Geodesic
On one effictive model of a fractured medium
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 31, Tome 285 (2002), pp. 150-164

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The homogeneous isotropic elastic medium, interested by three systems of fractures on which jumps of stresses are proportional to displacements, is considered. The effective model of this medium is described by equations differing from the corresponding equations of the elastic medium by additional terms. On the basis of the equations of the effective model the wave field excited by some point source is established. The investigation of the integral representation of the wave field shows that the velocities of the longitudinal and transversal waves and of the Rayleigh wave are functions of frequency and wave numbers. The formulas for the phase and group velocites of these waves are derived. 
@article{ZNSL_2002_285_a11,
     author = {L. A. Molotkov},
     title = {On one effictive model of a fractured medium},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {150--164},
     publisher = {mathdoc},
     volume = {285},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_285_a11/}
}
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L. A. Molotkov. On one effictive model of a fractured medium. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 31, Tome 285 (2002), pp. 150-164. http://geodesic.mathdoc.fr/item/ZNSL_2002_285_a11/