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Localisation and damping in resonators with complex geometry

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Abstract.

Based on numerical studies, we show that localisation is a common phenomenon in resonators exhibiting some kind of geometrical complexity. In two-dimensional (2d) shallow cavities of irregular shape, localisation effects are due to spatial decoherence in a major fraction of the volume. In 2d shallow cavities of regular geometry with embedded absorbing material of irregular shape, one observes the appearance of eigenmodes localised in both, the absorbing and the non-absorbing media. Those modes are thought to be responsible for increased dissipation. These results may be a hint to understand why natural or practical systems absorbing wave energy are found, or built, with complex geometry.

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References

  • D.J. Thouless, Phys. Rep. 13, 93 (1974)

    Google Scholar 

  • B. Sapoval, O. Haeberlé, S. Russ, J. Acoust. Soc. Am. 102, 2014 (1997)

  • S. Félix, M. Asch, M. Filoche, B. Sapoval, J. Sound Vib. 299, 965 (2007)

    Google Scholar 

  • H.P. Baltes, E.R. Hilf, Spectra of Finite Systems (BI Wissenschaftsverlag, Vienna, 1976)

  • C. Even, S. Russ, V. Repain, P. Pieranski, B. Sapoval, Phys. Rev. Lett. 83, 726 (1999)

    Google Scholar 

  • J.-P. Bérenger, J. Comp. Phys. 114, 185 (1994)

    Google Scholar 

  • F. Simón, R.M. Rodríguez, J. Pfretzschner, J. Vib. Ac. 124, 329 (2002)

    Google Scholar 

  • Fractal Wall, product of Colas Inc., French patent No. 0203404. US patent 10/508, p. 119

  • F.C. Sgard, X. Olny, N. Atalla, F. Castel, Appl. Acoust. 66, 625 (2005)

    Google Scholar 

  • E. Redon, Proceedings of the 17e Congrès Français de Mécanique (Troyes, France, 2005)

  • L.H. Hemming, Electromagnetic Anechoic Chambers: A Fundamental Design and Specification Guide (Wiley-IEEE Press, 2002)

  • M. Asch, G. Lebeau, Exper. Math. 12, 227 (2003)

    Google Scholar 

  • J.-F. Allard, Propagation of Sound in Porous Media – Modelling Sound Absorbing Materials (Chapman & Hall, London, 1993). The results given in the paper have been obtained with the following parameters of the porous foam: porosity φ=0.98, tortuosity α∞=1.2, air flow resistivity σ=40000N .m-4s, characteristic dimensions Λ=2×10-4 m and Λ'=4×10-4 m, and the cavity width a was taken equal to 0.2 m

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Authors and Affiliations

  1. Physique de la Matière Condensée, École Polytechnique, CNRS, 91128, Palaiseau, France

    B. Sapoval, S. Félix & M. Filoche

  2. CMLA, École Normale Supérieure, CNRS, 94235, Cachan, France

    B. Sapoval & M. Filoche

Authors
  1. B. Sapoval
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  2. S. Félix
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  3. M. Filoche
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Correspondence to B. Sapoval.

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Sapoval, B., Félix, S. & Filoche, M. Localisation and damping in resonators with complex geometry. Eur. Phys. J. Spec. Top. 161, 225–232 (2008). https://doi.org/10.1140/epjst/e2008-00763-2

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  • DOI: https://doi.org/10.1140/epjst/e2008-00763-2

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