Acoustic wave propagation and internal fields in rigid frame macroscopically inhomogeneous porous media

Abstract

International audienceA wave propagation model in macroscopically inhomogeneous porous media is derived from the alternative Biot's theory of 1962. As a first application, the wave equation is reduced and solved in the case of rigid frame inhomogeneous porous materials. The pressure field, as well as the reflection and transmission coefficients, are obtained numerically using a wave splitting and “transmission” Green's functions approach (WS-TGF). To validate both the wave equation and the method of resolution at normal and oblique incidence, results obtained by the WS-TGF method are compared to those calculated by the classical transfer matrix method and to experimental measurements for a known two-layered porous material, considered as a single inhomogeneous layer. Discussions are then given of the reflection and transmission coefficients for various inhomogeneity profiles as well as of the internal pressure field

Propagation of acoustic waves in a one-dimensional macroscopically inhomogeneous poroelastic material

“…They are designated by C L and C 0 and their x 2 coordinates are L and 0. The porous material M [1] occupies the domain X [1] . The inhomogeneity of the plate occurs along the x 2 direction, i.e., N, k (and v),…”

“…and the total stress tensor, the fluid pressure in the pores, the solid displacement, and solid/fluid relative displacement respectively with r [1] , p [1] , u [1] and w [1] in X [1] . The wavevector k i of the incident plane wave lies in the sagittal plane and the angle of incidence is h i measured counterclockwise from the positive x 1 axis.…”

Reconstruction of material properties profiles in one-dimensional macroscopically inhomogeneous rigid frame porous media in the frequency domain

“…[5][6][7][8] However, the equations of motion for macroscopically inhomogeneous porous materials were only recently derived from the alternative formulation of Biot's theory. 3,4,9,10 In particular, when the assumption of rigid frame is valid, [5][6][7]11 i.e., when the saturating fluid is light, such as air, and the frame is not moving, the equations of motion reduce to those of an equivalent inhomogeneous fluid with spatial and frequency dependent effective density and bulk modulus. 9,10,12 The frequency band suitable to this approximation is bounded at high frequency by the diffusion limit ͑when the wavelength is of the order of, or smaller than the pore size͒, and at low frequency by the Biot characteristic frequency, below the which the skeleton may vibrate.…”

“…3,4,9,10 In particular, when the assumption of rigid frame is valid, [5][6][7]11 i.e., when the saturating fluid is light, such as air, and the frame is not moving, the equations of motion reduce to those of an equivalent inhomogeneous fluid with spatial and frequency dependent effective density and bulk modulus. 9,10,12 The frequency band suitable to this approximation is bounded at high frequency by the diffusion limit ͑when the wavelength is of the order of, or smaller than the pore size͒, and at low frequency by the Biot characteristic frequency, below the which the skeleton may vibrate. Under these conditions, the reflected and transmitted pressure fields as well as the internal pressure field can be numerically determined 9,10 by means of the wave splitting and transmission Green's functions method.…”

Quantifying the through-thickness asymmetry of sound absorbing porous materials

“…This may lead to macroscopic asymmetrical behaviors. 7 Unfortunately, there is no mean of simply quantifying the level of asymmetry (or symmetry) of a single porous layer.…”