Diffraction of shear waves on cylindrical inclusions and cavities in an elastic half space

Abstract

Dynamic problems of the steady-state oscillations of a half space with different types of cylindrical homogeneities (cavities, rigid and stiff inclusions) are examined. The boundary of the half space is assumed to be fixed or free of forces. A harmonic shear wave radiating from infinity or a concentrated harmonic source may be radiators of the exciting wave field. Integral representations of displacement amplitudes, which automatically satisfy fixity conditions on the boundary of the half space and radiation conditions at infinity are constructed. The edge problems are reduced to Fredholm integral equations of the second kind and to singular integral equations. Selection of additional conditions for the latter is substantiated. Some computer-generated results are presented.