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Roncen R, Fellah ZEA, Ogam E. Bayesian inference of human bone sample properties using ultrasonic reflected signals. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2020; 148:3797. [PMID: 33379902 DOI: 10.1121/10.0002878] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2020] [Accepted: 11/15/2020] [Indexed: 06/12/2023]
Abstract
The non-intrusiveness and low cost of ultrasonic interrogation is motivating the development of new means of detection of osteoporosis and other bone deficiencies. Bone is a porous media saturated with a viscous fluid and could thus be well characterized by the Biot model. The main purpose of this work is to present an in vitro methodology for the identification of the properties and structural parameters of the bone, adopting a statistical Bayesian inference technique using ultrasonic reflected signals at normal incidence. It is, in this respect, a companion paper to a previous work [J. Acoust. Soc. Am. 146, 3 (2019), pp. 1629-1640], where ultrasonic transmitted signals were considered. This approach allows the retrieval of some important parameters that characterize the bone structure and associated uncertainties. The method was applied to seven samples of bone extracted from femoral heads, immersed in water, and exposed to ultrasonic signals with a center frequency of ≈500 kHz. For all seven samples, signals at different sites were acquired to check the method robustness. The porosity, pore mean size and standard deviation, and the porous frame bulk modulus were all successfully identified using only ultrasonic reflected signals.
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Affiliation(s)
- R Roncen
- ONERA/Département Multi-Physique pour l'Énergétique, Université de Toulouse, F-31055, Toulouse, France
| | - Z E A Fellah
- Laboratoire de Mécanique et d'Acoustique, Centre National de la Recherche Scientifique, Unité Mixte de Recherche 7031, Aix-Marseille Université, Centrale Marseille, F-13402 Marseille Cedex 20, France
| | - E Ogam
- Laboratoire de Mécanique et d'Acoustique, Centre National de la Recherche Scientifique, Unité Mixte de Recherche 7031, Aix-Marseille Université, Centrale Marseille, F-13402 Marseille Cedex 20, France
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2
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Cavalieri T, Boulvert J, Gabard G, Romero-García V, Escouflaire M, Regnard J, Groby JP. Graded and Anisotropic Porous Materials for Broadband and Angular Maximal Acoustic Absorption. MATERIALS 2020; 13:ma13204605. [PMID: 33081129 PMCID: PMC7602802 DOI: 10.3390/ma13204605] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/01/2020] [Revised: 09/28/2020] [Accepted: 09/30/2020] [Indexed: 11/16/2022]
Abstract
The design of graded and anisotropic materials has been of significant interest, especially for sound absorption purposes. Together with the rise of additive manufacturing techniques, new possibilities are emerging from engineered porous micro-structures. In this work, we present a theoretical and numerical study of graded and anisotropic porous materials, for optimal broadband and angular absorption. Through a parametric study, the effective acoustic and geometric parameters of homogenized anisotropic unit cells constitute a database in which the optimal anisotropic and graded material will be searched for. We develop an optimization technique based on the simplex method that is relying on this database. The concepts of average absorption and diffuse field absorption coefficients are introduced and used to maximize angular acoustic absorption. Numerical results present the optimized absorption of the designed anisotropic and graded porous materials for different acoustic targets. The designed materials have anisotropic and graded effective properties, which enhance its sound absorption capabilities. While the anisotropy largely enhances the diffuse field absorbing when optimized at a single frequency, graded properties appear to be crucial for optimal broadband diffuse field absorption.
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Affiliation(s)
- Théo Cavalieri
- Laboratoire d’Acoustique de l’Université du Mans, LAUM-UMR CNRS 6613, Le Mans Université, Avenue Olivier Messiaen, 72085 Le Mans CEDEX 9, France; (J.B.); (G.G.); (V.R.-G.); (J.-P.G.)
- Safran Aircraft Engines, Rond Point René Ravaud - Réau, 77550 Moissy-Cramayel, France; (M.E.); (J.R.)
