Homogenization of a coupled problem for sound propagation in porous media

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.