Scattering of plane waves by the junction of transmissive and soft-hard half-planes

Abstract

A uniform asymptotic high frequency solution is developed for the diffraction of plane waves by the junction of two half-planes. One of the half-planes is assumed to be characterized by "Senior's resistive-type" partially transmissive boundary conditions and the other is soft at the top and hard at the bottom. The related boundary-value problem is formulated as a matrix Wiener-Hopf equation which is solved explicitly through the Daniele-Khrapkov method. Some graphical results are also presented.

Line source and point source scattering of acoustic waves by the junction of transmissive and soft–hard half planes

“…The introduction of line source changes the incident field and the method of solution requires a careful analysis in calculating the scattered field. It is observed that when the source is shifted to a large distance our results differ from those of [13] by a multiplicative factor which agrees with, already known, facts given in the literature [2,14]. These observations can also be verified through the graphical results shown in this paper.…”

“…Recently, Büyükaksoy et al [13] considered the scattering of plane waves by a two part surface. They developed a high frequency solution for the diffraction of plane waves by the junction of two half planes.…”

“…One half plane is characterized by partially transmissive boundary conditions and the other is soft at the top and hard at the bottom. In [13], using the Fourier transform technique, the related boundary value problem is reduced to matrix Wiener-Hopf equation, which is solved by the usual Wiener-Hopf procedure [1].…”

“…In the first problem, we have extended the problem of plane wave scattering [13] to the problem of scattering due to a line source situated at (x 0 , y 0 ). It is perhaps the first attempt to look at the line source geometry discussed by [13] involving the matrix Wiener-Hopf approach. The introduction of line source changes the incident field and the method of solution requires a careful analysis in calculating the scattered field.…”

“…These observations can also be verified through the graphical results shown in this paper. It is observed that the graphs of plane wave situation [13] can be recovered by shifting the line source to a large distance. The problem of line source scattering is further extended to the case of point source excitation.…”