The diffraction of SH waves by an arbitrary shaped crack in two dimensions

In this paper we consider the two-dimensional scalar scattering problem for Helmholtz’s equation exterior to a smooth open arc of general shape. The problem has a number of physical applications including the diffraction of sound by a rigid barrier immersed in a compressible fluid and by a crack in an elastic solid which supports a state of anti-plane strain (SH-motion). The mathematical method used here is the crack Green function method introduced by G. R. Wickham. This enables the scattering problem to be reduced to the solution of a Fredholm integral equation of the second kind with a continuous kernel. The numerical solution of this equation is discussed and a number of examples are computed.