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We report a procedure to design two-dimensional acoustic structures with prescribed scattering properties. The structures are designed from targeted properties in the reciprocal space so that their structure factors, i.e. their scattering patterns under the Born approximation, exactly follow the desired scattering properties for a set of wavelengths. The structures are made of a distribution of rigid circular cross-sectional cylinders embedded in air. We demonstrate the efficiency of the procedure by designing two-dimensional stealth acoustic materials with broadband back-scattering suppression independent of the angle of incidence and equiluminous acoustic materials exhibiting broadband scattering of equal intensity also independent of the angle of incidence. The scattering intensities are described in terms of both single and multiple scattering formalisms, showing excellent agreement with each other, thus validating the scattering properties of each material. [ABSTRACT FROM AUTHOR]

The optimal absorption of flexural energy by the critical coupling of a locally resonant grating embedded in a thin plate is reported in this work for the reflection and transmission problems. The grating is made of a 1D-periodic array of local resonators. A viscoelastic coating is also placed on top of each resonator to control the intrinsic losses of the system. The scattering matrices for the propagative waves of both problems are obtained by means of the Layered Multiple Scattering Theory and validated by the Finite Element Method. In this work, we find that the perfect absorption can be obtained in the reflection problem and the maximal absorption in the transmission problem is limited to 50% by tuning the losses only. These results agree with the theoretical predictions since the eigenvalues reduce to the reflection coefficient in the reflection problem and only one of the two eigenvalues of the scattering matrix is critically coupled in the transmission problem. These results highlight the adaptability of the critical coupling method to optimize the absorption of locally resonant materials for flexural waves in 2D transmission and reflection problems, and pave the way to the design of resonators for efficient flexural wave absorption. [ABSTRACT FROM AUTHOR]

We employ the Baker–Campbell–Hausdorff formula to derive closed-form expressions for the effective properties, including emergent Willis coupling, of a one-dimensional heterogeneous poroelastic medium consisting of a periodically repeating two-layer unit-cell. In contrast to the elastic and fluidic analogs, the Willis coupling of this periodic poroelastic medium does not vanish in the low-frequency limit. However, the effective wavenumber and impedance of this asymmetric lamellar material demonstrate symmetric reflection and absorption behavior that is indicative of symmetric structures in the low-frequency limit due to the effect of Darcy's law on the dynamic effective density, which is inversely proportional to frequency. These closed-form expressions are validated against results obtained by direct numerical evaluation. The scattering coefficients, particularly the two reflection coefficients for incidence from either side of a finite length asymmetric structure, are different at non-zero frequencies but still in the metamaterial limit and are correct when the Willis coupling is included. The results show that asymmetry in poroelastic layers results in direction-dependent absorption coefficients, one of which could be optimized based on layer properties and asymmetry factors. As a consequence, the frequency range of validity of these scattering coefficients is wider when the Willis coupling matrix is accounted for than in its absence. This work paves the way for better control of elastic and acoustic waves in multiphase materials by considering poroelastic behavior. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper examines the feasibility of cloaking an obstacle using Plate-type Acoustic Metamaterials (PAMs). We present two distinct strategies to cloak this obstacle, using either the near-zero-density regime of a periodic arrangement of plates or the acoustic doping phenomenon to achieve simultaneous zero-phase propagation and impedance matching. The strong limitations induced by viscothermal and viscoelastic losses that cannot be avoided in such a system are studied. A hiding zone is reported analytically, numerically, and experimentally. In contrast to cloaking, where zero-phase propagation must be accompanied by total transmission and zero reflection, the hiding configuration requires that the scattering properties of the hiding device must not be affected by the presence of the obstacle embedded in it. Contrary to cloaking, the hiding phenomenon is achievable even with a realistic PAM possessing unavoidable losses. [ABSTRACT FROM AUTHOR]

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 100MHz, 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. [ABSTRACT FROM AUTHOR]

Stealthy hyperuniform point patterns are characterized by a vanishing spatial Fourier transform around the origin of the reciprocal vector space. The long-range point density fluctuations are suppressed as well in materials consisting of such distribution of scatterers, opening up opportunities to control waves. Beside wave transport in such structured materials are driven by several elements, such as the acoustic properties of the host material, the scatterer characteristics, i.e., dimensions or resonant features, and the scatterer distribution patterns. The effects of these three basic elements on the wave transport properties are usually hard to discriminate. In this work, we analyze the transport properties of acoustic waves in one-dimensional phononic materials constituted of either non-resonant or resonant scatterers distributed along stealthy hyperuniform patterns in air. The pattern is controlled by the stealthiness, allowing us to continuously vary from random phononic materials to phononic crystals. The properties of the scatterers are controlled by their size and/or the resonant frequencies. The properties of the host material are controlled by the viscothermal losses. Transport properties of stealthy hyperuniform materials are found to be robust to both the scatterer dimensions and inherent viscothermal losses, while strongly affected by the scatterer resonances, which introduce sharp dips in the transmission coefficient. [ABSTRACT FROM AUTHOR]

