Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-28T05:13:32.408Z Has data issue: false hasContentIssue false
  • English
  • Français

Acoustics of permeo-elastic materials

Published online by Cambridge University Press:  31 August 2017

Rodolfo Venegas Open the ORCID record for Rodolfo Venegas [Opens in a new window]  and
Claude Boutin
Rodolfo Venegas*
Affiliation:
Université de Lyon - Ecole Nationale des Travaux Publics de l’Etat - LGCB/LTDS - UMR-CNRS 5513, Rue Maurice Audin, 69518 Vaulx-en-Velin, France
Claude Boutin
Affiliation:
Université de Lyon - Ecole Nationale des Travaux Publics de l’Etat - LGCB/LTDS - UMR-CNRS 5513, Rue Maurice Audin, 69518 Vaulx-en-Velin, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

JFM classification

Acoustics: Acoustics Non-Newtonian Flows: Viscoelasticity
Type
Papers
Information
Journal of Fluid Mechanics , Volume 828 , 10 October 2017 , pp. 135 - 174
Check for updates
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Allard, J. F. & Atalla, N. 2009 Propagation of Sound in Porous Media: Modeling Sound Absorbing Materials. Wiley.Google Scholar
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), 1641–1650.Google Scholar
Auriault, J. L., Boutin, C. & Geindreau, C. 2009 Homogenization of Coupled Phenomena in Heterogeneous Media. ISTE Ltd and Wiley.Google Scholar
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, 168–178.CrossRefGoogle Scholar
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, 179–191.CrossRefGoogle Scholar
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.Google Scholar
Bongard, F., Lissek, H. & Mosig, J. R. 2010 Acoustic transmission line metamaterial with negative/zero/positive refractive index. Phys. Rev. B 82, 094306.CrossRefGoogle Scholar
Boutin, C. 2013 Acoustics of porous media with inner resonators. J. Acoust. Soc. Am. 134 (6), 4717–4729.Google Scholar
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), 1157–1181.Google Scholar
Boutin, C., Royer, P. & Auriault, J. L. 1998 Acoustic absorption of porous surfacing with dual porosity. Intl J. Solids Struct. 35, 4709–4737.Google Scholar
Bravo, T., Maudry, C. & Pinhède, C. 2012 Vibroacoustic properties of thin micro-perforated panel absorbers. J. Acoust. Soc. Am. 132 (2), 789–798.Google Scholar
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, 281–305.Google Scholar
Brown, D. L., Popov, P. & Efendiev, Y. 2014 Effective equations for fluid–structure interaction with applications to poroelasticity. Appl. Anal. 4, 771–790.CrossRefGoogle Scholar
Comsol2013 Comsol Multiphysics documentation version 4.3b.Google Scholar
Cummer, S. A., Christensen, J. & Alù, A. 2016 Controlling sound with acoustic metamaterials. Nav. Rev. Mater. 1, 16001.CrossRefGoogle Scholar
Dailey, H. L., Yalcin, H. C. & Ghadiali, S. N. 2007 Fluid–structure modeling of flow-induced alveolar epithelial cell deformation. Comput. Struct. 85, 1066–1071.CrossRefGoogle Scholar
Filippi, P. J. T. 2008 Vibrations and Acoustic Radiation of Thin Structures. ISTE Ltd and Wiley.Google Scholar
Griffiths, S., Nennig, B. & Job, S. 2017 Porogranular materials composed of elastic Helmholtz resonators for acoustic wave absorption. J. Acoust. Soc. Am. 141 (1), 254–264.Google Scholar
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), 273–280.CrossRefGoogle ScholarPubMed
Habault, D. 1999 Fluid–Structure Interactions in Acoustics. Springer.Google Scholar
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.Google Scholar
Johnson, D. L., Koplik, J. & Dashen, R. 1987 Theory of dynamic permeability and tortuosity in fluid-saturated porous media. J. Fluid Mech. 176, 379–402.Google Scholar
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), 3496–3506.CrossRefGoogle ScholarPubMed
Ladyzhenskaya, O. 1963 The Mathematical Theory of Viscous Incompressible Flow. Gordon and Breach Science Publishers.Google Scholar
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), 1995–2006.CrossRefGoogle Scholar
Lafarge, D. & Nemati, N. 2013 Nonlocal Maxwellian theory of sound propagation in fluid-saturated rigid-framed porous media. Wave Motion 50 (6), 1016–1035.Google Scholar
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), 1870–1886.Google Scholar
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), 1772–1782.Google Scholar
Lee, C. K. & Mei, C. C. 1997 Re-examination of the equations of poroelasticity. Intl J. Engng Sci. 35, 329–352.Google Scholar
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, 227–243.Google Scholar
Leroy, S. & Charlaix, E. 2011 Hydrodynamic interactions for the measurement of thin film elastic properties. J. Fluid Mech. 674, 389–407.Google Scholar
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), 93–103.CrossRefGoogle ScholarPubMed
López de Haro, M., Del Río, J. A. P. & Whitaker, S. 1996 Flow of Maxwell fluids in porous media. Trans. Porous Med. 25 (2), 167–192.CrossRefGoogle Scholar
Love, A. E. H. 1888 On the small free vibrations and deformations of elastic shells. Phil. Trans. R. Soc. Lond. A 179, 491–549.Google Scholar
Ma, G. & Sheng, P. 2016 Acoustic metamaterials: from local resonances to broad horizons. Sci. Adv. 2 (2), e1501595.Google Scholar
Norris, A. N. & Wickham, G. 1993 Elastic Helmholtz resonators. J. Acoust. Soc. Am. 93, 617–630.Google Scholar
Olny, X. & Boutin, C. 2003 Acoustic wave propagation in double porosity media. J. Acoust. Soc. Am. 113 (6), 73–89.Google Scholar
Panasenko, G. P. & Stavre, R. 2012 Asymptotic analysis of a viscous fluid–thin plate interaction: periodic flow. C. R. Méc. 340, 590–595.CrossRefGoogle Scholar
Pride, S. R., Morgan, F. D. & Gangi, A. F. 1993 Drag forces of porous-medium acoustics. Phys. Rev. B 47, 4964–4978.Google Scholar
Rubenstein, D. A., Yin, W. & Frame, M. D. 2015 Biofluid Mechanics, 2nd edn. Academic.Google Scholar
Sanchez-Palencia, E. 1980 Non-Homogeneous Media and Vibration Theory. Springer.Google Scholar
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, 211–227.Google Scholar
Venegas, R. & Boutin, C. 2017 Acoustics of sorptive porous materials. Wave Motion 68, 162–181.Google Scholar
Venegas, R. & Umnova, O. 2011 Acoustical properties of double porosity granular materials. J. Acoust. Soc. Am. 130 (5), 2765–2776.Google Scholar
Yang, Z., Mei, J., Yang, M., Chan, N. & Sheng, P. 2008 Membrane-type acoustic metamaterial with negative dynamic mass. Phys. Rev. Lett. 101, 204301.Google Scholar