A semi-analytical method of solving problems of the high-frequency diffraction of elastic waves by cracks

A semi-analytical approach is proposed for constructing an effective solution of the problem of high-frequency diffraction of elastic waves by a crack in an isotropic plane. It essentially consists of separating the strongly oscillating solution of the main integral equation of the problem, which holds uniformly over the whole crack length for high oscillation frequencies. The solution is sought in the form of the product of a strongly oscillating function, corresponding to the qualitative behaviour of the solution, and a certain slowly varying unknown modulating function, which also becomes the main unknown in the initial equation. It is shown that, to find this new unknown function correctly, it is sufficient to take an order of magnitude smaller number of collocation points than for the direct approach.