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Two-dimensional stealthy hyperuniform distributions of rigid scatterers embedded in a waveguide are experimentally characterized the wave transport properties for scalar waves in airborne audible acoustics. The non resonant nature of the scatterers allows us to directly links the these properties to the geometric distribution of points through the structure factor. The transport properties are analyzed as a function of the stealthiness $\chi$ of their hyperuniform point pattern and compared to those of a disordered material in the diffusive regime, which are characterized by the Ohm's law through the mean free path. Different scattering regimes are theoretically and numerically identified showing transparent regions, isotropic band gaps, and anisotropic scattering depending on $\chi$. The robustness of these scattering regimes to losses which are unavoidable in audible acoustics is experimentally unvealed.

By using a structured tungsten-polyurethane composite that is impedance-matched to water while simultaneously having a much slower longitudinal sound speed, we have theoretically designed, and experimentally realized, an underwater acoustic absorber exhibiting high absorption from 4 to 20 kHz, measured in a 5.6m times 3.6m water pool with the time-domain approach. The broadband functionality is achieved by optimally engineering the distribution of the Fabry-Perot resonances, based on an integration scheme, to attain impedance matching over a broad frequency range. The average thickness of the integrated absorber, 8.9 mm, is in the deep subwavelength regime (~{\lambda}/42 at 4 kHz) and close to the causal minimum thickness of 8.2 mm that is evaluated from the simulated absorption spectrum. The structured composite represents a new type of acoustic metamaterials that has high acoustic energy density and promises broad underwater applications.

The estimation of poroelastic material parameters based on ultrasound measurements is considered. The acoustical characterisation of poroelastic materials based on various measurements is typically carried out by minimising a cost functional of model residuals, such as the least squares functional. With a limited number of unknown parameters, least squares type approaches can provide both reliable parameter and error estimates. With an increasing number of parameters, both the least squares parameter estimates and, in particular, the error estimates often become unreliable. In this paper, the estimation of the material parameters of an inhomogeneous poroelastic (Biot) plate in the Bayesian framework for inverse problems is considered. Reflection and transmission measurements are performed and 11 poroelastic parameters, as well as 4 measurement setup-related nuisance parameters, are estimated. A Markov chain Monte Carlo algorithm is employed for the computational inference to assess the actual uncertainty of the estimated parameters. The results suggest that the proposed approach for poroelastic material characterisation can reveal the heterogeneities in the object, and yield reliable parameter and uncertainty estimates., Comment: Post-review, published version

The unusual viscoelastic properties of silica aerogel plates are efficiently used to design subwavelength perfect sound absorbers. We theoretically, numerically and experimentally report a perfect absorbing metamaterial panel made of periodically arranged resonant building blocks consisting of a slit loaded by a clamped aerogel plate backed by a closed cavity. The impedance matching condition is analyzed using the Argand diagram of the reflection coefficient, i.e., the trajectory of the reflection coefficient as a function of frequency in the complex plane. The lack or excess of losses in the system can be identified via this Argand diagram in order to achieve the impedance matching condition. The universality of this tool can be further exploited to design more complex metasurfaces for perfect sound absorption, thus allowing the rapid design of novel and efficient absorbing metamaterials.

Anisotropic fluid materials are of growing interest with the development of metamaterials and transformation acoustics. In the general three-dimensional case, such materials are characterized by a bulk modulus and a full symmetric matrix of density. Here, a method is presented to retrieve the bulk modulus and all six components of the density matrix from a selected set of six incident plane waves impinging on a layer of the material. From the six components of the density tensor, the three principal directions and the three principal densities of the material are recovered. The approach relies on the analytical expression of the reflection and transmission coefficients derived from a state vector analysis. It results in simple, closed-form, and easily-implementable inverse relations for the material parameters. As an illustration, the case of sound propagation through an orthorhombic lattice of overlapping air-filled ellipsoids is considered, the effective complex and frequency-dependent bulk modulus and density matrix of which are derived from homogenization cell problems and account for viscothermal losses. The retrieval method is then applied to the homogenized layer and results bear testament to its robustness to extract accurately all seven material parameters. This makes possible the characterization and design of anisotropic fluid materials in three dimensions.

