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Absorbing sound almost completely at specific frequencies with conventional acoustic materials whose thickness is at least 60 times smaller than the wavelength is a challenge, particularly at low frequencies. Fort this purpose, acoustic metamaterials are of a great interest. Here, the metamaterial is called multi-pancake cavities. It is composed of a main pore with a repetition of thin annular cavities (pancake cavities). Previous research has shown that this repetition increases the effective compressibility of the main pore. This increase makes it possible to decrease the effective sound speed in the material and, consequently, the main pore resonance frequencies. At these resonances, the metamaterial presents absorption peaks, the first one can have a wavelength to material thickness ratio of more than 60 (subwavelength material). To complete the analysis and prediction of absorption peaks (especially secondary peaks) of these metamaterials, it is proposed to adapt a conventional mass-spring model to this metamaterial. Due to the small cavity length-to-diameter ratios, radial propagation is considered inside the annular cavities. This model shows a good agreement with the results obtained by finite element method and by impedance tube measurements. Finally, comparisons with previous theoretical approaches are presented and discussed.

Simultaneously attenuation of multitonal and broadband noise at low frequencies is a challenge for the aerospace, ground transportation and building industries. The technologies proposed in the literature, using layered porous materials with embedded Helmholtz resonators (HR) with a structured neck, exhibited considerable potential when tuned at tonal, multi-tonal or narrow frequency bands. However, the resonance frequencies due to the structured necks of metamaterial are narrow. Our recent investigations have shown that parallel arrangements of several structured metamaterials separated by membranes can broaden the resonance frequencies and increase the number of resonance frequencies to be controlled. This paper presents a parallel assembly of four structured sub-metamaterials separated by membranes. Each of these sub-metamaterials is also a serial assembly of a periodic unit cell (PUC) with a half-neck + cavity + half-neck configuration. The metamaterial is embedded in a layer of glass wool. Coupled fluid-structure numerical calculations in the frequency domain were used to predict the sound absorption coefficient of the metamaterial. The results obtained show a broadening of the absorption peaks and the appearance of additional frequencies due to the membranes.

This article proposes a hybrid numerical-analytical approach to effectively predict the sound absorption coefficient of complex periodic metamaterials with a reasonably low computation time. A variation of an existing metamaterial, consisting of a periodic succession of necks and cavities, is also proposed. The design variation was intended to decrease the frequencies of the absorption coefficient resonant peaks and consists in adding eccentricity in the neck position. The hybrid approach combines a thermoviscous-acoustic (TVA) approach with the transfer matrix (TM) method. The TVA approach estimates the thermoviscous losses of acoustic waves in a periodic unit cell (PUC) of the metamaterial. The TM method is used to simulate the acoustic behaviour of the complete metamaterial from the TM of the PUC calculated numerically. The approach is compared to impedance tube measurements on prototypes of the metamaterial. The comparison shows that the proposed approach is in good agreement with the measured sound absorption coefficient. In addition, numerical simulations and experiments demonstrate that the proposed variation of the existing metamaterial results in a shift of the absorption peaks down in frequency without deteriorating their sound absorption performance.

The noise control at multiple tonal frequencies simultaneously, in the low frequency range, is a challenge for aerospace, ground transportation and building industries. In the past few decades, various low frequency noise control solutions based on acoustic metamaterial designs have been presented in the literature. These solutions showed promising performance and are considered a better alternative to conventional sound insulation materials. In the present investigation, it was noticed that subdividing the cavity of a Helmholtz resonator allowed the control of multi-tonal noise at several resonance frequencies simultaneously and a shift of the resonance peaks towards the low frequencies. This paper proposes concepts of Helmholtz resonators with subdivided cavities to improve the sound transmission loss (STL) performance and simultaneously control the noise at several tonal frequencies. HRs with cylindrical shaped cavities were embedded in a layer of porous material. The STL of the metamaterial noise insulation configuration was predicted using serial and parallel assemblies of transfer matrices (TMM) incorporating a thermo-viscous-acoustic approach to accurately account for the viscous and thermal losses of acoustic wave propagation within the metamaterial. The STL calculated using the proposed TMM approach were observed to be in excellent agreement with the finite element method (FEM) numerical results.

More frequently, recent low-frequency noise control techniques commonly implemented in aerospace and ground transportation as well as in building applications are based on acoustic metamaterial concepts. The technologies proposed in the literature, using layered porous materials with embedded Helmholtz resonators (HR), exhibited considerable potential when tuned at tonal, multi-tonal or narrow frequency bands. Our recent investigations have shown that the acoustical performance of these metamaterials can be further improved by the use of resonators with complex shaped necks. These necks can be designed and optimized to minimize the HR resonance frequencies (small form factor) and maximize the sound transmission loss (STL) performance. This paper presents the developed design optimization method for HRs with complex neck shapes recessed within the HR cavity. The HRs were embedded in a layer of porous material. The implemented approach was based on the transfer matrix methods (TMM) in series and in parallel coupled to a multi-objective optimization. Complex optimum neck shapes were obtained allowing for a shift towards the low frequencies of the resonator resonance with a good STL performance. Moreover the STL calculated using the TMM approach were observed to be in excellent agreement with the finite element method numerical results., InterNoise21, 50th International Congress and Exposition on Noise control Engineering, August 1-5, Washington, D.C.

