Scattering and diffraction of SH waves by a finite crack: an analytical solution

The diffraction of SH waves by a finite plane crack is studied. The classical Sommerfeld solution for a semi-infinite straight reflecting screen is used as a building block to calculate the diffracted field generated by a finite crack. The solution is derived from the analysis of the behaviour of diffracted waves. These waves, which are first generated at the edges of the crack, travel along the surfaces and are diffracted/reflected at the opposite edge. By iteratively taking into account the contribution to the total field of these travelling waves, an infinite series with a known limit is constructed, leading to an approximate analytical solution for the case of a finite plane crack. This solution is virtually exact for large frequencies and it is very good for incoming wavelengths of up to four times the size of the crack. Since the solution is explicit the computational cost is very low. Both frequency and time-domain results are included.