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D. A. Kosmodem’yanskii and A. S. Shamaev, "Spectral Properties of Some Problems in Mechanics of Strongly Inhomogeneous Media," Mech. Solids. 44 (6), 874-906 (2009)
Year 2009 Volume 44 Number 6 Pages 874-906
DOI 10.3103/S0025654409060077
Title Spectral Properties of Some Problems in Mechanics of Strongly Inhomogeneous Media
Author(s) D. A. Kosmodem’yanskii (Lomonosov Moscow State University, GSP-2, Leninskie Gory, Moscow, 119992 Russia)
A. S. Shamaev (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, sham@rambler.ru)
Abstract In the present paper, we derive effective dynamic equations and analyze the spectral properties of strongly inhomogeneous media such as elastic porous materials saturated by a fluid and two-fluid mixtures (suspensions). We also study the structure of the natural vibration spectrum of bounded volumes for several effective models and the convergence rate of solutions of the original boundary value problems for two-phase media to the corresponding solutions of the effective (homogenized) boundary value problems.
Keywords strongly inhomogeneous media, homogenization theory, two-scale convergence, natural vibration spectrum
References
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Received 19 July 2006
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