A transfer matrix approach that combines with finite element calculations is proposed to characterize homogeneous and non-homogeneous acoustic absorbing materials with in-plane periodicity. The characterized acoustic materials are mainly metamaterials made of multiple layers, where at least one layer consists of a non-homogeneous material (NHM). The NHM is a porous or solid matrix with embedded periodic simple or complex inclusions and Helmholtz resonators. The equivalent transfer matrix of the NHM is determined by the proposed approach which is similar to the three-microphone two-load method. By using the equivalent transfer matrix of the NHM coupled analytically in series with other transfer matrices, complex multilayer systems can be modeled easily and quickly in configurations wherein the use of finite element calculation alone will be more expensive and time consuming. The results of the normal incidence sound transmission loss predicted by the present method are compared with finite element results for different configurations of metamaterials and good agreements are obtained. The proposed method offers an efficient way to characterize and design at normal incidence complex multilayer acoustic metamaterials with periodic inclusions. It can be used to optimize multilayer system containing non-homogeneous materials.

International audience; The ability of air-saturated fibrous media to mitigate sound wavesiscontrolled by their transport properties that are themselves controlled by the geometrical characteristics of their microstructure such as the open porosity,fiber radius, and fiber orientation. Here, micro-macro relationships are proposed to link these microstructural features to the macroscopic transport properties of random fiber structures. These transport properties are the tortuosity, the viscous and thermal static permeabilities, and the viscous and thermal characteristic lengths. First, representative elementary volumes (REVs)ofrandom fiber structures are generated for different triplets of porosity,fiber radius and fiber orientation. The fibers are allowed to overlap and are motionless (rigid-frame assumption). The fiber orientation is derivedf rom as econd order orientation tensor.S econd, the transport equations are numerically solved on the REVs which are seen as periodic unit cells. These solutions yield the transport properties governing the sound propagation and dissipation in the respective fibrous media. From these solutions, micro-macro relationships are derivedt oe stimate the transport properties when the geometry of the fiber structure is known. Finally,these relationships are used to study the influence of the microstructural features on the acoustic properties of random fiber structures.

This paper examines the use of proper orthogonal decomposition (POD) and singular value decomposition (SVD) to identify zones on the surface of the source that contribute the most to the sound power the source radiates. First, computational fluid dynamics (CFD) is used to obtain the pressure field at the surface of the blade in a subsonic regime. Then the fluctuation of this pressure field is used as the input for the loading noise in the Ffowcs Williams and Hawkings (FW&H) acoustic analogy. The FW&H analogy is used to calculate the sound power that is radiated by the blade. Secondly, the most important acoustic modes of POD and SVD are used to reconstruct the radiated sound power. The results obtained through POD and SVD are similar to the acoustic power directly obtained with the FW&H analogy. It was observed that the importance of the modes to the radiated sound power is not necessarily in ascending order (for the studied case, the seventh mode was the main contributor). Finally, maps of the most contributing POD and SVD modes have been produced. These maps show the zones on the surface of the blade, where the dipolar aeroacoustic sources contribute the most to the radiated sound power. These identifications are expected to be used as a guide to design and shape the blade surface in order to reduce its radiated noise.

The transport and sound absorption properties of random close packings of monodisperse spherical particles are explored following a multiscale approach. First, the discrete element method is used to simulate the free fall of the monodisperse particles in a bounded domain to create virtual samples that are representative of real samples. Different particle diameters ranging from 1 to 16 mm are studied. From the virtual samples, representative volume elements (RVEs) are defined. Local partial differential equations governing the transport properties are numerically solved on the RVEs. From the discretized RVEs and the numerical solutions, eight transport properties (porosity, tortuosity, and viscous and thermal static tortuosities, permeabilities, and characteristic lengths) are derived. Micro-macro relationships between these properties and the particle diameter are developed. They are validated against experimental measurements of the open porosity and sound absorption coefficients. The relationships are used to analyze the salient sound absorption features of such media, notably the resonant sound absorption behavior. Expressions allowing identification of the optimal particle diameter for a given thickness, or conversely, the optimal thickness for a given particle diameter, for achieving 100% absorption at the first resonant absorption are derived.

The thickness of a dissipative fluid (or equivalent fluid in the case of a porous material) for which its acoustic absorption coefficient reaches an asymptotic value is reviewed. This thickness is called critical depth or penetration depth. It is approximately equal to two or three times the relaxation depth at which the amplitude of a sound pressure wave has been attenuated by a factor 1/e in the dissipative fluid. A simple expression allowing to estimate this critical depth on the only knowledge of the static airflow resistivity is proposed. Its validity is also discussed.

