Aroune Duclos

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.

Absorption of a rigid frame porous layer with periodic circular inclusions backed by a periodic grating

The acoustic properties of a periodic rigid frame porous layer with multiple irregularities in the rigid backing and embedded rigid circular inclusions are investigated theoretically and numerically. The theoretical representation of the sound field in the structure is obtained using a combination of multipole method that accounts for the periodic inclusions and multi-modal method that accounts for the multiple irregularities of the rigid backing. The theoretical model is validated against a finite element method. The predictions show that the acoustic response of this structure exhibits quasi-total, high absorption peaks at low frequencies which are below the frequency of the quarter-wavelength resonance typical for a flat homogeneous porous layer backed by a rigid plate. This result is explained by excitation of additional modes in the porous layer and by a complex interaction between various acoustic modes. These modes relate to the resonances associated with the presence of a profiled rigid backing and rigid inclusions in the porous layer.

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 100 MHz, 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.

Surface waves in granular phononic crystals.

The existence of surface elastic waves at a mechanically free surface of granular phononic crystals is studied. The granular phononic crystals are made of spherical particles distributed periodically on a simple cubic lattice. It is assumed that the particles are interacting by means of normal, shear, and bending contact rigidities. First, Rayleigh-type surface acoustic waves, where the displacement of the particles takes place in the sagittal plane while the particles possess one rotational and two translational degrees of freedom, are analyzed. Second, shear-horizontal-type waves, where the displacement of the particles is normal to the sagittal plane while the particles possess one translational and two rotational degrees of freedom are studied. The existence of zero-group-velocity surface acoustic waves of Rayleigh type is theoretically predicted and interpreted. A comparison with surface waves predicted by the reduced Cosserat theory is performed, and some limitations of the latter are established.

Including frequency-dependent attenuation for the deconvolution of ultrasonic signals

Ultrasonic non-destructive testing (NDT) is a standard process for detecting flaws or discontinuities in industrial parts. A pulse is emitted by an ultrasonic transducer through a material, and a reflected wave is produced at each impedance change. In many cases, echoes can overlap in the received signal and deconvolution can be applied to perform echo separation and to enhance the resolution. Common deconvolution techniques assume that the shape of the echoes is invariant to the propagation distance. This can cause poor performances with materials such as plastics or composites, in particular because acoustic propagation suffers from frequency-dependent attenuation. In geophysics, biomedical imaging or NDT, various frequency-dependent attenuation models have been proposed under different formulations. This communication compares the related possible constructions in order to account for attenuation in deconvolution methods. Especially, we introduce a discrete model for the data, that includes an attenuat...

Deterministic and statistical characterization of rigid frame porous materials from impedance tube measurements

A method to characterize macroscopically homogeneous rigid frame porous media from impedance tube measurements by deterministic and statistical inversion is presented. Equivalent density and bulk modulus of the samples are reconstructed with the scattering matrix formalism, and are then linked to its physical parameters via the Johnson-Champoux-Allard-Lafarge model. The model includes six parameters, namely the porosity, tortuosity, viscous and characteristic lengths, and static flow and thermal permeabilities. The parameters are estimated from the measurements in two ways. The first one is a deterministic procedure that finds the model parameters by minimizing a cost function in the least squares sense. The second approach is based on statistical inversion. It can be used to assess the validity of the least squares estimate, but also presents several advantages since it provides valuable information on the uncertainty and correlation between the parameters. Five porous samples with a range of pore properties are tested, and the pore parameter estimates given by the proposed inversion processes are compared to those given by other characterization methods. Joint parameter distributions are shown to demonstrate the correlations. Results show that the proposed methods find reliable parameter and uncertainty estimates to the six pore parameters quickly with minimal user input.

Ultrasonic measurements by means of continuous waves in a foam saturated with air

The study of porous materials has always been of great interest. Several characterization methods have been developed by means of ultrasonic waves, mainly because of their non-invasive behavior. A typical set-up involves transmission and reflection measurements through the test material using pulse signals. The received echoes are analyzed and compared with analytical models in order to estimate some specific acoustic properties of the sample itself. The main drawback of this approach is the low signal-to-noise ratio recorded when testing highly attenuating materials. This disadvantage is even more pronounced for measurements in air. The present work aims to overcome these limitations, replacing the excitation signals by continuous muti-harmonic waves. These signals have been developed by optimizing the phase of each harmonic, resulting in a low crest factor and consequently in a better signal-to-noise ratio Moreover their frequency content can be easily adapted to the different transducers used during th...

Acoustic media with pore size distribution and assignment of the pore characteristic lengths and permeabilities

The model by Champoux and Allard [J. Appl. Phys. 70(4), 1975-1979 (1991)] is used extensively for research and development of new porous media solutions and for predicting sound propagation in the presence of porous media. Four key non-acoustical parameters in this model which are rarely measured non-acoustically are: the viscous and thermal characteristic lengths, thermal permeability and Pride parameter Pride et al [Phys. Rev. B 47, 4964-4978 (1993)]. In this work we show how these parameters unambiguously relate to the pore size distribution which is a characteristic measured nonacoustically and more routinely. We compare the predictions by this model against the log-normal pore size distribution model by Horoshenkov et al. [J. Acoust. Soc. Am. 104, 1198-1209 (1998)] and show that these two models provide very close predictions when the four non-acoustic parameters are expressed through the mean pore size and its standard deviation. We also confirm these results through a 4-microphone impedance tube ex...

Theory of sound propagation in porous media allowing for spatial dispersion

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.

Multiple scattering and visco‐thermal effects

For modeling sound propagation in a rigid‐framed fluid‐saturated porous material it is customary to use frequency‐dependent density and compressibility functions. These functions, which describe ‘‘temporal’’ dispersion effects due to inertial/viscous and thermal effects, can be computed by FEM in simple geometries and give complete information about the long‐wavelength properties of the medium. When the wavelength is reduced, new effects due to scattering must be considered. To study this, we consider solving the sound propagation problem in a 2‐D ‘‘phononic crystal’’ made of an infinite square lattice of solid cylinders embedded in a fluid. An exact multiple‐scattering solution is first developed for an ideal saturating fluid and then generalized to the case of visco‐thermal fluid, by using the concept of visco‐thermal admittances. The condition to use this concept is that the viscous and thermal penetration depths are small compared to the cylinder radius. We validate our results in the long‐wavelength ...