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Acoustic wave propagation in a one-dimensional periodic and asymmetric duct is studied theoretically and numerically to derive the effective properties. Closed form expressions for these effective properties, including the asymmetric Willis coupling, are derived through truncation of the Peano-Baker series expansion of the matricant (which links the state vectors at the two sides of the unit-cell) and Padé's approximation of the matrix exponential. The results of the first-order and second-order homogenization (with Willis coupling) procedures are compared with the numerical results. The second-order homogenization procedure provides scattering coefficients that are valid over a much larger frequency range than the usual first-order procedure. The frequency well below which the effective description is valid is compared with the lower bound of the first Bragg bandgap when the profile is approximated by a two-step function of identical indicator function, i.e., two different cross-sectional areas over the same length. This validity limit is then questioned, particularly with a focus on impedance modeling. This article attempts to facilitate the engineering use of Willis materials., (© 2023 Acoustical Society of America.)

This broad review summarizes recent advances and "hot" research topics in nanophononics and elastic, acoustic, and mechanical metamaterials based on results presented by the authors at the EUROMECH 610 Colloquium held on April 25-27, 2022 in Benicássim, Spain. The key goal of the colloquium was to highlight important developments in these areas, particularly new results that emerged during the last two years. This work thus presents a "snapshot" of the state-of-the-art of different nanophononics- and metamaterial-related topics rather than a historical view on these subjects, in contrast to a conventional review article. The introduction of basic definitions for each topic is followed by an outline of design strategies for the media under consideration, recently developed analysis and implementation techniques, and discussions of current challenges and promising applications. This review, while not comprehensive, will be helpful especially for early-career researchers, among others, as it offers a broad view of the current state-of-the-art and highlights some unique and flourishing research in the mentioned fields, providing insight into multiple exciting research directions., (© 2023 the author(s), published by De Gruyter, Berlin/Boston.)

This work deals with wave absorption in reciprocal asymmetric scattering problem by addressing the acoustic problem of compact absorbers for perfect unidirectional absorption, flush mounted to the walls of wide ducts. These absorbers are composed of several side-by-side resonators that are usually of different geometry and thus detuned to yield an asymmetric acoustic response. A simple lumped-element model analysis is performed to link the dependence of the optimal resonators surface impedance, resonance frequency, and losses to the duct cross-sectional area and resonator spacing. This analysis unifies those of several specific configurations into a unique problem. In addition, the impact of the potential evanescent coupling between the resonators, which is usually neglected, is carefully studied. This coupling can have a strong impact especially on the behavior of compact absorbers lining wide ducts. To reduce the evanescent coupling, the resonators should be relatively small and therefore their resonances should be damped, and not arranged by order of increasing or decreasing resonant frequency. Finally, such an absorber is designed and optimized for perfect unidirectional absorption to prove the relevance of the analysis. The absorber is 30 cm long and 5 cm thick and covers a single side of a 14.8 × 15 cm 2 rectangular duct. A mean absorption coefficient of 99% is obtained experimentally between 700 and 800 Hz., (© 2022. The Author(s).)

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 5.6 m by 3.6 m 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 (~λ/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.

In this work, we show that scattered acoustic vortices generated by metasurfaces with chiral symmetry present broadband unusual properties in the far-field. These metasurfaces are designed to encode the holographic field of an acoustical vortex, resulting in structures with spiral geometry. In the near field, phase dislocations with tuned topological charge emerge when the scattered waves interference destructively along the axis of the spiral metasurface. In the far field, metasurfaces based on holographic vortices inhibit specular reflections because all scattered waves also interfere destructively in the normal direction. In addition, the scattering function in the far field is unusually uniform because the reflected waves diverge spherically from the holographic focal point. In this way, by triggering vorticity, energy can be evenly reflected in all directions except to the normal. As a consequence, the designed metasurface presents a mean correlation-scattering coefficient of 0.99 (0.98 in experiments) and a mean normalized diffusion coefficient of 0.73 (0.76 in experiments) over a 4 octave frequency band. The singular features of the resulting metasurfaces with chiral geometry allow the simultaneous generation of broadband, diffuse and non-specular scattering. These three exceptional features make spiral metasurfaces extraordinary candidates for controlling acoustic scattering and generating diffuse sound reflections in several applications and branches of wave physics as underwater acoustics, biomedical ultrasound, particle manipulation devices or room acoustics.