We demonstrate that the phenomenon of slow sound propagation associated with its inherent dissipation (dispersion + attenuation) can be efficiently used to design sound absorbing metamaterials. The dispersion relation of the wave propagating in narrow waveguides on one side of which quarter-wavelength resonators are plugged with a square lattice, whose periodicity is smaller than the wavelength, is analyzed. The thermal and viscous losses are accounted for in the modeling. We show that this structure slows down the sound below the bandgap associated with the resonance of quarter-wavelength resonators and dissipates energy. After deriving the effective parameters of both such a narrow waveguide and a periodic arrangement of them, we show that the combination of slow sound together with the dissipation can be efficiently used to design a sound absorbing metamaterial which totally absorbs sound for wavelength much larger than four times the thickness structure. This last claim is supported by experimental results. [ABSTRACT FROM AUTHOR]

Sound diffusion refers to the ability of a surface to evenly scatter sound energy in both time and space. However, omni-directional radiation of sound, or perfect diffusion, can be impractical or difficult to reach under traditional means. This is due to the considerable size required, and the lack of tunability, of typical quarter-wavelength scattering strategies necessary for producing the required complexity of the surface acoustic impedance. As such, it can be a challenge to design sound diffusing structures that can display near perfect diffusion performance within slim dimensions. In this work, we propose a method for obtaining quasi-perfect and broadband sound diffusion coefficients using deep-subwavelength acoustic diffusers, i.e., metadiffusers. The relation among the geometry of the metasurface, the bandwidth, and the diffusion performance is analytically and numerically studied. For moderate bandwidths, around 1/3 of an octave, the method results in nearly perfect sound diffusion, while for a bandwidth of 2.5 octaves, a normalized diffusion coefficient of 0.8 was obtained using panels 1/30th thinner than traditional phase-grating designs. The ratio between the wavelength and the size of the unit cell was identified as a limitation of the performance. This work demonstrates the versatility and effectiveness of metadiffusers to generate diffuse reflections outperforming those of classical sound diffusers. [ABSTRACT FROM AUTHOR]

We theoretically, numerically and experimentally report the localization of an acoustic wave at the interface between two one-dimensional hyperuniform materials of different geometrical representations. These materials suppress the acoustic scattering in the long wavelength regime, being rather disordered and degenerate, while possessing a wide band gap. In this work, these hyperuniform materials are made of an air-filled acoustic waveguide with rigid diaphragms acting as scatterers. A wide band gap and the emergence of the edge modes provide promising applications in wave control devices. [ABSTRACT FROM AUTHOR]

An omnidirectional sound absorber based on the acoustic analogy of the electromagnetic metamaterial "black hole" has been developed and tested. The resulting structure is composed of a hollow cylindrical porous absorbing core and a graded index matching layer which employs multiple rods of varying size and spacing to gradually adjust the impedance of the air to that of the porous absorbing core. A semi-analytical model is developed, and the practical challenges and their implications with respect to performance are considered. A full size device is built and tested in an anechoic chamber and the semi-analytical model used in the design process is validated. Finally, the theory is extended to allow for losses in the metamaterial matching layer, and it is shown that improved performance may be achieved with a dual purpose layer which acts as an absorber whilst also providing the required impedance matching condition. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A general approach to determine the acoustic reflection and transmission coefficients of multilayered panels is proposed in this paper. Contrary to the Transfer Matrix Method (TMM), this method does not become unstable for high frequencies or large layer thicknesses. This method is shown to be as general as the TMM and mathematically equivalent. Its principle is to consider a so called Information Vector which contains all the information necessary to deduce the State Vector through a Translation Matrix. The Information Vector is of reduced length compared to that of the State Vector and can be propagated in any layer without involving exponentially growing terms. In addition, this method enables the coupling between any type of physical media as far as proper boundary relations can be written. Moreover, the method does not lead to an enlargement of the systems' size in the case of interfaces between media of different physical type. Finally, this method can be easily implemented in numerical codes. The method is validated on three cases classically encountered in acoustic problems. However, it is general enough to model any type of multilayered problems in any field of applied physics. [ABSTRACT FROM AUTHOR]

A wave propagation model in macroscopically inhomogeneous porous media is derived from the alternative Biot’s theory of 1962. As a first application, the wave equation is reduced and solved in the case of rigid frame inhomogeneous porous materials. The pressure field, as well as the reflection and transmission coefficients, are obtained numerically using a wave splitting and “transmission” Green’s functions approach (WS-TGF). To validate both the wave equation and the method of resolution at normal and oblique incidence, results obtained by the WS-TGF method are compared to those calculated by the classical transfer matrix method and to experimental measurements for a known two-layered porous material, considered as a single inhomogeneous layer. Discussions are then given of the reflection and transmission coefficients for various inhomogeneity profiles as well as of the internal pressure field. [ABSTRACT FROM AUTHOR]

