Geodesic
Investigation of wave field in effective model of layered elastic medium with slide contact on interfaces
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 36, Tome 342 (2007), pp. 187-205

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The ellective model of the medium consisting of two alternating elastic layers with slide contact on boundaries is investigated. The wave field in this model is represented as Fourier and Mellin integrals. In the Mellin integrals we replace contour of integration by a stationary contours. In the obtained expressions, we rearrange the integrals and calculate the inner integral. The external integral is equal to two residues. The corresponding poles are roots of two equations of sixth order. These roots can be situated at the right half-plane and can be complex or real. The obtained representation of the wave field corresponds to expressions derived by the method of Smirnov–Sobolev. 
@article{ZNSL_2007_342_a8,
     author = {L. A. Molotkov},
     title = {Investigation of wave field in effective model of layered elastic medium with slide contact on interfaces},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {187--205},
     publisher = {mathdoc},
     volume = {342},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_342_a8/}
}
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L. A. Molotkov. Investigation of wave field in effective model of layered elastic medium with slide contact on interfaces. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 36, Tome 342 (2007), pp. 187-205. http://geodesic.mathdoc.fr/item/ZNSL_2007_342_a8/