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Acoustics of permeo-elastic materials

  • Rodolfo Venegas (a1) and Claude Boutin (a1)


In the dynamics of Biot poroelastic materials, the fluid flow is not affected by the deformation of the solid elastic frame. In contrast, in permeable materials whose solid stiff frames have flexible thin flat films attached, i.e. permeo-elastic materials, the fluid flow can be significantly modified by the presence of the films. As a consequence of the local fluid–film interaction, and in particular of the local resonances, the classical local physics is changed and departs from that leading to the Biot description. In this paper, the two-scale asymptotic homogenisation method is used to derive the macroscopic description of sound propagation in air-saturated permeo-elastic materials. This description is asymptotically analysed to determine the conditions for which the geometrical and mechanical properties of the films strongly affect the effective properties of the material. The developed theory is illustrated numerically and validated experimentally for a prototype material, evidencing the atypical acoustic behaviour.


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Allard, J. F. & Atalla, N. 2009 Propagation of Sound in Porous Media: Modeling Sound Absorbing Materials. Wiley.
Auriault, J. L., Borne, L. & Chambon, R. 1985 Dynamics of porous saturated media, checking of the generalized law of Darcy. J. Acoust. Soc. Am. 77 (5), 16411650.
Auriault, J. L., Boutin, C. & Geindreau, C. 2009 Homogenization of Coupled Phenomena in Heterogeneous Media. ISTE Ltd and Wiley.
Biot, M. A. 1956a Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range. J. Acoust. Soc. Am. 28, 168178.
Biot, M. A. 1956b Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range. J. Acoust. Soc. Am. 28, 179191.
Bolton, J. S. 2013 The modeling of unconventional sound absorbing materials: microperforated films and closed cell foams. In One-Day International Conference, Lightweighting and Acoustical Materials in Vehicles. Université de Technologie de Compiègne – 22 October 2014, Compiègne, France.
Bongard, F., Lissek, H. & Mosig, J. R. 2010 Acoustic transmission line metamaterial with negative/zero/positive refractive index. Phys. Rev. B 82, 094306.
Boutin, C. 2013 Acoustics of porous media with inner resonators. J. Acoust. Soc. Am. 134 (6), 47174729.
Boutin, C. & Auriault, J. L. 1990 Dynamic behaviour of porous media saturated by a viscoelastic fluid. Application to bituminous concretes. Intl J. Engng Sci. 28 (11), 11571181.
Boutin, C., Royer, P. & Auriault, J. L. 1998 Acoustic absorption of porous surfacing with dual porosity. Intl J. Solids Struct. 35, 47094737.
Bravo, T., Maudry, C. & Pinhède, C. 2012 Vibroacoustic properties of thin micro-perforated panel absorbers. J. Acoust. Soc. Am. 132 (2), 789798.
Brown, D. L., Popov, P. & Efendiev, Y. 2011 On homogenization of Stokes flow in slowly varying media with applications to fluid–structure interaction. Int. J. Geomath. 2, 281305.
Brown, D. L., Popov, P. & Efendiev, Y. 2014 Effective equations for fluid–structure interaction with applications to poroelasticity. Appl. Anal. 4, 771790.
Comsol2013 Comsol Multiphysics documentation version 4.3b.
Cummer, S. A., Christensen, J. & Alù, A. 2016 Controlling sound with acoustic metamaterials. Nav. Rev. Mater. 1, 16001.
Dailey, H. L., Yalcin, H. C. & Ghadiali, S. N. 2007 Fluid–structure modeling of flow-induced alveolar epithelial cell deformation. Comput. Struct. 85, 10661071.
Filippi, P. J. T. 2008 Vibrations and Acoustic Radiation of Thin Structures. ISTE Ltd and Wiley.
Griffiths, S., Nennig, B. & Job, S. 2017 Porogranular materials composed of elastic Helmholtz resonators for acoustic wave absorption. J. Acoust. Soc. Am. 141 (1), 254264.
