A mixture approach to the acoustic properties of a macroscopically inhomogeneous porous aluminum in the equivalent fluid approximation.

The acoustic properties of an air-saturated macroscopically inhomogeneous aluminum foam in the equivalent fluid approximation are studied. A reference sample built by forcing a highly compressible melamine foam with conical shape inside a constant diameter rigid tube is studied first. In this process, a radial compression varying with depth is applied. With the help of an assumption on the compressed pore geometry, properties of the reference sample can be modelled everywhere in the thickness and it is possible to use the classical transfer matrix method as theoretical reference. In the mixture approach, the material is viewed as a mixture of two known materials placed in a patchwork configuration and with proportions of each varying with depth. The properties are derived from the use of a mixing law. For the reference sample, the classical transfer matrix method is used to validate the experimental results. These results are used to validate the mixture approach. The mixture approach is then used to characterize a porous aluminium for which only the properties of the external faces are known. A porosity profile is needed and is obtained from the simulated annealing optimization process.

Acoustical properties of air-saturated porous material with periodically distributed dead-end pores.

A theoretical and numerical study of the sound propagation in air-saturated porous media with straight main pores bearing lateral cavities (dead-ends) is presented. The lateral cavities are located at "nodes" periodically spaced along each main pore. The effect of periodicity in the distribution of the lateral cavities is studied, and the low frequency limit valid for the closely spaced dead-ends is considered separately. It is shown that the absorption coefficient and transmission loss are influenced by the viscous and thermal losses in the main pores as well as their perforation rate. The presence of long or short dead-ends significantly alters the acoustical properties of the material and can increase significantly the absorption at low frequencies (a few hundred hertz). These depend strongly on the geometry (diameter and length) of the dead-ends, on their number per node, and on the periodicity along the propagation axis. These effects are primarily due to low sound speed in the main pores and to thermal losses in the dead-end pores. The model predictions are compared with experimental results. Possible designs of materials of a few cm thicknesses displaying enhanced low frequency absorption at a few hundred hertz are proposed.

Acoustics of porous materials with partially opened porosity.

A theoretical and experimental study of the acoustic properties of porous materials containing dead-end (or partially opened) porosity was recently proposed by Dupont, Leclaire, Sicot, Gong, and Panneton [J. Appl. Phys. 110, 094903 (2011)]. The present article provides a description of partially opened porosity systems and their numerous potential applications in the general context of the study of porous materials, the classical models describing them, and the characterization techniques. It is shown that the dead-end pore effect can be treated independently and that the description of this effect can be associated with any acoustic model of porous media. Different theoretical developments describing the dead-end porosity effect are proposed. In particular, a model involving the average effective length of the dead-end pores is presented. It is also shown that if the dead-end effect can be treated separately, the transfer matrix method is particularly well suited for the description of single or multilayer systems with dead-end porosity.

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.

A description of transversely isotropic sound absorbing porous materials by transfer matrices.

A description of wave propagation in transversely isotropic porous materials saturated by air with a recent reformulation of the Biot theory is carried out. The description is performed in terms of a transfer matrix method (TMM). The anisotropy is taken into account in the mechanical parameters (elastic constants) and in the acoustical parameters (flow resistivity, tortuosity, and characteristic lengths). As an illustration, the normal surface impedance at normal and oblique incidences of transversely isotropic porous layers is predicted. Comparisons are performed with experimental results.

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

The present paper deals with the inverse scattering problem involving macroscopically inhomogeneous rigid frame porous media. It consists of the recovery, from acoustic measurements, of the profiles of spatially varying material parameters by means of an optimization approach. The resolution is based on the modeling of acoustic wave propagation in macroscopically inhomogeneous rigid frame porous materials, which was recently derived from the generalized Biot's theory. In practice, the inverse problem is solved by minimizing an objective function defined in the least-square sense by the comparison of the calculated reflection (and transmission) coefficient(s) with the measured or synthetic one(s), affected or not by additive Gaussian noise. From an initial guess, the profiles of the x-dependent material parameters are reconstructed iteratively with the help of a standard conjugate gradient method. The convergence rate of the latter and the accuracy of the reconstructions are improved by the availability of an analytical gradient.

Acoustic probing of the jamming transition in an unconsolidated granular medium.

Experimentally determined dispersion relations for acoustic waves guided along the mechanically free surface of an unconsolidated granular packed structure provide information on the elasticity of granular media at very low pressures that are naturally controlled by the gravitational acceleration and the depth beneath the surface. The experiments confirm recent theoretical predictions that relaxation of the disordered granular packing through nonaffine motion leads to a peculiar scaling of shear rigidity with pressure near the jamming transition corresponding to zero pressure.

Investigation of the phase velocities of guided acoustic waves in soft porous layers.

A new experimental method for measuring the phase velocities of guided acoustic waves in soft poroelastic or poroviscoelastic plates is proposed. The method is based on the generation of standing waves in the material and on the spatial Fourier transform of the displacement profile of the upper surface. The plate is glued on a rigid substrate so that it has a free upper surface and a nonmoving lower surface. The displacement is measured with a laser Doppler vibrometer along a line corresponding to the direction of propagation of plane surface waves. A continuous sine with varying frequencies was chosen as excitation signal to maximize the precision of the measurements. The spatial Fourier transform provides the wave numbers, and the phase velocities are obtained from the relationship between wave number and frequency. The phase velocities of several guided modes could be measured in a highly porous foam saturated by air. The modes were also studied theoretically and, from the theoretical results, the experimental results, and a fitting procedure, it was possible to determine the frequency behavior of the complex shear modulus and of the complex Poisson ratio from 200 Hz to 1.4 kHz, in a frequency range higher than the traditional methods.

Response criteria for clinical trials on osteoarthritis of the knee and hip: a report of the Osteoarthritis Research Society International Standing Committee for Clinical Trials response criteria initiative.

BACKGROUND: The domains of pain, function and patient's global assessment are identified as core variables and frequently measured in clinical trials of patients with osteoarthritis (OA) of the hip and knee. OBJECTIVE: To develop response criteria for OA of hip and knee based on the domains of pain, function and patient's global assessment. METHODS: A methodology was developed by an interaction of the Osteoarthritis Research Society International Standing Committee on Clinical Trials, biostatisticians, pharmaceutical company representatives and health agency representatives. Data from previously conducted placebo-controlled clinical trials were normalized and collated. Data were subset by location of OA (knee, hip), active agent used in the clinical trial (non-steroidal anti-inflammatory drug, other agent) and route of administration (oral, intra-articular). Statistical analysis identified response criteria which best discriminate active agent from placebo. RESULTS: Based on the analysis of data from 14 studies (totaling 1886 patients) and consensus opinion, the optimal responder criteria set differed for location of OA, active agent to be used, and route of administration. Because of nearly identical statistical results, two sets of responder criteria are proposed: (1) 'high' pain response or, alternatively, a 'moderate' response for at least two of three domains: pain, function and patient's global assessment; (2) 'high' response for either pain or function or, alternatively, a 'moderate' response for at least two of three domains: pain, function and patient's global assessment. The sensitivity (i.e., the percentage of responders in the active group) ranged from 52 to 96% and the specificity (i.e., the percentage of nonresponders in the control group) from 47 to 73%. CONCLUSION: Based on data from clinical trials, two sets of responder criteria have been developed that can categorize an individual's responses to treatment in a clinical trial. These responder criteria require validation in additional datasets.

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.