This paper examines the capability of both the Proper Orthogonal Decomposition (POD) and the Singular Value Decomposition (SVD) to identify the zones on the surface blades of a centrifugal fan that contribute the most to the sound power radiated by moving blades. The Computational Fluid Dynamics (CFD) OpenFOAM\(^{\textregistered }\) source code is used as a first step to evaluate the pressure field at the surface of the blade moving in a subsonic regime. The fluctuating component of this pressure field makes it possible to directly estimate both the loading noise and the sound power that is radiated by the blade based on an acoustic analogy of Ffowcs Williams and Hawkings (FW&H). In the second step, the estimated loading noise is then employed to evaluate the radiated sound power using the POD and SVD approaches. It may be noted that the sound power reconstructed by the two latter approaches, when relying solely on the most important acoustic modes, is similar to the one predicted by the FW&H analogy. It is also noted that the contribution of the modes in the radiated sound power does not necessarily appear in ascending order in the decomposition (i.e., in descending order of energy). Moreover, the highest radiating SVD modes are mapped onto the blade surface so as to highlight the zones that contribute the most to the noise. It is then expected that this identification will be used as a guide in the design of the blade surface to reduce the radiated noise.

In this paper, an approach to predict the sound absorption coefficient and sound transmission loss of a parallel assembly of hollow cylinders is presented. This approach is based on image processing and the Parallel Transfer Matrix Method (PTMM) using four Johnson–Champoux–Allard effective fluids. First, effective parameters of each fluid are identified using geometrical considerations and numerical simulations. Then, the approach is validated for a stack of uniform plastic straws, and used to model a natural stack of non-uniform switchgrass straws. Finally, two parametric studies are conducted to evaluate the effects of the geometric parameters of the straws on the acoustic behavior of their stack. It is shown that there are optimal parameters that maximize the acoustic behavior at specific frequencies.

International audience; The ability of fibrous media to mitigate sound waves is controlled by their transport properties that are themselves greatly affected by the geometrical characteristics of their microstructure such as porosity, fiber radius, and fiber orientation. Here, the influence of these geometrical characteristics on the anisotropic transport properties of random fiber structures is investigated. First, representative elementary volumes (REVs) of random fiber structures are generated for different triplets of porosity, fiber radius and fiber orientation. The fibers are allowed to overlap and are motionless (rigid-frame assumption). The fiber orientation is derived from a second order orientation tensor. Second, the transport equations are numerically solved on the REVs which are seen as periodic unit cells (PUCs). These solutions yield the transport properties governing the sound propagation and dissipation in the respective fibrous media. These transport properties are the tortuosity, the viscous and thermal static permeabilities, and the viscous characteristic length. Finally, relations are proposed to estimate the transport properties and the thermal characteristic length when the geometry of the fiber structures is known.

Copyright 2017 Acoustical Society of America. This article may be downloaded for personal use only.Any other use requires prior permission of the author and the Acoustical Society of America.The following article appeared in the Journal of the Acoustical Society of America (JASA) and may be found at http://dx.doi.org/10.1121/1.4989373.; International audience; The main purpose of this article is to present, within a unified framework, a technique based on numerical homogenization, to model the acoustical properties of real fibrous media from their geometrical characteristics and to compare numerical results with experimental data. The authors introduce a reconstruction procedure for a random fibrous medium and use it as a basis for the computation of its geometrical, transport, and sound absorbing properties. The previously ad hoc " fiber anisotropies " and " volume weighted average radii, " used to describe the experimental data on microstructure, are here measured using scanning electron microscopy. The authors show that these parameters, in conjunction with the bulk porosity, contribute to a precise description of the acoustical characteristics of fibrous absorbents. They also lead to an accurate prediction of transport parameters which can be used to predict acoustical properties. The computed values of the perme-ability and frequency-dependent sound absorption coefficient are successfully compared with per-meability and impedance-tube measurements. The authors' results indicate the important effect of fiber orientation on flow properties associated with the different physical properties of fibrous materials. A direct link is provided between three-dimensional microstructure and the sound absorbing properties of non-woven fibrous materials, without the need for any empirical formulae or fitting parameters.

International audience; This presentation examines a perforated resonant material, in which the principal perforations comprise a network of periodically spaced dead-end pores. This material can show good sound absorption at low frequencies, particularly given its relatively small thickness. In a recent study, this kind of material was modeled by an effective fluid approach which allowed low frequency approximations. At low frequency, it was shown that the periodic array of dead-end pores increases the effective compressibility without modifying the effective dynamic density. Thereby, the resonance frequency of the material is reduced in a significant way, as is the frequency of the first sound absorption peak. Moreover, a bandgapeffect occurs at high frequency for the sound transmission problem. This study suggested a new concept of micro-structure for designing low-frequency resonant acoustic absorbers. A transfer matrix approach is now proposed to model and optimize such a concept. Prototypes have been made with 3D printing and tested in an acoustic tube for sound absorption and sound transmission loss. The resonant periodicity effects have been observed, and the measurements compare well with the predictions of the transfer matrix model. Finally, an optimization of the microstructure is proposed.

International audience; A transfer matrix method to predict absorption coefficient and transmission loss of parallel assemblies of materials which can be expressed by a 2 × 2 transfer matrix was published recently. However, the usual method based on the sum of admittances is largely used to predict also surface admittance of parallel assemblies. This paper aims to highlight differences between both methods through three examples on a parallel assembly backed by (1) a rigid wall, (2) an air cavity, and (3) an anechoic termination.