Groby, J.-P., Lagarrigue, C., Brouard, B., Dazel, O., Tournat, V. & Nennig, B. 2015 Enhancing the absorption properties of acoustic porous plates by periodically embedding Helmholtz resonators. J. Acoust. Soc. Am. 137 (1), 273280.
Habault, D. 1999 Fluid–Structure Interactions in Acoustics. Springer.
ISO 10534-2:2001 2001 Acoustics – Determination of sound absorption coefficient and impedance in impedance tubes – Part 2: Transfer-function method. Standard. International Organization for Standardization, Geneva, CH.
Johnson, D. L., Koplik, J. & Dashen, R. 1987 Theory of dynamic permeability and tortuosity in fluid-saturated porous media. J. Fluid Mech. 176, 379402.
Krynkin, A., Umnova, O., Boon Chong, A. Y., Taherzadeh, S. & Attenborough, K. 2010 Predictions and measurements of sound transmission through a periodic array of elastic shells in air. J. Acoust. Soc. Am. 128 (6), 34963506.
Ladyzhenskaya, O. 1963 The Mathematical Theory of Viscous Incompressible Flow. Gordon and Breach Science Publishers.
Lafarge, D., Lemarinier, P., Allard, J. F. & Tarnow, V. 1997 Dynamic compressibility of air in porous structures at audible frequencies. J. Acoust. Soc. Am. 102 (4), 19952006.
Lafarge, D. & Nemati, N. 2013 Nonlocal Maxwellian theory of sound propagation in fluid-saturated rigid-framed porous media. Wave Motion 50 (6), 10161035.
Lebental, B. & Bourquin, F. 2012 Visco-acoustic modelling of a vibrating plate interacting with water confined in a domain of micrometric size. J. Sound Vib. 331 (8), 18701886.
Leclaire, P., Umnova, O., Dupont, T. & Panneton, R. 2015 Acoustical properties of air-saturated porous material with periodically distributed dead-end pores. J. Acoust. Soc. Am. 137 (4), 17721782.
Lee, C. K. & Mei, C. C. 1997 Re-examination of the equations of poroelasticity. Intl J. Engng Sci. 35, 329352.
Lee, Y. Y., Lee, E. W. M. & Ng, C. F. 2005 Sound absorption of a finite flexible micro-perforated panel backed by an air cavity. J. Sound Vib. 287, 227243.
Leroy, S. & Charlaix, E. 2011 Hydrodynamic interactions for the measurement of thin film elastic properties. J. Fluid Mech. 674, 389407.
Li, C., Cazzolato, B. & Zander, A. 2016 Acoustic impedance of micro perforated membranes: velocity continuity condition at the perforation boundary. J. Acoust. Soc. Am. 139 (1), 93103.
López de Haro, M., Del Río, J. A. P. & Whitaker, S. 1996 Flow of Maxwell fluids in porous media. Trans. Porous Med. 25 (2), 167192.
Love, A. E. H. 1888 On the small free vibrations and deformations of elastic shells. Phil. Trans. R. Soc. Lond. A 179, 491549.
Ma, G. & Sheng, P. 2016 Acoustic metamaterials: from local resonances to broad horizons. Sci. Adv. 2 (2), e1501595.
Norris, A. N. & Wickham, G. 1993 Elastic Helmholtz resonators. J. Acoust. Soc. Am. 93, 617630.
Olny, X. & Boutin, C. 2003 Acoustic wave propagation in double porosity media. J. Acoust. Soc. Am. 113 (6), 7389.
Panasenko, G. P. & Stavre, R. 2012 Asymptotic analysis of a viscous fluid–thin plate interaction: periodic flow. C. R. Méc. 340, 590595.
Pride, S. R., Morgan, F. D. & Gangi, A. F. 1993 Drag forces of porous-medium acoustics. Phys. Rev. B 47, 49644978.
Rubenstein, D. A., Yin, W. & Frame, M. D. 2015 Biofluid Mechanics, 2nd edn. Academic.
Sanchez-Palencia, E. 1980 Non-Homogeneous Media and Vibration Theory. Springer.
Smeulders, D. M. J., Eggels, R. L. G. M. & van Dongen, M. E. H. 1992 Dynamic permeability: reformulation of theory and new experimental and numerical data. J. Fluid Mech. 245, 211227.
Venegas, R. & Boutin, C. 2017 Acoustics of sorptive porous materials. Wave Motion 68, 162181.
Venegas, R. & Umnova, O. 2011 Acoustical properties of double porosity granular materials. J. Acoust. Soc. Am. 130 (5), 27652776.
Yang, Z., Mei, J., Yang, M., Chan, N. & Sheng, P. 2008 Membrane-type acoustic metamaterial with negative dynamic mass. Phys. Rev. Lett. 101, 204301.
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