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Averaged model of vibration of a damped elastic medium

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Ukrainian Mathematical Journal Aims and scope

We consider an initial boundary-value problem used to describe the nonstationary vibration of an elastic medium with large number of small cavities filled with a viscous incompressible fluid. We study the asymptotic behavior of the solution in the case where the diameters of the cavities tend to zero, their number tends to infinity, and the cavities occupy a three-dimensional region. We construct an averaged equation to describe the leading term of the asymptotics. This equation serves as a model of propagation of waves in various media, such as damped soil, rocks, and some biological tissues.

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Authors and Affiliations

  1. Institute for Low-Temperature Physics and Engineering, Ukrainian National Academy of Sciences, Kharkov, Ukraine

    M. V. Goncharenko & E. Ya. Khruslov

Authors
  1. M. V. Goncharenko
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  2. E. Ya. Khruslov
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 10, pp. 1309–1329, October, 2010.

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Goncharenko, M.V., Khruslov, E.Y. Averaged model of vibration of a damped elastic medium. Ukr Math J 62, 1519–1542 (2011). https://doi.org/10.1007/s11253-011-0447-6

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  • DOI: https://doi.org/10.1007/s11253-011-0447-6

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