Diffraction of shear waves by an edge crack in an elastic wedge

Low frequency diffraction of plane harmonic shear (SH) wave by an edge crack in an elastic wedge of arbitrary vertex angle is studied. Kontorowich-Lebedev transform is used to solve the mixed boundary value problem under consideration. For low frequency case, i.e. wavelength large compared to the length of the crack, the displacement field is obtained by successive approximation of the resulting Wiener-Hopf equation. For the limiting case of an elastic half space the results agree with those obtained by the method of matched asymptotic expansions.