Interaction of plane harmonic waves with inclusions in the elastic space

We solve the problem of interaction of harmonic elastic waves with a thin elastic inclusion in the form of a strip in an unbounded body (matrix) under the conditions of plane deformation. In view of the small thickness of the inclusion, it is assumed that its bending and shear displacements coincide with the displacements of the corresponding points of its median plane. The displacements of the medium plane are found from the corresponding equations of the theory of plates. The method of solution is based on the representation of displacements in the form of singular solutions of the Lamé equations with subsequent determination of the unknown jumps from singular integral equations. The indicated integral equations are solved numerically (by the collocation method). The relations for the approximate evaluation of the stress intensity factors at the ends of the inclusion are obtained.