Diffraction of elastic waves by a penny-shaped crack

The diffraction of axisymmetric, harmonic elastic waves by a circular crack is considered. It is shown that the potential functions for the diffracted waves can be obtained from the solution of a pair of dual integral equations. The dual equations are transformed into integral equations of the second kind suitable for iteration at low frequencies. The principle of contraction mapping is used to discuss the convergence of the iteration scheme. The solution satisfies an edge condition.