Acoustic fields scattered by poroelastic materials contain key information about the materials' pore structure and elastic properties. Therefore, such materials are often characterised with inverse methods that use acoustic measurements. However, it has been shown that results from many existing inverse characterisation methods agree poorly. One reason is that inverse methods are typically sensitive to even small uncertainties in a measurement setup, but these uncertainties are difficult to model and hence often neglected. In this paper, we study characterising poroelastic materials in the Bayesian framework, where measurement uncertainties can be taken into account, and which allows us to quantify uncertainty in the results. Using the finite element method, we simulate measurements where ultrasonic waves are incident on a water-saturated poroelastic material in normal and oblique angles. We consider uncertainties in the incidence angle and level of measurement noise, and then explore the solution of the Bayesian inverse problem, the posterior density, with an adaptive parallel tempering Markov chain Monte Carlo algorithm. Results show that both the elastic and pore structure parameters can be feasibly estimated from ultrasonic measurements., Comment: Published in JSV. https://doi.org/10.1016/j.jsv.2019.05.026

In an effective medium description of acoustic metamaterials, the Willis coupling plays the same role as the bianisotropy in electromagnetism. Willis media can be described by a constitutive matrix composed of the classical effective bulk modulus and density and additional cross-coupling terms defining the acoustic bianisotropy. Based on an unifying theoretical model, we unite the properties of acoustic Willis coupling with $\mathcal{PT}$ symmetric systems under the same umbrella and show in either case that an exceptional point hosts a remarkably pronounced scattering asymmetry that is accompanied by one-way zero reflection for sound waves. The analytical treatment is backed up by experimental input in asymmetrically side-loaded wavesguides showing how gauge transformations and loss biasing can embrace both Willis materials and non-Hermitian physics to tailor unidirectional reflectionless acoustics, which is appealing for purposeful sound insulation and steering.

There is a considerable number of research publications on the acoustical properties of porous media with an elastic frame. A simple search through the Web of ScienceTM (last accessed 21 March 2018) suggests that there are at least 819 publications which deal with the acoustics of poroelastic media. A majority of these researches require accurate knowledge of the elastic properties over a broad frequency range. However, the accuracy of the measurement of the dynamic elastic properties of poroelastic media has been a contentious issue. The novelty of this paper is that it studies the reproducibility of some popular experimental methods which are used routinely to measure the key elastic properties such as the dynamic Young's modulus, loss factor and Poisson ratio of poroelastic media. In this paper, fourteen independent sets of laboratory measurements were performed on specimens of the same porous materials. The results from these measurements suggest that the reproducibility of this type of experimental method is poor. This work can be helpful to suggest improvements which can be developed to harmonize the way the elastic properties of poroelastic media are measured worldwide.

Perfect, broadband and asymmetric sound absorption is theoretically, numerically and experimentally reported by using subwavelength thickness panels in a transmission problem. The panels are composed of a periodic array of varying cross-section waveguides, each of them being loaded by an array of Helmholtz resonators (HRs) with graded dimensions. The low cut-off frequency of the absorption band is fixed by the resonance frequency of the deepest HR, that reduces drastically the transmission. The preceding HR is designed with a slightly higher resonance frequency with a geometry that allows the impedance matching to the surrounding medium. Therefore, reflection vanishes and the structure is critically coupled. This results in perfect sound absorption at a single frequency. We report perfect absorption at 300 Hz for a structure whose thickness is 40 times smaller than the wavelength. Moreover, this process is repeated by adding HRs to the waveguide, each of them with a higher resonance frequency than the preceding one. Using this frequency cascade effect, we report quasi-perfect sound absorption over almost two frequency octaves ranging from 300 to 1000 Hz for a panel composed of 9 resonators with a total thickness of 11 cm, i.e., 10 times smaller than the wavelength at 300 Hz.

We theoretically and experimentally report sub-wavelength resonant panels for low-frequency quasi-perfect sound absorption including transmission by using the accumulation of cavity resonances due to the slow sound phenomenon. The sub-wavelength panel is composed of periodic horizontal slits loaded by identical Helmholtz resonators (HRs). Due to the presence of the HRs, the propagation inside each slit is strongly dispersive, with near-zero phase velocity close to the resonance of the HRs. In this slow sound regime, the frequencies of the cavity modes inside the slit are down-shifted and the slit behaves as a subwavelength resonator. Moreover, due to strong dispersion, the cavity resonances accumulate at the limit of the bandgap below the resonance frequency of the HRs. Near this accumulation frequency, simultaneously symmetric and antisymmetric quasi-critical coupling can be achieved. In this way, using only monopolar resonators quasi-perfect absorption can be obtained in a material including transmission.

