ASYMPTOTIC BEHAVIOR OF A SOLUTION TO THE PROBLEM OF THE SCATTERING OF AN ELASTIC WAVE BY A THIN-WALLED FOREIGN INCLUSION

The stress-strain state of an elastic solid with a foreign local inclusion of small thickness subjected to the action of an elastic wave is investigated by the method of matching of asymptotic expansions. It is assumed that the inclusion is "adhered" to the medium and the ratio of their Lame coefficients is a quantity of order O(1) with respect to e, where e is the relative thickness of the inclusion. The behavior of the solutions in the remote zone and near the edge of the inclusion (where the boundary layer phenomenon manifests itself) is determined. Previously, with similar assumptions, the scalar problem of scattering of shear waves by a semi-infinite inclusion of constant thickness [1] and the two-dimensional static problem [2, 3] were studied.