Comptes Rendus
no. 12
Nonlocal description of sound propagation through an array of Helmholtz resonators
[Description non locale de la propagation du son dans une chaîne de résonateurs de Helmholtz]
Navid Nemati1  ; Anshuman Kumar1 ; Denis Lafarge2 ; Nicholas X. Fang1
1 Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
2 Laboratoire d'acoustique de l'université du Maine, UMR 6613, avenue Olivier-Messiaen, 72085 Le Mans cedex 9, France
Comptes Rendus. Mécanique, Volume 343 (2015) no. 12, pp. 656-669.

Une théorie macroscopique nonlocale générale de la propagation du son dans les milieux poreux à structure rigide saturés par un fluide viscothermique a récemment vu le jour. Tenant un compte complet des dispersions, tant temporelles que spatiales, elle décrit entièrement les résonances. Nous l'appliquons ici au cas de la propagation du son dans un réseau de résonateurs de Helmholtz, dont les propriétés non usuelles (modules de compressibilité négatifs) ont été établies expérimentalement. Trois calculs différents sont présentés, qui valident les résultats de la théorie non locale, relatifs au nombre d'onde et module de compressibilité, qui sont fonctions de la fréquence, du mode de Bloch principal (le moins atténué), pour une propagation 1D en géométries périodiques 2D ou 3D.

A generalized macroscopic nonlocal theory of sound propagation in rigid-framed porous media saturated with a viscothermal fluid has been recently proposed, which takes into account both temporal and spatial dispersion. Here, we consider applying this theory, which enables the description of resonance effects, to the case of sound propagation through an array of Helmholtz resonators whose unusual metamaterial properties, such as negative bulk moduli, have been experimentally demonstrated. Three different calculations are performed, validating the results of the nonlocal theory, related to the frequency-dependent Bloch wavenumber and bulk modulus of the first normal mode, for 1D propagation in 2D or 3D periodic structures.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2015.05.001
Keywords: Helmholtz resonators, Acoustic metamaterials, Nonlocal description, Spatial dispersion, Viscothermal fluid, Negative modulus
Mot clés : Résonateur d'Helmholtz, Métamatériaux acoustiques, Description non locale, Dispersion spatiale, Fluide viscothermique, Module de compressibilité négatif
Navid Nemati 1 ; Anshuman Kumar 1 ; Denis Lafarge 2 ; Nicholas X. Fang 1

1 Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
2 Laboratoire d'acoustique de l'université du Maine, UMR 6613, avenue Olivier-Messiaen, 72085 Le Mans cedex 9, France 
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Navid Nemati; Anshuman Kumar; Denis Lafarge; Nicholas X. Fang. Nonlocal description of sound propagation through an array of Helmholtz resonators. Comptes Rendus. Mécanique, Volume 343 (2015) no. 12, pp. 656-669. doi : 10.1016/j.crme.2015.05.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2015.05.001/

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