Scattering of SH-waves by circular and elliptical cylinders-A solution by the hilbert-schmidt method

Abstract

Near- and far-field solutions are presented for the scattering of SH-waves by a circular cavity and a rigid inclusion in infinite space while only far-field results are given for an elliptical geometry. Integral equations define the problem and these are solved in the spirit of Hilbert-Schmi/dt method.The results are given in graphical form and compared with the existing results. Simple geometrical nature of the circle renders an exact solution whereas some approximations are needed to solve the scattering problem if the cross-section of the scatterer is in the shape of an ellipse. Here Bessel functions are used instead of Mathieu functions as is customary in literature concerning elliptical geometries.The results obtained are in fair agreement with the known exact solutions for up to k ı (k:wave number). If k>ı only a good idea of the shape of the scattered wave could be obtained.