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Vinh, Pc; Tung, Dx; Kieu, Nt

Homogenization of very rough two-dimensional interfaces separating two dissimilar poroelastic solids with time-harmonic motions. (English) Zbl 1440.74344

Math. Mech. Solids 24, No. 5, 1349-1367 (2019).
Summary: The homogenization of a very rough three-dimensional interface separating two dissimilar isotropic poroelastic solids with time-harmonic motions was considered by R. P. Gilbert and M.-J. Ou [“Acoustic wave propagation in a composite of two different poroelastic materials with a very rough periodic interface: a homogenization approach”, Int. J. Multiscale Comput. Eng. 1, No. 4, 431–440 (2003; doi:10.1615/intjmultcompeng.v1.i4.80); also in: Proceedings of the international conference on acoustics, mechanics, and the related topics of mathematical analysis, 2002. River Edge, NJ: World Scientific. 157–163 (2002; Zbl 1053.74548)]. The homogenized equations have been derived; however, they are still in implicit form. In this paper, the homogenization of a very rough two-dimensional interface separating two dissimilar generally anisotropic poroelastic solids with time-harmonic motions is investigated. The main aim of the investigation is to derive homogenized equations in explicit form. By employing the homogenization method, along with the matrix formulation of the poroelasticity theory, the explicit homogenized equations have been derived. Since these equations are totally explicit, they are very useful in solving practical problems. As an example proving this, the reflection and transmission of SH waves at a very rough interface of the tooth-comb type is considered. The closed-form analytical expressions of the reflection and transmission coefficients are obtained. Based on these expressions, the dependence of the reflection and transmission coefficients on some parameters is examined numerically.

MSC:

74Q10 Homogenization and oscillations in dynamical problems of solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74J20 Wave scattering in solid mechanics
74A50 Structured surfaces and interfaces, coexistent phases

Keywords:

homogenization; homogenized equations; very rough interfaces; fluid-saturated porous media; SH waves

Citations:

Zbl 1053.74548
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Full Text: DOI

References:

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