Enhancing rigid frame porous layer absorption with three-dimensional periodic irregularities.

This papers reports a three-dimensional (3D) extension of the model proposed by Groby et al. [J. Acoust. Soc. Am. 127, 2865-2874 (2010)]. The acoustic properties of a porous layer backed by a rigid plate with periodic rectangular irregularities are investigated. The Johnson-Champoux-Allard model is used to predict the complex bulk modulus and density of the equivalent fluid in the porous material. The method of variable separation is used together with the radiation conditions and Floquet theorem to derive the analytical expression for the acoustic reflection coefficient from the porous layer with 3D inhomogeneities. Finite element method is also used to validate the proposed analytical solution. The theoretical and numerical predictions agree well with the experimental data obtained from an impedance tube experiment. It is shown that the measured acoustic absorption coefficient spectrum exhibits a quasi-total absorption peak at the predicted frequency of the mode trapped in the porous layer. When more than one irregularity per spatial period is considered, additional absorption peaks are observed.

Scattering of acoustic waves by macroscopically inhomogeneous poroelastic tubes.

Wave propagation in macroscopically inhomogeneous porous materials has received much attention in recent years. For planar configurations, the wave equation, derived from the alternative formulation of Biot's theory of 1962, was reduced and solved recently: first in the case of rigid frame inhomogeneous porous materials and then in the case of inhomogeneous poroelastic materials in the framework of Biot's theory. This paper focuses on the solution of the full wave equation in cylindrical coordinates for poroelastic tubes in which the acoustic and elastic properties of the poroelastic tube vary in the radial direction. The reflection coefficient is obtained numerically using the state vector (or the so-called Stroh) formalism and Peano series. This coefficient can then be used to straightforwardly calculate the scattered field. To validate the method of resolution, results obtained by the present method are compared to those calculated by the classical transfer matrix method in the case of a two-layer poroelastic tube. As an example, a long bone excited in the sagittal plane is considered. Finally, a discussion is given of ultrasonic time domain scattered field for various inhomogeneity profiles, which could lead to the prospect of long bone characterization.

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

Wave propagation in macroscopically inhomogeneous porous materials has received much attention in recent years. The wave equation, derived from the alternative formulation of Biot's theory of 1962, was reduced and solved recently in the case of rigid frame inhomogeneous porous materials. This paper focuses on the solution of the full wave equation in which the acoustic and the elastic properties of the poroelastic material vary in one-dimension. The reflection coefficient of a one-dimensional macroscopically inhomogeneous porous material on a rigid backing is obtained numerically using the state vector (or the so-called Stroh) formalism and Peano series. This coefficient can then be used to straightforwardly calculate the scattered field. To validate the method of resolution, results obtained by the present method are compared to those calculated by the classical transfer matrix method at both normal and oblique incidence and to experimental measurements at normal incidence for a known two-layers porous material, considered as a single inhomogeneous layer. Finally, discussion about the absorption coefficient for various inhomogeneity profiles gives further perspectives.

Enhancing the absorption coefficient of a backed rigid frame porous layer by embedding circular periodic inclusions.

The acoustic properties of a porous sheet of medium static air flow resistivity (around 10,000 N m s(-4)), in which a periodic set of circular inclusions is embedded and which is backed by a rigid plate, are investigated. The inclusions and porous skeleton are assumed motionless. Such a structure behaves like a multi-component diffraction grating. Numerical results show that this structure presents a quasi-total (close to unity) absorption peak below the quarter-wavelength resonance of the porous sheet in absence of inclusions. This result is explained by the excitation of a complex trapped mode. When more than one inclusion per spatial period is considered, additional quasi-total absorption peaks are observed. The numerical results, as calculated with the help of the mode-matching method described in this paper, agree with those calculated using a finite element method.

Transmission of ultrasonic waves through porous layers of high flow resistivity saturated by air.

Transmission of ultrasonic waves through porous materials of high flow resistivity and porosity (in contact with air at both faces) is modelled and measured for an open-bubble foam at normal and oblique incidence. The importance of the airborne wave and the differences with the case of an elastic nonporous solid are demonstrated. A simple method to measure the shear modulus and the Poisson coefficient of the frame is suggested for similar materials.

Ultrasonic wave propagation in porous media: determination of acoustic parameters and high frequency limit of the classical models.

Results on the ultrasonic wave propagation in porous materials are presented with emphasis on the measurement of acoustic parameters and on the discrepancy between experimental results and theoretical predictions for the attenuation at high frequencies. This discrepancy can be observed in Biomedical Engineering where the propagation in different sorts of bones is studied as well as in the fields of Geophysics and Material Science. In the present study, the slow wave propagation in polyurethane foams saturated by different gases is investigated in a frequency range of [70-800 kHz]. Methods are presented to determine the tortuosity and the viscous and thermal characteristic lengths. The experimental results, obtained using standard ultrasonic and vacuum equipments, show that an excess attenuation occurs when the wavelength is not sufficiently large compared to the lateral dimensions of the fibers. This effect constitutes a limit of the classical models of equivalent phases. It is evaluated with the help of a model of ultrasonic scattering. A numerical simulation of osteoporosis using Biot's model is also presented.