We present a 3-dimensional fully natural sonic crystal composed of spherical aggregates of fibers (called Aegagropilae) resulting from the decomposition of Posidonia Oceanica. The fiber network is first acoustically characterized, providing insights on this natural fiber entanglement due to turbulent flow. The Aegagropilae are then arranged on a principal cubic lattice. The band diagram and topology of this structure are analyzed, notably via Argand representation of its scattering elements. This fully natural sonic crystal exhibits excellent sound absorbing properties and thus represents a sustainable alternative that could outperform conventional acoustic materials.

The design of graded and anisotropic materials has been of significant interest, especially for sound absorption purposes. Together with the rise of additive manufacturing techniques, new possibilities are emerging from engineered porous micro-structures. In this work, we present a theoretical and numerical study of graded and anisotropic porous materials, for optimal broadband and angular absorption. Through a parametric study, the effective acoustic and geometric parameters of homogenized anisotropic unit cells constitute a database in which the optimal anisotropic and graded material will be searched for. We develop an optimization technique based on the simplex method that is relying on this database. The concepts of average absorption and diffuse field absorption coefficients are introduced and used to maximize angular acoustic absorption. Numerical results present the optimized absorption of the designed anisotropic and graded porous materials for different acoustic targets. The designed materials have anisotropic and graded effective properties, which enhance its sound absorption capabilities. While the anisotropy largely enhances the diffuse field absorbing when optimized at a single frequency, graded properties appear to be crucial for optimal broadband diffuse field absorption.

Nowadays, fibrous polyester materials are becoming one of the most important alternatives for controlling reverberation time by absorbing unwanted sound energy in the automobile and construction fields. Thus, it is worthy and meaningful to characterize their acoustic behavior. To do so, non-acoustic parameters, such as tortuosity, viscous and thermal characteristic lengths and thermal permeability, must be determined. Representative panels of polyester fibrous material manufactured by perpendicular laying technology are thus tested via the Bayesian reconstruction procedure. The estimated porosity and airflow resistivity are found in good agreement with those tested via direct measurements. In addition, the homogeneity of polyester fibrous panels was characterized by investigating the mean relative differences of inferred non-acoustic parameters from the direct and reverse orientation measurements. Some parameters, such as tortuosity, porosity and airflow resistivity, exhibit very low relative differences. It is found that most of the panels can be assumed homogeneous along with the panel thickness, the slight inhomogeneity mostly affecting the thermal characteristic length.

This work deals with the sound wave propagation modeling in anisotropic and heterogeneous media. The considered scattering problem involves an infinite layer of finite thickness containing an anisotropic fluid whose properties can vary along the layer depth. The specular transmission and reflection of an acoustic plane wave by such a layer is modeled through the state vector formalism for the acoustic fields. This is solved using three different numerical techniques, namely, the transfer matrix method, Peano series, and transfer Green's function. These three methods are compared to demonstrate the convergence of the numerical solutions. Moreover, the implemented numerical procedures allow the authors to retrieve the internal acoustic fields and show their dependency along with the fluid anisotropic properties. Results are presented to illustrate the changes in absorption that can be achieved by tuning the fluid anisotropy as well as the variation of these properties across the depth of the layer. The results presented are in very good agreement across the different methods. Given that many porous materials can be modeled as equivalent fluids, the results presented show the potential offered by such numerical techniques, and can further give more insight into inhomogeneous anisotropic porous materials.

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.

Used as building biomaterials for centuries, cereal straws are known for their remarkable acoustic performances in sound absorption. Yet, their use as fibrous media disregards their internal structure made of nodes partitioning stems. Here, we show that such nodes can impart negative acoustic bulk modulus to straw balls when straws are cut on either side of a node. Such metafluid inspired by cereal straws combines visco-thermal diffusion with strong wave dispersion arising from quarter-wavelength resonances within straws. Large spectral bandgaps and slow sound regimes are theoretically predicted and experimental data from impedance tube measurements on an idealised 3D-printed sample layer are in good agreement with the theoretical model. Perfect absorption is achieved at wavelengths 13 times larger than the thickness of the metafluid layer, and slow sound entails an increased density of states causing a cascade of high absorption peaks. Such features could lead cereal straws to serve as cheap acoustic bio-metamaterials.