A simple equivalent fluid model is proposed to describe the acoustic behavior of post-consumer and post-industrial recycled fibers otherwise known as Shoddies. The model requires knowledge of the bulk density only, a parameter that is easily measured. Characterization testing was completed on nine Shoddy fiber constructions processed by one of three different methods: thermal bonding, resin bonding, and mechanical bonding. The parameters measured directly were bulk density, open porosity, tortuosity, static airflow resistivity, and normal incidence sound absorption. The materials’ viscous and thermal characteristic lengths and static thermal permeability are determined using indirect acoustical techniques. Empirical relationships linking the material parameters to the bulk density are then substituted into several popular equivalent fluid models. The most accurate ‘simplified’ model is selected by comparing each model’s ability to accurately predict the materials’ acoustic behavior using normal incidence sound absorption to assess performance. The present work is of interest to sound engineers in predicting the acoustic performance of Shoddy-based absorbers.

International audience; The acoustic properties of an air-saturated macroscopically inhomogeneous aluminum foam in the equivalent fluid approximation are studied. A reference sample built by forcing a highly compressible melamine foam with conical shape inside a constant diameter rigid tube is studied first. In this process, a radial compression varying with depth is applied. With the help of an assumption on the compressed pore geometry, properties of the reference sample can be modelled everywhere in the thickness and it is possible to use the classical transfer matrix method as theoretical reference. In the mixture approach, the material is viewed as a mixture of two known materials placed in a patchwork configuration and with proportions of each varying with depth. The properties are derived from the use of a mixing law. For the reference sample, the classical transfer matrix method is used to validate the experimental results. These results are used to validate the mixture approach. The mixture approach is then used to characterize a porous aluminium for which only the properties of the external faces are known. A porosity profile is needed and is obtained from the simulated annealing optimization process.

Complement to standard E2611-09 of the American Society for Testing and Materials [Standard Test Method for Measurement of Normal Incidence Sound Transmission of Acoustical Materials Based on the Transfer Matrix Method (American Society for Testing and Materials, New York, 2009)] is proposed in order to measure normal incidence sound transmission loss of materials in a modified impedance tube using a three-microphone two-load or one-load method. The modified tube is a standard two-microphone impedance tube, where a third microphone is mounted on a movable hard termination. This method is conceptually identical to the four-microphone two-load or one-load method described in the standard; however, it requires fewer transfer functions and one microphone less. The method is validated on (1) symmetrical homogeneous and (2) non-symmetrical non-homogeneous specimens.

This paper exposes a procedure to couple multiport transfer matrices to finite elements for analyzing the acoustics of automotive hollow body networks with a minimum of memory requirements and computational time. Generally, hollow body networks are made up from a series of elongated fluid partitions similar to ducts or waveguides. These fluid partitions generally contain complex elements: junctions, noise control elements, and cavities. The location and type of these elements in the network, mainly the noise control elements (e.g., sealing parts), may impact the noise inside a car. In the proposed hybrid method, the elongated fluid partitions are modeled with fluid finite elements. All complexities are modeled with two-port or multiport transfer matrices. The coupling of these matrices to finite elements is naturally done at the weak integral formulation stage of the acoustical problem. The coupling does not add any degrees of freedom to, nor modify, the original finite element matrix system. Consequently, changing locations and types of noise control elements in the hollow body network is fast and does not require rebuilding the finite element system. This enables optimizing the acoustics of a complex network on a desktop computer. The hybrid method is compared to experimental results on a tee-shaped hollow body networks. Good correlations are obtained.

Several methods for measuring the complex wave number and the characteristic impedance of sound absorbers have been proposed in the literature. These methods can be classified into single frequency and wideband methods. In this paper, the main existing methods are revisited and discussed. An alternative method which is not well known or discussed in the literature while exhibiting great potential is also discussed. This method is essentially an improvement of the wideband method described by Iwase et al., rewritten so that the setup is more ISO 10534-2 standard-compliant. Glass wool, melamine foam and acoustical/thermal insulator wool are used to compare the main existing wideband non-iterative methods with this alternative method. It is found that, in the middle and high frequency ranges the alternative method yields results that are comparable in accuracy to the classical two-cavity method and the four-microphone transfer-matrix method. However, in the low frequency range, the alternative method appears to be more accurate than the other methods, especially when measuring the complex wave number.

Two types of general methods can be found in the literature for the determination of the normal incidence sound transmission loss (nSTL) of acoustical elements. The first one is based on the transfer matrix (TM) approach, and the second one is based on the wavefield decomposition (WD) theory. From all the techniques proposed in the literature, the general TM methods (two-load or two-source location) are the only methods yielding the exact nSTL of an acoustical element without any assumptions on its symmetry and on the termination (i.e., the load). Except for the case of an anechoic termination, there is no method based on the WD theory which yields exact nSTL. This paper presents a general WD method to measure the exact nSTL of an acoustical element without any assumptions on its symmetry and on the termination. Similar to general TM methods for non-symmetrical elements, four microphones and two loads will be required. As a first validation of the method, symmetrical and non-symmetrical porous materials are investigated. Results are discussed and compared with some existing methods and with the classical two-load method. A perfect agreement is found with the classical two-load method.