- Correspondence:
| | - Jean Boulvert
- Laboratoire d’Acoustique de l’Université du Mans, LAUM-UMR CNRS 6613, Le Mans Université, Avenue Olivier Messiaen, 72085 Le Mans CEDEX 9, France; (J.B.); (G.G.); (V.R.-G.); (J.-P.G.)
- Safran Aircraft Engines, Rond Point René Ravaud - Réau, 77550 Moissy-Cramayel, France; (M.E.); (J.R.)
- Laboratoire d’Analyse Vibratoire et Acoustique, LAVA, Department of Mechanical Engineering, École Polytechnique de Montréal, P.O. Box 6079 Station Centre-ville, Montréal, QC H3C 3A7, Canada
| | - Gwénaël Gabard
- Laboratoire d’Acoustique de l’Université du Mans, LAUM-UMR CNRS 6613, Le Mans Université, Avenue Olivier Messiaen, 72085 Le Mans CEDEX 9, France; (J.B.); (G.G.); (V.R.-G.); (J.-P.G.)
| | - Vicent Romero-García
- Laboratoire d’Acoustique de l’Université du Mans, LAUM-UMR CNRS 6613, Le Mans Université, Avenue Olivier Messiaen, 72085 Le Mans CEDEX 9, France; (J.B.); (G.G.); (V.R.-G.); (J.-P.G.)
| | - Marie Escouflaire
- Safran Aircraft Engines, Rond Point René Ravaud - Réau, 77550 Moissy-Cramayel, France; (M.E.); (J.R.)
| | - Josselin Regnard
- Safran Aircraft Engines, Rond Point René Ravaud - Réau, 77550 Moissy-Cramayel, France; (M.E.); (J.R.)
| | - Jean-Philippe Groby
- Laboratoire d’Acoustique de l’Université du Mans, LAUM-UMR CNRS 6613, Le Mans Université, Avenue Olivier Messiaen, 72085 Le Mans CEDEX 9, France; (J.B.); (G.G.); (V.R.-G.); (J.-P.G.)
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Cavalieri T, Boulvert J, Schwan L, Gabard G, Romero-Garcìa V, Groby JP, Escouflaire M, Mardjono J. Acoustic wave propagation in effective graded fully anisotropic fluid layers. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2019; 146:3400. [PMID: 31795708 DOI: 10.1121/1.5131653] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2019] [Accepted: 10/11/2019] [Indexed: 06/10/2023]
Abstract
This work deals with the sound wave propagation modeling in anisotropic and heterogeneous media. The considered scattering problem involves an infinite layer of finite thickness containing an anisotropic fluid whose properties can vary along the layer depth. The specular transmission and reflection of an acoustic plane wave by such a layer is modeled through the state vector formalism for the acoustic fields. This is solved using three different numerical techniques, namely, the transfer matrix method, Peano series, and transfer Green's function. These three methods are compared to demonstrate the convergence of the numerical solutions. Moreover, the implemented numerical procedures allow the authors to retrieve the internal acoustic fields and show their dependency along with the fluid anisotropic properties. Results are presented to illustrate the changes in absorption that can be achieved by tuning the fluid anisotropy as well as the variation of these properties across the depth of the layer. The results presented are in very good agreement across the different methods. Given that many porous materials can be modeled as equivalent fluids, the results presented show the potential offered by such numerical techniques, and can further give more insight into inhomogeneous anisotropic porous materials.
