Diffraction of torsional wave or plane harmonic compressional wave by an annular rigid disc

Abstract

In this paper we have considered the following two problems. Firstly the diffraction of normally incident SH waves by a rigid annular disc situated at the interface of two elastic half-spaces is considered. The solution of the problem is reduced into the solution of triple integral equations involving Bessel functions. The solution of the triple integral equations is reduced into Fredholm integral equations of th second kind. By finding the solution of the Fredholm integral equation, the numerical values for the moment required to produce the rotation of disc are obtained. Secondly, the problem of diffraction of plane harmonic compressional wave by an annular circular disc embedded in an infinite elastic space is considered. The annular disc is assumed to be perfectly welded with the infinite solid. The solution of the problem is reduced into the solution of Fredholm integral equation of the second kind. The Fredholm integral equation is solved numerically and the numerical values for the couple applied on the disc are obtained.