A method is developed to obtain the normal incidence sound transmission loss of noise control elements used in piping systems from upstream surface impedance measurements only. The noise control element may be a small material specimen in an impedance tube, a sealing part in an automotive hollow body network, an expansion chamber, a resonator, or a muffler. The developments are based on a transfer matrix (four-pole) representation of the noise control element and on the assumption that only plane waves propagate upstream and downstream the element. No assumptions are made on its boundary conditions, dimensions, shape, and material properties (i.e., the element may be symmetrical or not along its thickness, homogeneous or not, isotropic or not). One-load and two-load procedures are also proposed to identify the transfer matrix coefficients needed to obtain the true transmission loss of the tested element. The method can be used with a classical two-microphone impedance tube setup (i.e., no additional downstream tube and downstream acoustical measurements). The method is tested on three different noise control elements: two impedance tube multilayered specimens and one expansion chamber. The results found using the developed method are validated using numerical simulations.

In this letter, the low and high frequency limits of the effective density characterizing a limp frame porous medium are investigated. These theoretical limits are compared to the ones found for a classical rigid frame porous medium, and to experimental measurements. While the high frequency asymptotic behaviors of both limp and rigid effective densities are usually only slightly different, their low frequency behaviors are significantly different. Compared to experimental measurements performed on a limp frame fibrous layer, only the limp frame effective density yields good correlations over the whole frequency range.

International audience; A theoretical and numerical study of the sound propagation in air-saturated porous media with straight main pores bearing lateral cavities (dead-ends) is presented. The lateral cavities are located at " nodes " periodically spaced along each main pore. The effect of periodicity in the distribution of the lateral cavities is studied, and the low frequency limit valid for the closely spaced dead-ends is considered separately. It is shown that the absorption coefficient and transmission loss are influenced by the viscous and thermal losses in the main pores as well as their perforation rate. The presence of long or short dead-ends significantly alters the acoustical properties of the material and can increase significantly the absorption at low frequencies (a few hundred hertz). These depend strongly on the geometry (diameter and length) of the dead-ends, on their number per node, and on the periodicity along the propagation axis. These effects are primarily due to low sound speed in the main pores and to thermal losses in the dead-end pores. The model predictions are compared with experimental results. Possible designs of materials of a few cm thicknesses displaying enhanced low frequency absorption at a few hundred hertz are proposed.

The Oberst method is widely used for the measurement of the mechanical properties of viscoelastic or damping materials. The application of this method, as described in the ASTM E756 standard, gives good results as long as the experimental set-up does not interfere with the system under test. The main difficulty is to avoid adding damping and mass to the beam owing to the excitation and response measurement. In this paper, a method is proposed to skirt those problems. The classical cantilever Oberst beam is replaced by a double sized free-free beam excited in its center. The analysis is based on a frequency response function measured between the imposed velocity at the center (measured with an accelerometer) and an arbitrary point on the beam (measured with a laser vibrometer). The composite beam (base beam + material) properties are first extracted from the measurement by an optimization algorithm. Young’s modulus and structural damping coefficient of the material under test can be deduced using classical...

The influence of mounting conditions on the measurement of the absorption coefficient in the standing wave tube (swt) is investigated. In a previous paper [D. Pilon, R. Panneton, and F. Sgard, J. Acoust. Soc. Am. 114, 1980–1987 (2003)], a behavioral criterion was developed to access the effect of a circumferential edge constraint on elastic foams. Similarly, the effect of circumferential air gaps on porous materials is studied here. The objective is to identify the materials, in terms of a ratio based on their physical properties, for which it is possible to measure the theoretical absorption coefficient when mounted inside the swt with a circumferential air gap. The difference between the measured and theoretical absorption coefficient is evaluated for a wide range of materials with various sample sizes. These errors are then sorted in terms of the chosen ratio. It is shown that for certain values of the ratio, the theoretical absorption coefficient can be efficiently measured using the swt. Through the use of this acousto-visco-inertial criterion, an experimenter can determine which absorption is going to be measured: the theoretical absorption or one that will be influenced by the circumferential air gaps.

This paper proposes a quasi-static method for the characterization of the elastic properties of poroelastic materials. The method is based on the development of polynomial relations among compression stiffness, Young’s modulus, Poisson’s ratio, and shape factor derived from high order axisymmetrical finite element simulations on a disk-shaped poroelastic sample under static compression. The shape factor is defined as half the radius to thickness ratio of the sample. The polynomial relations account for the fact that the disk sample “wants” to bulge sideways when compressed between two rigid plates on which it is bonded. A compression test setup is used to measure the compression stiffness of two disk samples of different large shape factors. The measured stiffnesses together with the polynomial relations lead to a system of two equations and two unknowns. The solution of the system yields the Young’s modulus and Poisson’s ratio of the poroelastic material. Employing the proposed quasi-static method, Young...