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Affiliation(s)
- Théo Cavalieri
- Laboratoire d'Acoustique de l'Université du Mans, LAUM-UMR CNRS 6613, Le Mans Université, Avenue Olivier Messiaen, 72085 LE MANS CEDEX 9, France
| | - Jean Boulvert
- Laboratoire d'Acoustique de l'Université du Mans, LAUM-UMR CNRS 6613, Le Mans Université, Avenue Olivier Messiaen, 72085 LE MANS CEDEX 9, France
| | - Logan Schwan
- Laboratoire d'Acoustique de l'Université du Mans, LAUM-UMR CNRS 6613, Le Mans Université, Avenue Olivier Messiaen, 72085 LE MANS CEDEX 9, France
| | - Gwénaël Gabard
- Laboratoire d'Acoustique de l'Université du Mans, LAUM-UMR CNRS 6613, Le Mans Université, Avenue Olivier Messiaen, 72085 LE MANS CEDEX 9, France
| | - Vicent Romero-Garcìa
- Laboratoire d'Acoustique de l'Université du Mans, LAUM-UMR CNRS 6613, Le Mans Université, Avenue Olivier Messiaen, 72085 LE MANS CEDEX 9, France
| | - Jean-Philippe Groby
- Laboratoire d'Acoustique de l'Université du Mans, LAUM-UMR CNRS 6613, Le Mans Université, Avenue Olivier Messiaen, 72085 LE MANS CEDEX 9, France
| | - Marie Escouflaire
- Safran Aircraft Engines, Rond Point René Ravaud-Réau, 77550 Moissy-Cramayel, France
| | - Jacky Mardjono
- Safran Aircraft Engines, Rond Point René Ravaud-Réau, 77550 Moissy-Cramayel, France
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Niskanen M, Duclos A, Dazel O, Groby JP, Kaipio J, Lähivaara T. Estimating the material parameters of an inhomogeneous poroelastic plate from ultrasonic measurements in water. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2019; 146:2596. [PMID: 31671978 DOI: 10.1121/1.5129369] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2019] [Accepted: 09/25/2019] [Indexed: 06/10/2023]
Abstract
The estimation of poroelastic material parameters based on ultrasound measurements is considered. The acoustical characterisation of poroelastic materials based on various measurements is typically carried out by minimising a cost functional of model residuals, such as the least squares functional. With a limited number of unknown parameters, least squares type approaches can provide both reliable parameter and error estimates. With an increasing number of parameters, both the least squares parameter estimates and, in particular, the error estimates often become unreliable. In this paper, the estimation of the material parameters of an inhomogeneous poroelastic (Biot) plate in the Bayesian framework for inverse problems is considered. Reflection and transmission measurements are performed and 11 poroelastic parameters, as well as 4 measurement setup-related nuisance parameters, are estimated. A Markov chain Monte Carlo algorithm is employed for the computational inference to assess the actual uncertainty of the estimated parameters. The results suggest that the proposed approach for poroelastic material characterisation can reveal the heterogeneities in the object, and yield reliable parameter and uncertainty estimates.
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Affiliation(s)
- Matti Niskanen
- Department of Applied Physics, University of Eastern Finland, Postal Box 1627, FIN-70211 Kuopio, Finland
| | - Aroune Duclos
- Laboratoire d'Acoustique de l'Université du Mans, LAUM - Unité mixte de recherche Centre national de la recherche scientifique, UMR CNRS 6613, Le Mans Université, Avenue Olivier Messiaen, F-72085 Le Mans Cedex 9, France
| | - Olivier Dazel
- Laboratoire d'Acoustique de l'Université du Mans, LAUM - Unité mixte de recherche Centre national de la recherche scientifique, UMR CNRS 6613, Le Mans Université, Avenue Olivier Messiaen, F-72085 Le Mans Cedex 9, France
| | - Jean-Philippe Groby
- Laboratoire d'Acoustique de l'Université du Mans, LAUM - Unité mixte de recherche Centre national de la recherche scientifique, UMR CNRS 6613, Le Mans Université, Avenue Olivier Messiaen, F-72085 Le Mans Cedex 9, France
| | - Jari Kaipio
- Department of Mathematics, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
| | - Timo Lähivaara
- Department of Applied Physics, University of Eastern Finland, Postal Box 1627, FIN-70211 Kuopio, Finland
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5
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Roncen R, Fellah ZEA, Piot E, Ogam E. Bayesian inference of a human bone and biomaterials using ultrasonic transmitted signals. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2019; 146:1629. [PMID: 31590502 DOI: 10.1121/1.5125263] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2019] [Accepted: 08/20/2019] [Indexed: 06/10/2023]
Abstract
Ultrasonic techniques could be good candidates to aid the assessment of osteoporosis detection, due to their non-intrusiveness and low cost. While earlier studies made use of the measured ultrasonic phase velocity and attenuation inside the bone, very few have considered an inverse identification of both the intrinsic pore microstructure and the mechanical properties of the bone, based on Biot's model. The main purpose of this work is to present an in vitro methodology for bone identification, adopting a statistical Bayesian inference technique using ultrasonic transmitted signals, which allows the retrieval of the identified parameters and their uncertainty. In addition to the bone density, Young's modulus and Poisson's ratio, the bone pore microstructure parameters (porosity, tortuosity, and viscous length) are identified. These additional microstructural terms could improve the knowledge on the correlations between bone microstructure and bone diseases, since they provide more information on the trabecular structure. In general, the exact properties of the saturating fluid are unknown (bone marrow and blood in the case of bone study) so in this work, the fluid properties (water) are identified during the inference as a proof of concept.
