Geodesic
Investigation of wave field in effective model of layered elastic-fluid medium
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 35, Tome 332 (2006), pp. 175-192 Cet article a éte moissonné depuis la source Math-Net.Ru

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For the medium consisting of alternating elastic and fluid layers, the effective model is constructed and investigated. This model is a special case of the Biot medium. The wave field is represented as Fourier and Mellin integrals. In the Mellin integral we replace contour of integration by a stationary contour. 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 fourth order. These roots are situated at the right half-plane and can be complex or real. The obtained representation for the wave field corresponds to the expressions derived by the method of Smirnov–Sobolev. 
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L. A. Molotkov; M. N. Perekareva. Investigation of wave field in effective model of layered elastic-fluid medium. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 35, Tome 332 (2006), pp. 175-192. http://geodesic.mathdoc.fr/item/ZNSL_2006_332_a11/

[1] L. A. Molotkov, “Ob ekvivalentnosti sloisto-periodicheskikh i transversalno-izotropnykh sred”, Zap. nauchn. semin. LOMI, 89, 1979, 219–233 | MR | Zbl

[2] L. A. Molotkov, A. V. Bakulin, “Effektivnaya model sloistoi uprugo-zhidkoi sredy kak chastnyi sluchai modeli Bio”, Zap. nauchn. semin. POMI, 230, 1995, 172–195 | MR | Zbl

[3] L. A. Molotkov, A. E. Khilo, “Issledovanie odnofaznykh i mnogofaznykh effektivnykh modelei, opisyvayuschikh periodicheskie sredy”, Zap. nauchn. semin. LOMI, 140, 1984, 105–123

[4] M. Schoenberg, “Wave propagating in alternating fluid and solid layers”, Wave Motion, 6 (1984), 303–320 | DOI | Zbl

[5] T. J. Plona, K. W. Winkler, M. Schoenberg, “Acoustic waves in alternating fluid/solid layers”, J. Acoust. Soc. Amer, 81:5 (1987), 1227–1234 | DOI

[6] L. A. Molotkov, Issledovanie rasprostraneniya voln v poristykh i treschinovatykh sredakh na osnove effektivnykh modelei Bio i sloistykh sred, Nauka, SPb, 2001

[7] L. A. Molotkov, “O zatukhanii voln v effektivnoi modeli, opisyvayuschei poristye i treschinovatye sredy, nasyschennye zhidkostyu”, Zap. nauchn. semin. POMI, 297, 2003, 216–229 | MR | Zbl

[8] S. L. Sobolev, “Nekotorye voprosy teorii rasprostraneniya kolebanii, XII”, V kn.: F. Frank i R. Mizes, Differentsialnye i integralnye uravneniya matematicheskoi fiziki, L.–M., 1937, 468–617