Dynamic interfacial trapping of flexural waves in structured plates.
The paper presents new results on the localization and transmission of flexural waves in a structured plate containing a semi-infinite two-dimensional array of rigid pins. In particular, localized waves are identified and studied at the interface boundary between the homogeneous part of the flexural plate and the part occupied by rigid pins. A formal connection has been made with the dispersion properties of flexural Bloch waves in an infinite doubly periodic array of rigid pins. Special attention is given to regimes corresponding to standing waves of different types as well as Dirac-like points that may occur on the dispersion surfaces. A single half-grating problem, hitherto unreported in the literature, is also shown to bring interesting solutions.
Department of Mathematical Sciences , Mathematical Sciences Building, University of Liverpool , Peach Street, Liverpool L69 7ZL, UK.
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0000-0003-0790-1701
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Haslinger
Department of Mathematics , Imperial College London , London SW7 2AZ, UK.
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Craster
Department of Mathematical Sciences , Mathematical Sciences Building, University of Liverpool , Peach Street, Liverpool L69 7ZL, UK.
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Movchan
Department of Mathematical Sciences , Mathematical Sciences Building, University of Liverpool , Peach Street, Liverpool L69 7ZL, UK.
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Movchan
School of Engineering , Liverpool John Moores University , Liverpool L3 3AF, UK.
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Jones
discrete Wiener–Hopf method; flexural waves; localization; neutrality; platonic crystals