Recently Atalla et al. [J. Acoust. Soc. Am. 104, 1444–1452 (1998)] and Debergue et al. [J. Acoust. Soc. Am. 106, 2383–2390 (1999)] presented a weak integral formulation and the general boundary conditions for a mixed pressure-displacement version of the Biot’s poroelasticity equations. Finite element discretization was applied to the formulation to solve 3D vibro-acoustic problems involving elastic, acoustic, and poroelastic domains. In this letter, an enhancement of the weak integral formulation is proposed to facilitate its finite element implementation. It is shown that this formulation simplifies the assembly process of the poroelastic medium, the imposition of its boundary conditions, and its coupling with elastic and acoustic media.

International audience; The transfer matrix method (TMM) is used conventionally to predict the acoustic properties of laterally infinite homogeneous layers assembled in series to form a multilayer. In this work, a parallel assembly process of transfer matrices is used to model heterogeneous materials such as patchworks, acoustic mosaics, or a collection of acoustic elements in parallel. In this method, it is assumed that each parallel element can be modeled by a 2 × 2 transfer matrix, and no diffusion exists between elements. The resulting transfer matrix of the parallel assembly is also a 2 × 2 matrix that can be assembled in series with the classical TMM. The method is validated by comparison with finite element (FE) simulations and acoustical tube measurements on different parallel/series configurations at normal and oblique incidence. The comparisons are in terms of sound absorption coefficient and transmission loss on experimental and simulated data and published data, notably published data on a parallel array of resonators. From these comparisons, the limitations of the method are discussed. Finally, applications to three-dimensional geometries are studied, where the geometries are discretized as in a FE concept. Compared to FE simulations, the extended TMM yields similar results with a trivial computation time.

International audience; A theoretical and experimental study of the acoustic properties of porous materials containing dead-end (or partially opened) porosity was recently proposed by Dupont et al. The present article provides a description of partially opened porosity systems and their numerous potential applications in the general context of the study of porous materials, the classical models describing them, and the characterization techniques. It is shown that the dead-end pore effect can be treated independently and that the description of this effect can be associated with any acoustic model of porous media. Different theoretical developments describing the dead-end porosity effect are proposed. In particular, a model involving the average effective length of the dead-end pores is presented. It is also shown that if the dead-end effect can be treated separately, the transfer matrix method is particularly well suited for the description of single or multilayer systems with dead-end porosity.

This paper presents the boundary conditions that apply to the weak integral formulation of the Biot mixed (u_,p) poroelasticity equations. These boundary conditions are derived from the classical boundary conditions of the Biot displacement (u_,U_) poroelasticity equations. They are applied to the surface integrals of the associated weak form to account for exterior excitations, supports, and couplings with exterior elastic, acoustic, poroelastic media, and a septum. It will be shown that the derived boundary conditions for the (u_,p) formulation lead to simpler finite element equations compared to those obtained from the (u_,U_) formulation. Finally, two numerical examples are presented to validate the poroelastic-septum coupling condition, and to highlight the limitations of the free edge condition on a poroelastic medium.

Recently, finite element models based on Biot’s displacement (u¯,U¯) formulation for poroelastic materials have been extensively used to predict the acoustical and structural behavior of multilayer structures. These models while accurate lead to large frequency dependent matrices for three-dimensional problems necessitating important setup time, computer storage and solution time. In this paper, a novel exact mixed displacement pressure (u¯,p) formulation is presented. The formulation derives directly from Biot’s poroelasticity equations. It has the form of a classical coupled fluid-structure problem involving the dynamic equations of the skeleton in vacuo and the equivalent fluid in the rigid skeleton limit. The governing (u¯,p) equations and their weak integral form are given together with the coupling conditions with acoustic media. The numerical implementation of the presented approach in a finite element code is discussed. Examples are presented to show the accuracy and effectiveness of the presented formulation.

In this paper, the finite element method (FEM) is used to solve the three-dimensional poroelasticity problem in acoustics based on the isotropic Biot–Allard theory. A displacement finite element model is derived using the Lagrangian approach together with an analogy with solid elements. From this model, it is seen that the “damping” and “stiffness” matrices of the poroelastic media are complex and frequency dependent. This leads to cumbersome calculations for large finite element models and spectral analyses. To overcome this difficulty, an efficient algorithm is proposed. It is based on low-frequency approximations of the frequency-dependent dissipation mechanisms in poroelastic media. This efficient algorithm allows the poroelastic materials to be modeled with classical FEM codes. Also, the acoustic–poroelastic and the poroelastic–poroelastic coupling conditions are presented. The proposed model is compared to existing literature for both two-dimensional and three-dimensional problems. Excellent compari...

