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Trapped Modes and Edge Resonances in Acoustics and Elasticity

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Dynamic Localization Phenomena in Elasticity, Acoustics and Electromagnetism

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 547))

Abstract

This chapter considers localized modes for acoustic and elastic waves. We first discuss trapped modes for acoustic scalar waves that are perfectly localized solutions near defects in waveguides with a real resonance frequency. Emphasis is given on the trapping mechanism coming from the evanescent nature of transverse modes in waveguides. We then study the case of quasi-trapped modes where the wave is strongly localized but can radiate energy. Complex resonance frequencies are shown to appear through approximate models and general principles. Eventually, we focus on elastic wave localization near traction free edges in plates and rods. The complicated polarization of the wave in elasticity is shown to increase the ability for trapping with very simple geometries.

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Author information

Authors and Affiliations

  1. Laboratoire d’Acoustique, LAUM UMR CNRS 6613, Université du Maine, Le Mans, France

    Vincent Pagneux

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  1. Vincent Pagneux
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Editors and Affiliations

  1. Imperial College London, London, UK

    Richard V. Craster

  2. Keele University, Keele, UK

    Julius Kaplunov

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Pagneux, V. (2013). Trapped Modes and Edge Resonances in Acoustics and Elasticity. In: Craster, R.V., Kaplunov, J. (eds) Dynamic Localization Phenomena in Elasticity, Acoustics and Electromagnetism. CISM International Centre for Mechanical Sciences, vol 547. Springer, Vienna. https://doi.org/10.1007/978-3-7091-1619-7_5

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  • DOI: https://doi.org/10.1007/978-3-7091-1619-7_5

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-7091-1618-0

  • Online ISBN: 978-3-7091-1619-7

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