Advances in Differential Equations

Homogenization of a coupled problem for sound propagation in porous media

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

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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

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

Dates
First available in Project Euclid: 17 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355702937

Mathematical Reviews number (MathSciNet)
MR3013411

Zentralblatt MATH identifier
1261.35014

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

Citation

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. https://projecteuclid.org/euclid.ade/1355702937.


Export citation