International audience; This study presents a method to measure the acoustic properties of a homogeneous porous material with a support or a reduction element in an acoustic tube. Some materials tested have a lateral size much smaller than the tube's diameter, as they cannot be produced in the correct dimensions without corrupting the material; this also permits the testing of the same samples in a large frequency bandwidth by using different section tubes. Moreover, the acoustic leaks on the material boundaries can significantly change the transmission loss measured in tubes. To rectify these problems, rings can be placed on each material surface. The presence of these rings can influence the acoustic indicator measurement; while this effect is negligible for tubes with a large cross section, it is not for tubes with a small cross section. To correct, or remove, the influence of the rings, we propose to use an application of the parallel assembly process of the transfer matrix method which has recently been proposed by Panneton et al. [Proceeding Internoise New York (2012)]. Measurements on classical porous materials with and without reductions are proposed and compared to simulated results. The ring's effects and the proposed corrections are discussed for different materials.

International audience; The Transfer Matrix Method (TMM) is used conventionally to predict the acoustic properties of laterally infinite homogeneous layers assembled in series to form a multilayer. In this work, a parallel assembly process of transfer matrices is used to model heterogeneous materials such as patchworks, acoustic mosaics, or a collection of acoustic elements in parallel. In this method, it is assumed that each parallel element can be modeled by a 2x2 transfer matrix, and no diffusion exists between elements. The method is validated by comparison with finite element method (FEM). Then, an overview of the possibilities, such as the combination of series and parallel matrices, the sound absorption coefficient and the transmission loss of a parallel array of resonators or three-dimensional geometries is presented and discussed.

International audience; The acoustic properties of porous materials containing dead-end (DE) pores have been proposed by Dupont et al. [J. Appl. Phys. 110, 094903 (2011)]. In the theoretical description, two physical parameters were defined (the dead-end porosity and the average length of the dead-end pores). With the knowledge of the open porosity (measured with non-acoustic methods), and the measurement of kinematic porosity (also called the Biot porosity in this article), it is possible to deduce the dead-end porosity. Two acoustic methods for measuring the Biot porosity for a wide range of porosities are proposed. These methods are based on acoustic transmission and on the low and high frequency behaviors of acoustic indicators. The low frequency method is valid for high porosities. It involves measurements in a transmission tube and the knowledge of the theoretical asymptotic behavior of the phase velocity at high frequencies. The high frequency method is based on ultrasonic measurements and on the high frequency asymptotic behavior of the transmission coefficient. It is well adapted for material with relatively low values of porosity. Good precision was found for both methods and materials containing dead end porosity were tested.

The sound transmission performance of finite multilayer systems containing poroelastic materials is of utmost importance for noise control in automobiles, aircrafts, buildings, and several other engineering applications. Currently, the need for tools predicting the acoustical and structural behaviors of such structures is considerably increasing. In this paper, such a tool is presented. It is applied to the sound transmission loss through multilayer structures made from a combination of elastic, air, and poroelastic materials. The presented approach is based on a three‐dimensional finite element model. It uses classical elastic and fluid elements to model the elastic and fluid media. For the poroelastic material, it uses a two‐field displacement formulation derived from the Biot theory. Furthermore, it couples with a boundary element approach to account, when important, for fluid–structure coupling and to calculate the transmission loss through the multilayer structure. Numerical predictions of the transm...

Recently, a displacement (u,U) finite element model for the three‐dimensional poroelasticity problem has been developed by Panneton and Atalla [J. Acoust. Soc. Am. 98, 2976(A) (1995)]. This model, while accurate, has the disadvantage of requiring cumbersome calculations for large finite element models and spectral analyses. To overcome this difficulty, this paper presents a mixed displacement‐pressure (u,P) finite element model. First, the classical Biot–Allard equations are rewritten in terms of the solid phase macroscopic displacement vector and the fluid phase macroscopic pressure. The new coupled equations have the advantage of writing the poroelasticity equations in the form of the coupling between an equivalent elastodynamic equation for the solid phase and an equivalent Helmholtz equation for the fluid phase. In particular, the equivalent fluid model is transparent in the developed equations. Next, the associated variational formulation is presented together with its numerical implementation. Also the acoustic–poroelastic, elastic–poroelastic, and poroelastic–poroelastic coupling conditions are derived. Several examples are presented to show the accuracy and effectiveness of the proposed model and its coupling with elastic and acoustic media. In particular a systematic comparison is made with the (u,U) finite element formulation. [Work supported by Canadair, CRSNG, and FCAR.]

Vibrations and sound radiation by finite cylindrical shells have been extensively studied in the past few years. Usually, the authors have studied the vibrations and the sound radiation by cylinders in the case of a non-moving harmonic driving force. Most papers dealing with a moving force on a cylindrical shell (axially or circumferentially) were only concerned about the mechanical vibrations. This is a presentation of the work under progress to develop a model including both the vibrations and the sound radiation of a simply supported cylindrical shell excited by a circumferentially moving radial point force. The motivation behind this work is the modelisation of the `pressure screens' used in the pulp and paper industry. The theoretical formulation presented is based on a variational approach. The case of a homogeneous cylindrical shell in air is treated as a first step towards more complex structures. Numerical results in terms of quadratic velocity and radiated sound power are presented, and principal phenomena related to the moving force rotational speed are discussed