Using the concepts of slow sound and of critical coupling, an ultra-thin acoustic metamaterial panel for perfect and omnidirectional absorption is theoretically and experimentally conceived in this work. The system is made of a rigid panel with a periodic distribution of thin closed slits, the upper wall of which is loaded by Helmholtz Resonators (HRs). The presence of resonators produces a slow sound propagation shifting the resonance frequency of the slit to the deep sub-wavelength regime ($\lambda/88$). By controlling the geometry of the slit and the HRs, the intrinsic visco-thermal losses can be tuned in order to exactly compensate the energy leakage of the system and fulfill the critical coupling condition to create the perfect absorption of sound in a large range of incidence angles due to the deep subwavelength behavior.

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 Cosserat theory is performed, and its limitations are established.

We present a thin subwavelength material that can be flush mounted to a duct and which gives a large wide band attenuation at remarkably low frequencies in air flow channels. To decrease the material thickness, the sound is slowed in the material using folded side branch tubes. The impedance of the material is compared to the optimal value, which differs greatly from the characteristic impedance. In particular, the viscous and thermal effects have to be very small to have high transmission losses. Grazing flow on this material increases the losses at the interface between the flow and the material.

The absorption properties of a metaporous material made of non-resonant simple shape three-dimensional inclusions (cube, cylinder, sphere, cone and torus) embedded in a rigidly backed rigid frame porous material is studied. A nearly total absorption can be obtained for a frequency lower than the quarter-wavelength resonance frequency due to the excitation of a trapped mode. To be correctly excited, this mode requires a filling fraction larger in the three-dimensions than in the two-dimensions for purely convex (cube, cylinder, sphere, and cone) shapes. At low frequencies, a cube is found to be the best purely convex inclusion shape to embed in a cubic unit cell, while the embedment of a sphere or a cone cannot lead to an optimal absorption for some porous materials. At fixed position of purely convex shape inclusion barycentre, the absorption coefficient only depends on and filling fraction and does not depend on the shape below the Bragg frequency arising from the interaction between the inclusion and its image with respect to the rigid backing. The influence of the angle of incidence is also shown. The results, in particular the excitation of the trapped mode, are validated experimentally in case of cubic inclusions., Comment: Submitted version to Journal of the Acoustical Society of America in June 2013. A revised version has been resubmitted in February 2014

The acoustic properties of a porous sheet of medium resistivity backed by a rigid plate in which are embedded a periodic set of circular inclusions is investigated. Such a structure behaves like a multi-component diffraction gratings. Numerical results show that this structure presents a quasi-total absorption peak below the essential spectrum, i.e. below the frequence of the fundamental quarter-wavelength resonance of the porous sheet in absence of inclusions. This result is explained either by the excitation of a complex trapped mode, or by the increase of viscous loss associated with a larger velocity gradient inside the layer at the modified quarter-wavelength resonance frequency. When more than one inclusion per spatial period are considered, additional quasi-total frequency peak are observed. The numerical results as calculated with the help of the mode-matching method described in the paper agree those as calculated with the help of a Finite Element method., Comment: Submitted to Journal of Applied Physics

The acoustic response of a rigid frame porous slab with a periodic set of inclusions is calculated by use of a multipole method. The acoustic properties, in particular the absorption, of such a structure are then derived and studied. Numerical results together with a modal analysis show that the addition of a periodic set of high-contrast inclusions leads to quasi-modes excitation of both the slab and the gratings, and to a large increase of the acoustic absorption of the initial slab, this being partly due to the quasi-modes excitation., Comment: submitted to Journal of Sound and Vibration

We address the problem of the response to a seismic wave of an urban site consisting of a large and infinite number ($N\_{b}$) of identical, equispaced blocks overlying a soft layer underlain by a hard substratum. The results of the theoretical analysis, appealing to a space-frequency mode-matching (MM) technique, are compared to those obtained by a space-time finite element (FE) method. The two methods are shown to give rise to much the same prediction of seismic response for $N\_{b}=10$. The MM technique is also applied to the case $N\_{b}=\infty$, notably to reveal the structure and natural frequencies of the vibration modes of the urban site. The mechanism of the interaction between blocks and the ground, as well as that of the collective effects of the blocks, are studied. It is shown that the presence of a large number of blocks modifies the seismic disturbance in a manner which evokes, and may partially account for, what was observed during many earthquakes in Mexico City. Disturbances at a much smaller level, induced by a small number of blocks are studied in the companion paper., Comment: soumis a Geophys.J.Intl

We address the problem of the response to a seismic wave of an urban site consisting of $N$ non-identical, non-equispaced blocks overlying a soft layer underlain by a hard substratum. The results of a theoretical analysis, appealing to a space-frequency mode-matching (MM) technique, are compared to those obtained by a space-time finite element (FE) technique. The two methods are shown to give rise to the same prediction of the seismic response for N=1 and N=2 blocks. The mechanism of the interaction between blocks and the ground, as well as that of the mutual interaction between blocks, are studied. It is shown that the presence of a small number of blocks modifies the seismic disturbance in a manner which evokes qualitatively, but not quantitatively, what was observed during the 1985 Michoacan earthquake in Mexico City. Disturbances at a much greater level, induced by a large number of blocks (in fact, a periodic set) are studied in the companion paper., Comment: submitted to Geophys.J.Intl

