Theory of sound propagation in porous media allowing for spatial dispersion

Abstract

We present here a new nonlocal theory of long-wavelength sound propagation in rigid-framed porous media saturated with a viscothermal fluid. For unbounded macroscopically homogeneous media, isotropic or having a preferred wave-guide axis; the symmetry of the problem suggests that the wave propagation should be described in terms of an Equivalent-fluid having frequency- and wavenumber-dependent density and bulk modulus. Based on considerations borrowed from electromagnetic theory, a definite procedure is proposed to compute these two quantities from microstructure. Using the finite element method to implement the computation procedure, the possible relevance of the new theory is tested in two simple types of 2D geometries: that of the so-called ultrasonic metamaterials made of an array of Helmholtz resonators, and that of an array of cylindrical circular solid inclusions.