This paper reports a theoretical study of the sound propagation in a rectangular waveguide loaded by closely-spaced elongated side-branch resonators forming a simple low-frequency broadband reactive silencer. Semi-analytical calculations account for the evanescent modes both in the main waveguide and side-branch resonators and for the viscothermal losses in the silencer elements. Reasonable accuracy is maintained in the evaluation of transmission, reflection, and absorption coefficients, while the calculation time is reduced by a few hundred times in comparison with the finite element method. Therefore, the proposed method is particularly suitable for optimization procedure. The lengths of the individual equally spaced side-branch resonators are optimized by a heuristic evolutionary algorithm that maximizes the minimum transmission loss (TL) over a pre-defined frequency range. Numerical results indicate that the minimum TL of the optimized silencers is reduced due to the destructive effect of the evanescent coupling from the resonators of the nearest side-branches. In the opposite, the TL increases linearly with the number of the side-branch resonators.

Many models for the prediction of the acoustical properties of porous media require non-acoustical parameters few of which are directly measurable. One popular prediction model by Johnson, Champoux, Allard, and Lafarge [J. Appl. Phys. 70(4), 1975-1979 (1991)] (459 citations, Scopus, April 2019) requires six non-acoustical parameters. This paper proves that the use of more than three parameters in the Johnson-Champoux-Allard-Lafarge model is not necessary at all. Here the authors present theoretical and experimental evidence that the acoustical impedance of a range of porous media with pore size distribution close to log-normal (granular, fibrous, and foams) can be predicted through the knowledge of the porosity, median pore size, and standard deviation in the pore size only. A unique feature of this paper is that it effectively halves the number of parameters required to predict the acoustical properties of porous media very accurately. The significance of this paper is that it proposes an unambiguous relationship between the pore microstructure and key acoustical properties of porous media with log-normal pore size distribution. This unique model is well suited for using acoustical data for measuring and inverting key non-acoustical properties of a wider range of porous media used in a range of applications which are not necessarily acoustic.

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 crosssection waveguides, each of them being loaded by 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.

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.

We present deep-subwavelength diffusing surfaces based on acoustic metamaterials, namely metadiffusers. These sound diffusers are rigidly backed slotted panels, with each slit being loaded by an array of Helmholtz resonators. Strong dispersion is produced in the slits and slow sound conditions are induced. Thus, the effective thickness of the panel is lengthened introducing its quarter wavelength resonance in the deep-subwavelength regime. By tuning the geometry of the metamaterial, the reflection coefficient of the panel can be tailored to obtain either a custom reflection phase, moderate or even perfect absorption. Using these concepts, we present ultra-thin diffusers where the geometry of the metadiffuser has been tuned to obtain surfaces with spatially dependent reflection coefficients having uniform magnitude Fourier transforms. Various designs are presented where, quadratic residue, primitive root and ternary sequence diffusers are mimicked by metadiffusers whose thickness are 1/46 to 1/20 times the design wavelength, i.e., between about a twentieth and a tenth of the thickness of traditional designs. Finally, a broadband metadiffuser panel of 3 cm thick was designed using optimization methods for frequencies ranging from 250 Hz to 2 kHz.

Modeling of sound propagation in porous media requires the knowledge of several intrinsic material parameters, some of which are difficult or impossible to measure directly, particularly in the case of a porous medium which is composed of pores with a wide range of scales and random interconnections. Four particular parameters which are rarely measured non-acoustically, but used extensively in a number of acoustical models, are the viscous and thermal characteristic lengths, thermal permeability, and Pride parameter. The main purpose of this work is to show how these parameters relate to the pore size distribution which is a routine characteristic measured non-acoustically. This is achieved through the analysis of the asymptotic behavior of four analytical models which have been developed previously to predict the dynamic density and/or compressibility of the equivalent fluid in a porous medium. In this work the models proposed by Johnson, Koplik, and Dashn [J. Fluid Mech. 176, 379-402 (1987)], Champoux and Allard [J. Appl. Phys. 70(4), 1975-1979 (1991)], Pride, Morgan, and Gangi [Phys. Rev. B 47, 4964-4978 (1993)], and Horoshenkov, Attenborough, and Chandler-Wilde [J. Acoust. Soc. Am. 104, 1198-1209 (1998)] are compared. The findings are then used to compare the behavior of the complex dynamic density and compressibility of the fluid in a material pore with uniform and variable cross-sections.

A thin subwavelength material that can be flush mounted in a duct and that gives an attenuation band at low frequencies in air flow channels is presented. 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 given by the Cremer condition, which can differ greatly from the air characteristic impedance. Grazing flow on this material increases the losses at the interface between the flow and the material.