We theoretically, numerically, and experimentally analyze the Density-Near-Zero (DNZ) regime of a one-dimensional acoustic metamaterial. This acoustic metamaterial is composed of thin elastic plates periodically clamped in an air-filled waveguide, and the effective dynamic zero mass density is obtained from the strong dispersion around the bandgaps associated with the resonances of the plates. We emphasize the importance of the impedance mismatch between the acoustic metamaterial and the surrounding waveguide at the frequency of the zero effective density in addition to the consequences of the inherent losses. As a result, the frequency of the zero phase propagation, i.e., the acoustic propagation with zero phase delay, is not exactly the frequency of the zero density and lies in the frequency bandgap where the effective density is negative. Considering these limitations, the zero phase propagation is still experimentally observed and a subwavelength acoustic dipole is numerically designed, thus demonstrating the possible realistic implementations of DNZ acoustic metamaterials. [ABSTRACT FROM AUTHOR]

An acoustic metadiffuser is a subwavelength locally resonant surface relying on slow sound propagation. Its design consists of rigidly backed slotted panels, with each slit being loaded by an array of Helmholtz resonators. Due to the slow sound properties, the effective thickness of the panel can therefore be dramatically reduced when compared to traditional diffusers made of quarter-wavelength resonators. The aim of this work is to experimentally validate the concept of metadiffusers from the scattering measurements of a specific metadiffuser design, i.e., a quadratic residue metadiffuser. The experimental results reported herein are in close agreement with analytical and numerical predictions, therefore showing the potential of metadiffusers for controlling sound diffusion at very low frequencies. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Using the concepts of slow sound and critical coupling, an ultra-thin acoustic metamaterial panel for perfect and quasi-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 subwavelength regime (λ=88). By controlling the geometry of the slit and the HRs, the intrinsic viscothermal 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

SUMMARY A reduced-order model for structures involving poroelastic materials is proposed in this paper. The approach is based on a separation of the solid and fluid phases of the porous material into separate substructures. For each individual substructure, a decoupled normal mode basis is considered, from which a set of vectors for the decomposition is selected. The preserved modes are completed by an additional family to correct for the influence of the static response of the non-preserved. It is shown that the only neglected phenomenons in the model are the inertia of the non-preserved modes and part of their intercoupling. The following three features render the proposed scheme computationally attractive: (i) real valued matrices are involved in the transformations; (ii) the assembly of complex, frequency dependent matrices is only performed at the stage of solving for a particular frequency; and (iii) the number of normal modes required are selected using a novel method. The computational efficacy is demonstrated, on a simple but realistic 3D case, through numerical results obtained using a reduced number of DOFs, showing a significant reduction of computational cost compared with traditional methods. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The tunable and the engineering possibilities of waveguides in periodic arrays made of rigid square-rod scatterers are theoretically and experimentally reported in this work. Due to the square shape of the scatterers, the control of their orientation with respect to the direction of the incident wave can be used for moulding the propagating acoustic waves inside the periodic structure. On the one hand, the plane wave expansion with supercell approximation is used to obtain the band structure of the periodic system. On the other hand, the scattering of waves in finite periodic arrays is analysed using the finite elements method. Experimentally, a prototype made of rigid square-rod scatterers is used to validate the theoretical predictions. A spatial-frequency filter and some applications in waveguiding for audible sound are discussed in this work. Good agreement between theory and experiments and the high tunability of the system are demonstrated. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The acoustic properties of a porous sheet of medium static air flow resistivity (around 10 000Nms-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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The acoustic response (in particular, the transmission) of a periodic distribution of macroscopic inclusions within a rigid frame porous plate (similar to a sonic crystal) is studied by the multipole method. Numerical results show that the addition of grating stacks leads to bandgaps within the audible frequency range for a small number of stacks, this being associated with a large decrease of the transmission coefficient of the initial plate. The first bandgap is of practical interest for noise shielding, i.e. very low transmission. The second bandgap enables total acoustic absorption within a narrow frequency range due to the fact that a modified mode of the plate lies within this bandgap. [ABSTRACT FROM AUTHOR]

The equations of motion in a macroscopically inhomogeneous porous medium saturated by a fluid are derived. As a verification of their validity, these equations are reduced and solved for rigid frame porous systems. The reflection and transmission coefficients and their corresponding time signals are calculated numerically using wave splitting Green’s function approach for a two-layer porous system considered as one single porous layer with a sudden change in physical properties. The results are compared to experimental results and to those of the classical transfer matrix method for materials saturated by air in the ultrasonic frequency range. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]