Geodesic
An asymptotic model for the far-field of Rayleigh wave in multilayered plate
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 4, pp. 74-86

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An asymptotic model is proposed, which allows to calculate far-field of Rayleigh wave in an infinite multilayered plate subjected to non-stationary surface load. The model is derived by using of the standard asymptotic techniques. As a result, a system of two one-dimensional integro-differential equations (head system) is obtained, which describes the propagation of Rayleigh waves along the plate surfaces. For the decaying wave fields in layers the boundary problems for elliptic equations are obtained. Head system is closed and can be solved separately, thus the problem is reduced to one-dimensional one. By deriving of the model it is assumed that the elastic properties of the layers satisfy the following condition: the speed of Rayleigh wave, for which the model is derived, is less than the shear wave speeds in all the layers. 
@article{ISU_2011_11_4_a9,
     author = {M. V. Wilde and L. Yu. Kossovich},
     title = {An asymptotic model for the far-field of {Rayleigh} wave in multilayered plate},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {74--86},
     publisher = {mathdoc},
     volume = {11},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2011_11_4_a9/}
}
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M. V. Wilde; L. Yu. Kossovich. An asymptotic model for the far-field of Rayleigh wave in multilayered plate. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 4, pp. 74-86. http://geodesic.mathdoc.fr/item/ISU_2011_11_4_a9/