Rayleigh–Bloch waves along elastic diffraction gratings

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 whet...

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Bibliographic Details
Published in:Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2015-01, Vol.471 (2173), p.1-19
Main Authors: Colquitt, D. J., Craster, R. V., Antonakakis, T., Guenneau, S.
Format: Article
Language:English
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Summary: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 inplane 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.
ISSN:1364-5021