P Leclaire

Determination of the viscous characteristic length in air‐filled porous materials by ultrasonic attenuation measurements

The concept of viscous characteristic length is used to describe the acoustical behavior of fluid‐saturated porous media in the high‐frequency regime. A method to determine this parameter consists of measuring the wave attenuation in the high‐frequency limit. This method has already been used for porous materials saturated by superfluid 2He. It is tested in the case of air‐filled absorbent materials in a frequency range of [50–600 kHz]. The thermal characteristic length is assumed to be known or measured independently. Two examples are presented. In the first one the method is usable and the viscous characteristic length Λ is deduced from the high‐frequency behavior of the attenuation per cycle. In the second example, an additional attenuation occurs at high frequencies and only an estimate of Λ can be given. Nevertheless, the estimation appears to be rather accurate. The values obtained by this method are compared to those determined by a nonlinear fit of the dispersion curves.

ULTRASONIC WAVE PROPAGATION IN RETICULATED FOAMS SATURATED BY DIFFERENT GASES : HIGH FREQUENCY LIMIT OF THE CLASSICAL MODELS

Transmission experiments are performed on high porosity reticulated polyurethane foams saturated by different gases at ultrasonic frequencies up to 800 kHz. An excess attenuation is observed at high frequencies, when the wavelength is not sufficiently large compared to the lateral dimensions of the fibers. At lower frequencies, these experiments lead by using classical models of equivalent fluids, to a fast and reliable method for determining the characteristic length Λ.

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 Biots 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.

Guided elastic waves in porous materials saturated by air under Lamb conditions

The propagation of guided elastic waves in porous materials saturated by air under Lamb conditions is studied theoretically and experimentally. The modes are derived from expressing the boundary conditions on the normal and tangential stresses and the displacements at the interfaces between the porous layer and the surrounding fluid. The stresses and the fluid pressure inside the porous medium are obtained from Biot’s equations of poroelasticity. Symmetrical and antisymmetrical modes are found when the porous layer is loaded by the same fluid on both sides. Damping mechanisms include viscous and thermal exchanges between the solid and the fluid, in addition to the classical structural damping. Using an experimental setup based on the generation of standing waves in the layer and taking the spatial Fourier transform of the displacement profile, the phase velocities of three modes were measured for two porous materials in a frequency range between 80 Hz and 4 kHz. The measurements confirm the theoretical pr...

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 Biots 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.

Surface acoustic wave depth profiling of a functionally graded material

The potential and limitations of Rayleigh wave spectroscopy to characterize the elastic depth profile of heterogeneous functional gradient materials are investigated by comparing simulations of the surface acoustic wave dispersion curves of different profile-spectrum pairs. This inverse problem is shown to be quite ill posed. The method is then applied to extract information on the depth structure of a glass-ceramic (alumina) functionally graded material from experimental data. The surface acoustic wave analysis suggests the presence of a uniform coating region consisting of a mixture of Al2O3 and glass, with a sharp transition between the coating and the substrate. This is confirmed by scanning electron microscope with energy dispersive x-ray analysis.

Spatial Laplace transform for complex wavenumber recovery and its application to the analysis of attenuation in acoustic systems

We present a method for the recovery of complex wavenumber information via spatial Laplace transforms of spatiotemporal wave propagation measurements. The method aids in the analysis of acoustic attenuation phenomena and is applied in three different scenarios: (i) Lamb-like modes in air-saturated porous materials in the low kHz regime, where the method enables the recovery of viscoelastic parameters; (ii) Lamb modes in a Duralumin plate in the MHz regime, where the method demonstrates the effect of leakage on the splitting of the forward S1 and backward S2 modes around the Zero-Group Velocity point; and (iii) surface acoustic waves in a two-dimensional microscale granular crystal adhered to a substrate near 100u2009MHz, where the method reveals the complex wavenumbers for an out-of-plane translational and two in-plane translational-rotational resonances. This method provides physical insight into each system and serves as a unique tool for analyzing spatiotemporal measurements of propagating waves.

Study of the bending modes in circular quartz resonators

An experimental and theoretical study of bending modes in a partially electroded circular piezoelectric quartz (AT-cut) with free edge is presented. The quartz is excited by a voltage pulse applied on the electrodes, and its surface is scanned by a laser vibrometer that measures the out-of-plane displacements. The classical theory of bending of thin disks is used to describe the flexural modes at frequencies lower than the first thickness shear resonance (6 MHz). A fairly good agreement is found between experimental and theoretical results for the forced mode shapes and for the resonance frequencies. However, it appears that the two springs used to maintain the disk in position introduce extra clamping conditions. Several source shapes were studied, among which a collection of an arbitrary number of forces is particularly useful. The two-dimensional wavenumber representation shows the presence of anisotropy related to the crystallographic axes at higher frequencies, which is not predicted by the model. The experimental phase velocities are compared to those given by the classical theory of disks and to those of Lamb A0 mode. This study confirms the correspondence at low frequencies between the A0 mode and the bending eigenmodes of a disk with finite size

Study of Circumferential Waves on a Poroelastic Cylinder

J. Descheemaeker1), C. Glorieux1), W. Lauriks1), J. P. Groby2), P. Leclaire3), L. Boeckx4) 1) Laborature Acoustical and Thermal Fysica, Katholieke Universiteit Leuven, Celestijnenlaan 200D, 3001 Heverlee, Belgium. jan.descheemaeker@fys.kuleuven.be 2) Laboratoire d’Acoustique de l’Université du Maine, UMR CNRS 6613, Avenue Olivier Messiaen, 72085 Le Mans Cedex 9, France. 3) Institut Supérieur de l’Automobile et des Transports Université de Bourgogne, 49 Rue Mademoiselle Bourgeois, 58027 Nevers Cedex, France. 4) Huntsman Europe, Everslaan 45, 3078 Everberg, Belgium.