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Affiliation(s)
- R Roncen
- ONERA/Département Multi-Physique pour l'énergétique, Université de Toulouse, F-31055, Toulouse, France
| | - Z E A Fellah
- Laboratoire de Mécanique et d'Acoustique, Centre National de la Recherche Scientifique, Unité Mixte de Recherche 7031, Aix-Marseille Université, Centrale Marseille, F-13402 Marseille Cedex 20, France
| | - E Piot
- ONERA/Département Multi-Physique pour l'énergétique, Université de Toulouse, F-31055, Toulouse, France
| | - E Ogam
- Laboratoire de Mécanique et d'Acoustique, Centre National de la Recherche Scientifique, Unité Mixte de Recherche 7031, Aix-Marseille Université, Centrale Marseille, F-13402 Marseille Cedex 20, France
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6
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Nennig B, Binois R, Dauchez N, Perrey-Debain E, Foucart F. A transverse isotropic equivalent fluid model combining both limp and rigid frame behaviors for fibrous materials. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2018; 143:2089. [PMID: 29716263 DOI: 10.1121/1.5030925] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Due to the manufacturing process, some fibrous materials like glasswool may be transversely isotropic (TI): fibers are mostly parallel to a plane of isotropy within which material properties are identical in all directions whereas properties are different along the transverse direction. The behavior of TI fibrous material is well described by the TI Biot's model, but it requires one to measure several mechanical parameters and to solve the TI Biot's equations. This paper presents an equivalent fluid model that can be suitable for TI materials under certain assumptions. It takes the form of a classical wave equation for the pressure involving an effective density tensor combining both limp and rigid frame behaviors of the material. This scalar wave equation is easily amenable to analytical and numerical treatments with a finite element method. Numerical results, based on the proposed model, are compared with experimental results obtained for two configurations with a fibrous material. The first concerns the absorption of an incident plane wave impinging on a fibrous slab and the second corresponds to the transmission loss of a splitter-type silencer in a duct. Both configurations highlight the effect of the sample orientation and give an illustration of the unusual TI behavior for fluids.
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Affiliation(s)
- Benoit Nennig
- Institut supérieur de mécanique de Paris (SUPMECA), Laboratoire Quartz EA 7393, 3 rue Fernand Hainaut, 93407 Saint-Ouen, France
| | - Rémy Binois
- Institut supérieur de mécanique de Paris (SUPMECA), Laboratoire Quartz EA 7393, 3 rue Fernand Hainaut, 93407 Saint-Ouen, France
| | - Nicolas Dauchez
- Sorbonne universités, Université de Technologie de Compiègne, Laboratoire Roberval, UMR CNRS 7337, CS 60319, 60203 Compiègne cedex, France
| | - Emmanuel Perrey-Debain
- Sorbonne universités, Université de Technologie de Compiègne, Laboratoire Roberval, UMR CNRS 7337, CS 60319, 60203 Compiègne cedex, France
| | - Félix Foucart
- Sorbonne universités, Université de Technologie de Compiègne, Laboratoire Roberval, UMR CNRS 7337, CS 60319, 60203 Compiègne cedex, France
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7
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Sacristan CJ, Dupont T, Sicot O, Leclaire P, Verdière K, Panneton R, Gong XL. A mixture approach to the acoustic properties of a macroscopically inhomogeneous porous aluminum in the equivalent fluid approximation. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2016; 140:2847. [PMID: 27794315 DOI: 10.1121/1.4965300] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
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.
