Diffraction of elastic waves by three-dimensional cracks of arbitrary shape in a plane

Abstract

A variational-difference method, proposed for solving two-dimensional integral equations of the convolution type in arbitrary regions [1], and highly recommended for solving dynamic contact problems [2,3], is modified for the case of three-dimensional cracks. A general scheme of the method is given and ways of overcoming the difficulties that arise due to the singularity of the kernel, the increase in its symbol at infinity and taking into account the behaviour of the solution at the boundary of the region, are indicated. Calculations are carried out for rectangular and L-shaped cracks which show the effects of the shape of the crack, the angle of incidence, the type of incident wave and the frequency on the reflection coefficient, the radiation pattern and the redistribution of the energy in the reflected field.