Abstract:
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.
Citation:
L. A. Molotkov, M. N. Perekareva, “Investigation of wave field in effective model of layered elastic-fluid medium”, Mathematical problems in the theory of wave propagation. Part 35, Zap. Nauchn. Sem. POMI, 332, POMI, St. Petersburg, 2006, 175–192; J. Math. Sci. (N. Y.), 142:6 (2007), 2620–2629
\Bibitem{MolPer06}
\by L.~A.~Molotkov, M.~N.~Perekareva
\paper Investigation of wave field in effective model of layered elastic-fluid medium
\inbook Mathematical problems in the theory of wave propagation. Part~35
\serial Zap. Nauchn. Sem. POMI
\yr 2006
\vol 332
\pages 175--192
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl269}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2252994}
\zmath{https://zbmath.org/?q=an:1096.74031}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 142
\issue 6
\pages 2620--2629
\crossref{https://doi.org/10.1007/s10958-007-0150-1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34247244719}
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https://www.mathnet.ru/eng/znsl269
https://www.mathnet.ru/eng/znsl/v332/p175
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