Perfect (100%) absorption by thin structures consisting of a periodic arrangement of rectangular quarter-wavelength channels with side detuned quarter-wavelength resonators is demonstrated. The thickness of these structures is 13-17 times thinner than the acoustic wavelength. This low frequency absorption is due to a slow sound wave propagating in the main rectangular channel. A theoretical model is proposed to predict the complex wavenumber in this channel. It is shown that the speed of sound in the channel is much lower than in the air, almost independent of the frequency in the low frequency range, and it is dispersive inside the induced transparency band which is observed. The perfect absorption condition is found to be caused by a critical coupling between the rectangular channel (sub-wavelength resonators) and the incoming wave. It is shown that the width of a large absorption peak in the frequency spectrum can be broadened if several rectangular channels in the unit cell are detuned. The detuning is achieved by varying the length of the side resonators for each channel. The predicted absorption coefficients are validated experimentally. Two resonant cells were produced with stereolithography which enabled the authors to incorporate curved side resonators.

The acoustic response of a rigidly backed poroelastic layer with a periodic set of elastic cylindrical inclusions embedded is studied. A semi-analytical approach is presented, based on Biot's 1956 theory to account for the deformation of the skeleton, coupling mode matching technique, Bloch wave representation, and multiple scattering theory. This model is validated by comparing the derived absorption coefficients to finite element simulations. Numerical results are further exposed to investigate the influence of the properties of the inclusions (type, material properties, size) of this structure, while a modal analysis is performed to characterize the dynamic behaviors leading to high acoustic absorption. Particularly, in the case of thin viscoelastic membranes, an absorption coefficient larger than 0.8 is observed on a wide frequency band. This property is found to be due to the coupling between the first volume mode of the inclusion and the trapped mode induced by the periodic array and the rigid backing, for a wavelength in the air smaller than 11 times the material thickness.

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.

This paper studies the acoustical properties of hard-backed porous layers with periodically embedded air filled Helmholtz resonators. It is demonstrated that some enhancements in the acoustic absorption coefficient can be achieved in the viscous and inertial regimes at wavelengths much larger than the layer thickness. This enhancement is attributed to the excitation of two specific modes: Helmholtz resonance in the viscous regime and a trapped mode in the inertial regime. The enhancement in the absorption that is attributed to the Helmholtz resonance can be further improved when a small amount of porous material is removed from the resonator necks. In this way the frequency range in which these porous materials exhibit high values of the absorption coefficient can be extended by using Helmholtz resonators with a range of carefully tuned neck lengths.

The measurement of acoustic material characteristics using a standard impedance tube method is generally limited to the plane wave regime below the tube cut-on frequency. This implies that the size of the tube and, consequently, the size of the material specimen must remain smaller than a half of the wavelength. This paper presents a method that enables the extension of the frequency range beyond the plane wave regime by at least a factor of 3, so that the size of the material specimen can be much larger than the wavelength. The proposed method is based on measuring of the sound pressure at different axial locations and applying the spatial Fourier transform. A normal mode decomposition approach is used together with an optimization algorithm to minimize the discrepancy between the measured and predicted sound pressure spectra. This allows the frequency and angle dependent reflection and absorption coefficients of the material specimen to be calculated in an extended frequency range. The method has been tested successfully on samples of melamine foam and wood fiber. The measured data are in close agreement with the predictions by the equivalent fluid model for the acoustical properties of porous media.

The absorption properties of a metaporous material made of non-resonant simple shape three-dimensional rigid inclusions (cube, cylinder, sphere, cone, and ring torus) embedded in a rigidly backed rigid-frame porous material are 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 three-dimensions than in two-dimensions for purely convex (cube, cylinder, sphere, and cone) shapes. At long wavelengths compared to the spatial period, 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 material properties and dimensions of the unit cell. At a fixed position of purely convex shape inclusion barycenter, the absorption coefficient only depends on the 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 incidence angle and of the material properties, namely, the flow resistivity is also shown. The results of the modeling are validated experimentally in the case of cubic and cylindrical inclusions.

The propagation and localization of transversal-rotational waves in a two-dimensional granular chain of equal masses are analyzed in this study. The masses are infinitely long cylinders possessing one translational and one rotational degree of freedom. Two dispersive propagating modes are predicted in this granular crystal. By considering the semi-infinite chain with a boundary condition applied at its beginning, the analytical study demonstrates the existence of localized modes, each mode composed of two evanescent modes. Their existence, position (either in the gap between the propagating modes or in the gap above the upper propagating mode), and structure of spatial localization are analyzed as a function of the relative strength of the shear and bending interparticle interactions and for different boundary conditions. This demonstrates the existence of a localized mode in a semi-infinite monatomic chain when transversal-rotational waves are considered, while it is well known that these types of modes do not exist when longitudinal waves are considered.