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Affiliation(s)
- C J Sacristan
- Département de Recherche en Ingénierie des Véhicules pour l'Environnement - EA1859, Université Bourgogne Franche Comté, Nevers F-58000, France
| | - T Dupont
- Département de Recherche en Ingénierie des Véhicules pour l'Environnement - EA1859, Université Bourgogne Franche Comté, Nevers F-58000, France
| | - O Sicot
- Département de Recherche en Ingénierie des Véhicules pour l'Environnement - EA1859, Université Bourgogne Franche Comté, Nevers F-58000, France
| | - P Leclaire
- Département de Recherche en Ingénierie des Véhicules pour l'Environnement - EA1859, Université Bourgogne Franche Comté, Nevers F-58000, France
| | - K Verdière
- Groupe d'acoustique de l'Université de Sherbrooke, Département de Génie Mécanique, Université de Sherbrooke, Sherbrooke, Quebec J1K 2R1, Canada
| | - R Panneton
- Groupe d'acoustique de l'Université de Sherbrooke, Département de Génie Mécanique, Université de Sherbrooke, Sherbrooke, Quebec J1K 2R1, Canada
| | - X L Gong
- Laboratoire des Systèmes Mécaniques et Ingénierie Simultanée, Institut Charles Delaunay, Unité Mixte de Recherche CNRS UMR 6281, Université de Technologie de Troyes, 10010 Troyes, France
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8
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Weisser T, Groby JP, Dazel O, Gaultier F, Deckers E, Futatsugi S, Monteiro L. Acoustic behavior of a rigidly backed poroelastic layer with periodic resonant inclusions by a multiple scattering approach. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2016; 139:617-629. [PMID: 26936546 DOI: 10.1121/1.4940669] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The acoustic response of a rigidly backed poroelastic layer with a periodic set of elastic cylindrical inclusions embedded is studied. A semi-analytical approach is presented, based on Biot's 1956 theory to account for the deformation of the skeleton, coupling mode matching technique, Bloch wave representation, and multiple scattering theory. This model is validated by comparing the derived absorption coefficients to finite element simulations. Numerical results are further exposed to investigate the influence of the properties of the inclusions (type, material properties, size) of this structure, while a modal analysis is performed to characterize the dynamic behaviors leading to high acoustic absorption. Particularly, in the case of thin viscoelastic membranes, an absorption coefficient larger than 0.8 is observed on a wide frequency band. This property is found to be due to the coupling between the first volume mode of the inclusion and the trapped mode induced by the periodic array and the rigid backing, for a wavelength in the air smaller than 11 times the material thickness.
