Rayleigh–Bloch waves along elastic diffraction gratings

Daniel Colquitt 1 Richard V. Craster 1 Tryfon Antonakakis 1 Sébastien Guenneau 2
1 Department of Mathematics [Imperial College London]
2 EPSILON - EPSILON
FRESNEL - Institut FRESNEL
Abstract : Rayleigh–Bloch (RB) waves in elasticity, in contrast to those in scalar wave systems, appear to have had little attention. Despite the importance of RB waves in applications, their connections to trapped modes and the ubiquitous nature of diffraction gratings, there has been no investigation of whether such waves occur within elastic diffraction gratings for the in-plane vector elastic system. We identify boundary conditions that support such waves and numerical simulations confirm their presence. An asymptotic technique is also developed to generate effective medium homogenized equations for the grating that allows us to replace the detailed microstructure by a continuum representation. Further numerical simulations confirm that the asymptotic scheme captures the essential features of these waves.
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Contributor : Sébastien Guenneau <>
Submitted on : Saturday, March 5, 2016 - 6:14:19 PM
Last modification on : Monday, March 4, 2019 - 2:04:25 PM

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Daniel Colquitt, Richard V. Craster, Tryfon Antonakakis, Sébastien Guenneau. Rayleigh–Bloch waves along elastic diffraction gratings. Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences, Royal Society, The, 2014, 471 (19), pp.0140465. ⟨10.1098/rspa.2014.0465⟩. ⟨hal-01283610⟩

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