The aim of this work is to design a layer of porous material with a high value of the absorption coefficient in a wide range of frequencies. It is shown that low frequency performance can be significantly improved by embedding periodically arranged resonant inclusions (slotted cylinders) into the porous matrix. The dissipation of the acoustic energy in a porous material due to viscous and thermal losses inside the pores is enhanced by the low frequency resonances of the inclusions and energy trapping between the inclusion and the rigid backing. A parametric study is performed in order to determine the influence of the geometry and the arrangement of the inclusions embedded in a porous layer on the absorption coefficient. The experiments confirm that low frequency absorption coefficient of a composite material is significantly higher than that of the porous layer without the inclusions.

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.

The acoustic transmission coefficient of a resonant sonic crystal made of hollow bamboo rods is studied experimentally and theoretically. The plane wave expansion and multiple scattering theory (MST) are used to predict the bandgap in transmission coefficient of a non-resonant sonic crystal composed of rods without holes. The predicted results are validated against experimental data for the acoustic transmission coefficient. It is shown that a sonic crystal made from a natural material with some irregularities can exhibit a clear transmission bandgap. Then, the hollow bamboo rods are drilled between each node to create an array of Helmholtz resonators. It is shown that the presence of Helmholtz resonators leads to an additional bandgap in the low-frequency part of the transmission coefficient. The MST is modified in order to account for the resonance effect of the holes in the drilled bamboo rods. This resonant multiple scattering theory is validated experimentally and could be further used for the description and optimization of more complex resonant sonic crystals.

The propagation of audible acoustic waves in two-dimensional square lattice tunable sonic crystals (SC) made of square cross-section infinitely rigid rods embedded in air is investigated experimentally. The band structure is calculated with the plane wave expansion (PWE) method and compared with experimental measurements carried out on a finite extend structure of 200 cm width, 70 cm depth and 15 cm height. The structure is made of square inclusions of 5 cm side with a periodicity of L = 7.5 cm placed inbetween two rigid plates. The existence of tunable complete band gaps in the audible frequency range is demonstrated experimentally by rotating the scatterers around their vertical axis. Negative refraction is then analyzed by use of the anisotropy of the equi-frequency surface (EFS) in the first band and of a finite difference time domain (FDTD) method. Experimental results finally show negative refraction in the audible frequency range.

This work reports on an application of the state vector (Stroh) formalism and Peano series expansion to solve the problem of sound propagation in a material with continuous pore stratification. An alternative Biot formulation is used to link the equivalent velocity in the oscillatory flow in the material pores with the acoustic pressure gradient. In this formulation, the complex dynamic density and bulk modulus are predicted using the equivalent fluid flow model developed by Horoshenkov and Swift [J. Acoust. Soc. Am. 110(5), 2371-2378 (2001)] under the rigid frame approximation. This model is validated against experimental data obtained for a 140 mm thick material specimen with continuous pore size stratification and relatively constant porosity. This material has been produced from polyurethane binder solution placed in a container with a vented top and sealed bottom to achieve a gradient in the reaction time which caused a pore size stratification to develop as a function of depth [Mahasaranon et al., J. Appl. Phys. 111, 084901 (2012)]. It is shown that the acoustical properties of this class of materials can be accurately predicted with the adopted theoretical model.

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.

This work investigates the acoustical properties of a multilayer porous material in which periodic inclusions are embedded. The material is assumed to be backed by a rigid wall. Most of the studies performed in this field used the multipole method and are limited to circular shape inclusions. Here, a mode matching approach, more convenient for a layered system, is adopted. The inclusions can be in the form of rigid scatterers of an arbitrary shape, in the form of an air-filled cavity or in the form of a porous medium with contrasting properties. The computational approach is validated on simple geometries against other numerical schemes and with experimental results obtained in an anechoic room on a rigid grating embedded in a porous material made of 2 mm glass beads. The method is used to study the acoustic absorption behavior of this class of materials in the low frequency range and at a range of angles of incidence.

