Advances in Differential Equations

Homogenization of a coupled problem for sound propagation in porous media

François Alouges, Adeline Augier, Benjamin Graille, and Benoît Merlet

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In this paper we study the acoustic properties of a microstructured material such as glass, wool, or foam. In our model, the solid matrix is governed by linear elasticity and the surrounding fluid obeys the Stokes equations. The microstructure is assumed to be periodic at some small scale ${\varepsilon}$ and the viscosity coefficient of the fluid is assumed to be of order ${\varepsilon}^2$. We consider the time-harmonic regime forced by vibrations applied on a part of the boundary. We use the two-scale convergence theory to prove the convergence of the displacements to the solution of a homogeneous problem as the size of the microstructure shrinks to 0.

Article information

Adv. Differential Equations, Volume 17, Number 11/12 (2012), 1001-1030.

First available in Project Euclid: 17 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B27: Homogenization; equations in media with periodic structure [See also 74Qxx, 76M50] 74F10: Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)


Alouges, François; Augier, Adeline; Graille, Benjamin; Merlet, Benoît. Homogenization of a coupled problem for sound propagation in porous media. Adv. Differential Equations 17 (2012), no. 11/12, 1001--1030.

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