A domain integral method employing a specific Green's function (i.e., incorporating some features of the global problem of wave propagation in an inhomogeneous medium) is developed for solving direct and inverse scattering problems relative to slab-like macroscopically inhomogeneous porous obstacles. It is shown how to numerically solve such problems, involving both spatially-varying density and compressibility, by means of an iterative scheme initialized with a Born approximation. A numerical solution is obtained for a canonical problem involving a two-layer slab., Comment: submitted to Math.Meth.Appl.Sci

The equations of motion in a macroscopically inhomogeneous porous medium saturated by a fluid are derived. As a first verification of the validity of these equations, a two-layer rigid frame porous system considered as one single porous layer with a sudden change in physical properties is studied. A simple wave equation is derived and solved for this system. The reflection and transmission coefficients are calculated numerically using a wave splitting-Green's function approach (WS-GF). The reflected and transmitted wave time histories are also simulated. Experimental results obtained for materials saturated by air are compared to the results given by this approach and to those of the classical transfer matrix method (TMM)., Comment: Submitted to Phys.Rev.Lett

When a flat stress-free surface (i.e., the ground in seismological applications) separating air from a isotropic, homogeneous or horizontally-layered, solid substratum is solicited by a SH plane body wave incident in the substratum, the response in the substratum is a single specularly-reflected body wave. When the stress-free condition, equivalent to vanishing surface impedance, is relaxed by the introduction of a {spatially- constant, non- vanishing surface impedance}, the response in the substratum is again a single reflected body wave whose amplitude is less than the one in the situation of a stress-free ground. When the stress-free condition is relaxed by the introduction of a a {spatially-modulated surface impedance}, which simulates the action of an uneven (i.e., not entirely-flat) ground, the frequency-domain response takes the form of a spectrum of {plane body waves} and {surface waves} and {resonances} are produced at the frequencies of which one or several surface wave amplitudes can become large. It is shown, that at resonance, the amplitude of one, or of several, components of the motion on the surface can be amplified with respect to the situation in which the surface impedance is either constant or vanishes. Also, when the solicitation is pulse-like, the integrated time history of the square of surface displacement and of the square of velocity can be larger, and the duration of the signal can be considerably longer, for a spatially-modulated impedance surface than for a constant, or vanishing, impedance surface., Comment: Third International Symposium on the Effects of Surface Geology on Seismic Motion, Grenoble, 2006

We show how to cope with the acoustic identification of poroelastic materials when the specimen is in the form of a cylinder. We apply our formulation, based on the Biot model, approximated by the equivalent elastic solid model, to a long bone-like or borehole sample specimen probed by low frequency sound.

We study the seismic response of idealized 2D cities, constituted by non equally-spaced, non equally-sized homogenized blocks anchored in a soft layer overlying a hard half space. The blocks and soft layer are occupied by dissipative media. To simulate such response, we use an approximation of the viscoelastic modulus by a low-order rational function of frequency and incorporate this approximation into a first-order-in-time scheme. Our results display spatially-variable, strong, long-duration responses inside the blocks and on the ground, which qualitatively match the responses observed in some earthquake-prone cities of Mexico, France, the USA, etc., Comment: 22 pages, 8 figures, submitted to SDEE

In many applications, and in particular in seismology, realistic propagation media disperse and attenuate waves. This dissipative behavior can be taken into account by using a viscoacoustic propagation model, which incorporates a complex and frequency-dependent viscoacoustic modulus in the constitutive relation. The main difficulty then lies in finding an efficient way to discretize the constitutive equation as it becomes a convolution integral in the time domain. To overcome this difficulty the usual approach consists in approximating the viscoacoustic modulus by a low-order rational function of frequency. We use here such an approximation and show how it can be incorporated in the velocity-pressure formulation for viscoacoustic waves. This formulation is coupled with the fictitious domain method which permit us to model efficiently diffraction by objects of complicated geometry and with the Perfectly Matched Layer Model which allows us to model wave propagation in unbounded domains. The space discretization of the problem is based on a mixed finite element method and for the discretization in time a 2nd order centered finite difference scheme is employed. Several numerical examples illustrate the efficiency of the method., Comment: 29 pages, 25 figures, submitted to JCA