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., (© 2011 Acoustical Society of America)

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., (© 2011 Acoustical Society of America)

The modification of elastic properties of compressed acoustic foams is investigated. The porous sample is first submitted to a static compression and then to a dynamic excitation of smaller amplitude, corresponding to acoustical applications. The static compression induces the modification of the dynamic elastic parameters of the material. This work focuses on Young's modulus. The variation is measured with two different experimental methods: The classical rigidimeter and an absorption measurement. The effective Young's modulus is directly measured with the first method and is indirectly determined through the quarter-wave length resonance of the frame with the second one. The results of the two measurements are compared and give similar tendencies. The variation of the dynamic Young's modulus as a function of the degree of compression of the sample is shown to be separated in several zones. In the zones associated with weak compression (those usually zones encountered in practice), the variation of the effective Young's modulus can be approximated by a simple affine function. The results are compared for different foams. A simple model of the dependency of the Young's modulus with respect to the static degree of compression is finally proposed for weak compressions.

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.

The coupled mode (CM) and finite-element methods (FEMs) are developed and used to predict the acoustic reflection coefficient of a semi-infinite porous medium with closely spaced two-dimensional (2D) periodical corrugations. These methods are also applied to predict the reflection coefficient of a periodic array of porous corrugations installed on an acoustically rigid surface. It is shown that the predictions by the both methods agree closely. The reflection coefficient and Brewster angle of total refraction for the corrugated semi-infinite medium predicted with these methods are compared against that predicted by the Biot/Tolstoy/Howe/Twersky and extended Twersky models. A similar analysis is carried out for porous corrugations set on a rigid backing. The behavior of the reflection coefficient and the pole in the expression for the reflection coefficient located close to grazing incidence is studied.

The acoustic properties of a low resistivity porous layer backed by a rigid plate containing periodic rectangular irregularities, creating a multicomponent diffraction gratings, are investigated. Numerical and experimental results show that the structure possesses a total absorption peak at the frequency of the modified mode of the layer, when designed as proposed in the article. These results are explained by an analysis of the acoustic response of the whole structure and especially by the modal analysis of the configuration. When more than one irregularity per spatial period is considered, additional higher frequency peaks are observed.

A frequency domain method dedicated to the analytic recovery of the four relevant parameters of macroscopically homogeneous rigid frame porous materials, e.g., plastic foams, at the high frequency range of the Johnson-Champoux-Allard model is developed and presented. The reconstructions appeal to experimental data concerning time domain measurements of the ultrasonic fields reflected and transmitted by a plate of the material at normal incidence. The effective density and bulk modulus of the material are first reconstructed from the frequency domain reflection and transmission coefficients. From the latter, the porosity, tortuosity, and thermal and viscous characteristic lengths are recovered. In a sense, the method presented herein is quite similar in the ultrasonic range, but also quite complementary, to the method developed by Panneton and Olny [J. Acoust. Soc. Am. 119, 2027-2040 (2006); 123, 814-824 (2008)] at low frequency, which appeal to experimental data measured in an impedance tube.

The acoustic response of a rigid-frame porous plate with a periodic set of inclusions is investigated by 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 the excitation of the modes of the plate and to a large increase in the acoustic absorption.

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.

Structured materials like photonic crystals require for optimal use a high degree of precision with respect to both position and optical characteristics of their components. Here we present a simple tomographic algorithm, based on a specific Green's function together with a first-order Born approximation, which enables us to localize and characterize identical defects in finite-sized photonic crystals. This algorithm is proposed as a first step to the monitoring of such materials. Illustrative numerical results show in particular the possibility of focalization beyond the Rayleigh criterion.

Among the many factors involved in ultrasound attenuation phenomena, scattering effects play a major role, even in the unexpected case of soft tissues. It is proposed in this study to quantitatively evaluate the scattering affecting the measurements before reconstructing the absorption parameter alone. The reconstruction procedure involves three steps: (1) Estimating the sound speed map using a transmission tomography algorithm. This estimation procedure provides a numerical phantom of the organ probed, cleared of all dissipative components. This absorption free phantom mimics the (viscoacoustic) tissues imaged except for the density and absorption characteristics: the density a priori equals 1000 kg/m3 and the absorption is not taken into account. The impedance fluctuations in the object are therefore approximated on the basis of the sound speed contrast. (2) Synthesing the field scattered by the absorption free phantom; the attenuation observed here results solely from the scattering phenomenon. The synthesis is carried out using a finite-element time domain code simulating the ultrasonic propagation through the phantom. It provides the scattering distortion reference introduced into the log spectral absorption estimator. (3) Reducing the scattering distortions affecting the integrated absorption measured along the ray paths using a log spectral procedure. The corrected integrated absorption is then processed using a tomographic reconstruction procedure that provides an estimate of the absorption distribution. Simple numerical simulations show the improvement obtained in the absorption estimates with this approach.