Copyright 2010 Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America.; International audience; Closed-cell metallic foams are known for their rigidity, lightness, thermal conductivity as well as their low production cost compared to open-cell metallic foams. However, they are also poor sound absorbers. Similarly to a rigid solid, a method to enhance their sound absorption is to perforate them. This method has shown good preliminary results but has not yet been analyzed from a microstructure point of view. The objective of this work is to better understand how perforations interact with closed-cell foam microstructure and how it modifies the sound absorption of the foam. A simple two-dimensional microstructural model of the perforated closed-cell metallic foam is presented and numerically solved. A rough three-dimensional conversion of the two-dimensional results is proposed. The results obtained with the calculation method show that the perforated closed-cell foam behaves similarly to a perforated solid; however, its sound absorption is modulated by the foam microstructure, and most particularly by the diameters of both perforation and pore. A comparison with measurements demonstrates that the proposed calculation method yields realistic trends. Some design guides are also proposed. (C) 2010 Acoustical Society of America. [DOI: 10.1121/1.3473696]

International audience; This paper presents a straightforward application of an indirect method based on a three-microphone impedance tube setup to determine the non-acoustic properties of a sound absorbing porous material. First, a three-microphone impedance tube technique is used to measure some acoustic properties of the material (i.e., sound absorption coefficient, sound transmission loss, effective density and effective bulk modulus) regarded here as an equivalent fluid. Second, an indirect characterization allows one to extract its non-acoustic properties (i.e., static airflow resistivity, tortuosity, viscous and thermal characteristic lengths) from the measured effective properties and the material open porosity. The procedure is applied to four different sound absorbing materials and results of the characterization are compared with existing direct and inverse methods. Predictions of the acoustic behavior using an equivalent fluid model and the found non-acoustic properties are in good agreement with impedance tube measurements.

In this paper, the question of the acoustical determination of macroscopic thermal parameters used to describe heat exchanges in rigid open-cell porous media subjected to acoustical excitations is addressed. The proposed method is based on the measurement of the dynamic bulk modulus of the material, and analytical inverse solutions derived from different semiphenomenological models governing the thermal dissipation of acoustic waves in the material. Three models are considered: (1) Champoux-Allard model [J. Appl. Phys. 20, 1975-1979 (1991)] requiring knowledge of the porosity and thermal characteristic length, (2) Lafarge et al. model [J. Acoust. Soc. Am. 102, 1995-2006 (1997)] using the same parameters and the thermal permeability, and (3) Wilson model [J. Acoust. Soc. Am. 94, 1136-1145 (1993)] that requires two adjusted parameters. Except for the porosity that is obtained from direct measurement, all the other thermal parameters are derived from the analytical inversion of the models. The method is applied to three porous materials-a foam, a glass wool, and a rock wool-with very different thermal properties. It is shown that the method can be used to assess the validity of the descriptive models for a given material.

Copyright 2008 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.; International audience; Is it possible to find a two-dimensional (2D) periodic unit cell representative of the dynamic viscous dissipation properties of a real porous media? This is a challenging question addressed in this paper through a review of tools and methods of experimental and computational micro(poro)mechanics. The combination of advanced experimental imaging and numerical homogenization techniques provides a unique opportunity to understand and assess the limits of two-dimensional models of microstructures, as a potential basis for the engineering prediction of macroscopic properties of acoustical materials. This is illustrated for a real sample of open-cell aluminum foam. The conclusion, based on this analysis, is that the 2D periodic foam model geometry provides a reliable estimate of the dynamic permeability, except in the low frequency range. This is not surprising because in the 2D periodic foam model geometry, ligaments are always perpendicular to the flow direction, thus decreasing artificially the static permeability of the viscous flow.

Copyright 2008 Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America.; International audience; Based on a direct generalization of a proof given by Torquato for symmetry property in static regime, this express letter clarifies the reasons why the dynamic permeability tensor is symmetric for spatially periodic structures having symmetrical axes which do not coincide with orthogonal pairs being perpendicular to the axis of three-, four-, and sixfold symmetry. This somewhat nonintuitive property is illustrated by providing detailed numerical examples for a hexagonal lattice of solid cylinders in the asymptotic and frequency dependent regimes. It may be practically useful for numerical implementation validation and∕or convergence assessment.

This work shows how to couple transfer matrix method to finite element method with a view to analyze the acoustic response of hollow body structures with a minimum of memory requirements and computational time. An hollow body structure is made up from a series of elongated rigid‐walled fluid partitions (i.e., waveguides). These fluid partitions are separated by any passive (e.g., multilayered sound barrier) or reactive elements (e.g., expansion chamber). In the proposed hybrid model, the elongated fluid partitions are modeled using 1D fluid finite elements, and the passive or reactive elements using transfer matrices. From the weak integral formulation of the acoustic problem, it is shown how the coupling with the transfer matrix is taken into account through a mixed boundary condition. After discretization of the acoustic pressure and application of the variational principle, the finite element matrix system is obtained, where only the nodal pressures in the fluid partitions remain. The transfer matrix has been converted into a kind of admittance matrix, where no additional degrees of freedom are necessary to account for the passive or reactive elements. The method is used to predict the acoustic response of a real hollow body structure. Good correlations are obtained with experimentations.