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Affiliation(s)
- Thomas Weisser
- Laboratoire d'Acoustique de l'Université du Maine, UMR6613 CNRS/Université du Maine, 72085 Le Mans Cedex 9, France
| | - Jean-Philippe Groby
- Laboratoire d'Acoustique de l'Université du Maine, UMR6613 CNRS/Université du Maine, 72085 Le Mans Cedex 9, France
| | - Olivier Dazel
- Laboratoire d'Acoustique de l'Université du Maine, UMR6613 CNRS/Université du Maine, 72085 Le Mans Cedex 9, France
| | - François Gaultier
- Laboratoire d'Acoustique de l'Université du Maine, UMR6613 CNRS/Université du Maine, 72085 Le Mans Cedex 9, France
| | - Elke Deckers
- Department of Mechanical Engineering, Katholieke Universiteit Leuven, 3001 Heverlee, Belgium
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Blanc E, Chiavassa G, Lombard B. A time-domain numerical modeling of two-dimensional wave propagation in porous media with frequency-dependent dynamic permeability. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2013; 134:4610. [PMID: 25669273 DOI: 10.1121/1.4824832] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
An explicit finite-difference scheme is presented for solving the two-dimensional Biot equations of poroelasticity across the full range of frequencies. The key difficulty is to discretize the Johnson-Koplik-Dashen (JKD) model which describes the viscous dissipations in the pores. Indeed, the time-domain version of Biot-JKD model involves order 1/2 fractional derivatives which amount to a time convolution product. To avoid storing the past values of the solution, a diffusive representation of fractional derivatives is used: The convolution kernel is replaced by a finite number of memory variables that satisfy local-in-time ordinary differential equations. The coefficients of the diffusive representation follow from an optimization procedure of the dispersion relation. Then, various methods of scientific computing are applied: The propagative part of the equations is discretized using a fourth-order finite-difference scheme, whereas the diffusive part is solved exactly. An immersed interface method is implemented to discretize the geometry on a Cartesian grid, and also to discretize the jump conditions at interfaces. Numerical experiments are proposed in various realistic configurations.
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Affiliation(s)
- Emilie Blanc
- Laboratoire de Mécanique et d'Acoustique, UPR 7051, CNRS, 31 Chemin Joseph-Aiguier, Marseille Cedex 20, 13402, France
| | - Guillaume Chiavassa
- Laboratoire de Mécanique et d'Acoustique, UPR 7051, CNRS, 31 Chemin Joseph-Aiguier, Marseille Cedex 20, 13402, France
| | - Bruno Lombard
- Laboratoire de Mécanique et d'Acoustique, UPR 7051, CNRS, 31 Chemin Joseph-Aiguier, Marseille Cedex 20, 13402, France
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10
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Leclaire P, Dupont T, Panneton R. Acoustics of porous materials with partially opened porosity. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2013; 134:4630. [PMID: 25669275 DOI: 10.1121/1.4824836] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
A theoretical and experimental study of the acoustic properties of porous materials containing dead-end (or partially opened) porosity was recently proposed by Dupont, Leclaire, Sicot, Gong, and Panneton [J. Appl. Phys. 110, 094903 (2011)]. 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.
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Affiliation(s)
- P Leclaire
- DRIVE, Université de Bourgogne, 49 rue Mademoiselle Bourgeois, 58027 Nevers cedex, Bourgogne 58027, France
| | - T Dupont
- DRIVE, Université de Bourgogne, 49 rue Mademoiselle Bourgeois, 58027 Nevers cedex, Bourgogne 58027, France
| | - R Panneton
- GAUS, Department of Mechanical Engineering, Université de Sherbrooke, Sherbrooke, Quebec, J1K 2R1, Canada
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11
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Groby JP, Dazel O, Depollier C, Ogam E, Kelders L. Scattering of acoustic waves by macroscopically inhomogeneous poroelastic tubes. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2012; 132:477-486. [PMID: 22779494 DOI: 10.1121/1.4725763] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
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.
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Affiliation(s)
- J-P Groby
- Laboratoire d'Acoustique de l'Université du Maine, UMR6613 Centre National de la Recherche Scientifique/Université du Maine, Avenue Olivier Messiaen, F-72085 Le Mans Cedex 9, France.
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12
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Geslain A, Groby JP, Dazel O, Mahasaranon S, Horoshenkov KV, Khan A. An application of the Peano series expansion to predict sound propagation in materials with continuous pore stratification. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2012; 132:208-215. [PMID: 22779470 DOI: 10.1121/1.4728188] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
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.
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Affiliation(s)
- A Geslain
- Laboratoire d'Acoustique de l'Université du Maine, UMR6613 Centre National de la Recherche Scientifique/Université du Maine, F-72085 Le Mans Cedex 9, France
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