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Introduction to Acoustics of Phononic Crystals. Homogenization at Low Frequencies

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Phononic Crystals

Abstract

A short introduction to propagation of sound in phononic crystals is given. Special emphasis is put to the description of the properties of phononic crystals in the long-wavelength limit when periodic inhomogeneous medium can be replaced by a homogeneous one with effective parameters (speed of sound, elastic modulus, and mass density). Two approaches to calculate these effective parameters are given: the plane-wave method and the multiple-scattering method. Metafluid with anisotropic mass density is discussed.

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Acknowledgements

JSD acknowledges useful discussions with D. Torrent and the support from the ONR (USA) grant N00014-12-1-0216, and the MINECO (Spain) grants #TEC2010-19751 and #CSD2008-66 (CONSOLIDER program). AAK acknowledges support from the DOE grant # DE-FG02-06ER46312.

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Authors and Affiliations

  1. Grupo de Fenómenos Ondulatorios, Departamento de Ingeniería Electrónica, Universitat Politècnica de València, Camino de Vera s/n, Valencia, 46022, Spain

    José Sánchez-Dehesa

  2. Department of Physics, University of North Texas, 1155 Union Circle #311427, Denton, TX, 76203, USA

    Arkadii Krokhin

Authors
  1. José Sánchez-Dehesa
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  2. Arkadii Krokhin
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Correspondence to José Sánchez-Dehesa .

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Editors and Affiliations

  1. Institut FEMTO-ST, Centre National de la Recherche Scientifique, Besançon Cedex, France

    Abdelkrim Khelif

  2. School of Electrical Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA

    Ali Adibi

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Sánchez-Dehesa, J., Krokhin, A. (2016). Introduction to Acoustics of Phononic Crystals. Homogenization at Low Frequencies. In: Khelif, A., Adibi, A. (eds) Phononic Crystals. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9393-8_1

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  • DOI: https://doi.org/10.1007/978-1-4614-9393-8_1

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-9392-1

  • Online ISBN: 978-1-4614-9393-8

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