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 Zap. Nauchn. Sem. POMI, 2011, Volume 393, Pages 191–210 (Mi znsl4624)

Propagation of normal waves in porous rod with closed pores on boundaries

L. A. Molotkov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: Propagation of normal waves in porous cylindrical rod with closed pores on boundaries is investigated. For this medium the dispersion equation is derived. At low-frequency this equation has two roots which are velocities of the normal waves. While in the cases of elastic rod and of porous rod with opened pores there is unique low-frequence wave. At high-frequency the dispersion equation has one special root. With such velocity the Rayleigh wave propagates along free boundary of the porous medium with closed pores. In this case the Rayleigh wave can exist always.

Key words and phrases: porous rod, closed pores, two rod waves, the Rayleigh wave propagates always.

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English version:
Journal of Mathematical Sciences (New York), 2012, 185:4, 619–629

Bibliographic databases:

Document Type: Article
UDC: 550.24

Citation: L. A. Molotkov, “Propagation of normal waves in porous rod with closed pores on boundaries”, Mathematical problems in the theory of wave propagation. Part 41, Zap. Nauchn. Sem. POMI, 393, POMI, St. Petersburg, 2011, 191–210; J. Math. Sci. (N. Y.), 185:4 (2012), 619–629

Citation in format AMSBIB
\Bibitem{Mol11} \by L.~A.~Molotkov \paper Propagation of normal waves in porous rod with closed pores on boundaries \inbook Mathematical problems in the theory of wave propagation. Part~41 \serial Zap. Nauchn. Sem. POMI \yr 2011 \vol 393 \pages 191--210 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl4624} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2870213} \transl \jour J. Math. Sci. (N. Y.) \yr 2012 \vol 185 \issue 4 \pages 619--629 \crossref{https://doi.org/10.1007/s10958-012-0946-5} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84866543694} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. L. A. Molotkov, “Normal waves in porous layer with opened pores on one boundary and with closed pores on other boundary”, J. Math. Sci. (N. Y.), 185:4 (2012), 611–618
2. L. A. Molotkov, “Propagation of normal waves in porous rod with opened pores on boundaries”, J. Math. Sci. (N. Y.), 185:4 (2012), 630–637
3. G. L. Zavorokhin, “The wave field of a point source that acts on the impermeable stress free boundary of a Biot half-plane”, J. Math. Sci. (N. Y.), 226:6 (2017), 727–733
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