Nonlocal macroscopic theory of sound propagation in rigid-framed porous materials

Denis Lafarge (1) , Navid Nemati (1) , Aroune Duclos (2)

1 LAUM - Laboratoire d'Acoustique de l'Université du Mans
2 LMFA - Laboratoire de Mecanique des Fluides et d'Acoustique

Macroscopic acoustic properties of rigid-framed fluid-saturated porous materials are generally well described by the existing Equivalent-fluid macroscopic theory. This (local) theory, however, is incomplete. Indeed, it describes temporal dispersion but not spatial dispersion. In particular, it is in error when the wavelengths reduce so as to become comparable to the size of an elementary representative volume. This may always be the case at high enough frequencies. This may also be the case at lower frequencies, near resonances, when the material contains structured elements such as Helmholtz resonators. We propose here a new (nonlocal) macroscopic Equivalent-fluid theory that is intended to describe both temporal and spatial dispersion. As such, this theory is expected to be more generally applicable than the conventional one. Here, we solve it by the method of finite elements and compute the wavenumber of the least attenuated mode for a 2D porous medium made of a viscothermal fluid saturating a square array of identical cylindrical-circular rigid solid inclusions. The same least attenuated mode wavenumber is independently computed using a direct multiple scattering technique. Excellent agreement betweeen the two is obtained, validating our proposed new nonlocal Equivalent-fluid theory. Finally, this new theory is illustrated for the case of materials with Helmholtz resonators.

Domaines: Acoustique [physics.class-ph]

Denis Lafarge, Navid Nemati, Aroune Duclos. Nonlocal macroscopic theory of sound propagation in rigid-framed porous materials. Acoustics 2012, Apr 2012, Nantes, France. ⟨hal-00810663⟩