Investigation of the wave field in an effective model of layered elastic media with slide contact on the interfaces

An effective model of media consisting of two alternating elastic layers with slide contact on the boundaries is investigated. The wave field in this model is represented as Fourier and Mellin integrals. In the Mellin integrals we replace the contours of integration by stationary contours. In the expressions obtained, we change the order of integration and calculate the inner integral. The outer integral is equal to two residues. The corresponding poles are roots of two equations of the sixth order. These roots may be situated in the right half-plane and may be complex or real. The representation obtained of the wave field corresponds to expressions derived by the Smirnov-Sobolev method. Bibliography: 5 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 342, 2007, pp. 187–205.