Plane Wave by Infinite Hemicylindrical Bosses with Random Radii on a Plane Surface

Abstract

This paper extends previous work on the subject of scattering of a plane wave incident on infinite hemicylindrical bosses of a given radius with periodic spacing to those with random radii; the surface described above may be considered as one possible representation of certain surfaces encountered in practice. The probability-density function of the radius is assumed to be uniform, and the spacing between the centers of adjacent bosses is maintained constant. The spacing is assumed to be so selected that the shadow effects are negligible for the angles of incidence considered in this study. The scalar form of Helmholtz integral formulation was used to solve this problem. Obviously, some of the inherent assumptions in this technique are invalid at the intersection of the hemicylinders and the plane background surface. This work shows that the presence of such discontinuities in the surface does not reduce the usefulness of this simple theoretical approach in calculating the scattered field in a closed form. Some numerical calculations were made using the IBM 1401 computer, and a comparison between the theoretical and experimental results for the scattered acoustic fields from various models of such surfaces supports the above results. [This work is sponsored by the Office of Naval Research.]