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We present a solution methodology for dynamic problems of the theory of elasticity based on the fundamental (F)-solutions approach for layers and semilayers containing cavities. Under the proposed solution framework boundary-value problems for three-dimensional cylindrical bodies are reduced to well-studied systems of one-dimensional singular integral equations. With the aid of the integral Fourier transform in time, we study the problem of impulse loading at the sides of cavities. We also demonstrate how the combination of the proposed methodology with the approach of reflections can be used for the solution of analogous problems for semi-infinite layers.

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