On a Method for Solving Boundary Value Problems of the Dynamical Theory of Elasticity in a Quarter Plane

In the paper, using the coordinate block element method, an exact solution in the first quadrant of a plane boundary value problem of the second kind for the dynamic Lame elasticity equations is constructed for the first time and is expanded in terms of solutions of boundary value problems for the Helmholtz equation. In the earlier paper of the authors, the solution was constructed by an integro-differential method. Exact solutions of vector boundary value problems using scalar ones in nonclassical domains make it possible to simplify the solutions of boundary value problems in media of complex rheology and to get information on some processes and phenomena in mechanics and physics that was previously overlooked when other approaches were used.