Asymptotic Approach in the Dynamic Problems of the Theory of Elasticity for Bodies with Thin Elastic Inclusions

We propose a unified approach to the investigation of the processes of dynamic interaction of thin elastic inhomogeneities with an elastic medium. It is based on the methods of the theory of singular perturbations in constructing mathematical models of contact of the components of elastic systems with subsequent application of the null-field method for the analysis of the wave fields in composites. This approach proves to be efficient in studying the phenomenon of interaction of elastic waves with local or multiple thin elastic inhomogeneities, as well as in solving the corresponding inverse problems.