A short remark on the band structure of free-edge platonic crystals

Smith, MJA; Meylan, MH; McPhedran, RC; Poulton, CG

A short remark on the band structure of free-edge platonic crystals

Smith, MJA Meylan, MH McPhedran, RC Poulton, CG

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Publication Type:: Journal Article
Citation:: Waves in Random and Complex Media, 2014, 24 (4), pp. 421 - 430
Issue Date:: 2014-10-13

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Field	Value	Language
dc.contributor.author	Smith, MJA	en_US
dc.contributor.author	Meylan, MH	en_US
dc.contributor.author	McPhedran, RC	en_US
dc.contributor.author	Poulton, CG https://orcid.org/0000-0002-2707-3424	en_US
dc.date.issued	2014-10-13	en_US
dc.identifier.citation	Waves in Random and Complex Media, 2014, 24 (4), pp. 421 - 430	en_US
dc.identifier.issn	1745-5030	en_US
dc.identifier.uri	http://hdl.handle.net/10453/41261
dc.description.abstract	© 2014 © 2014 Taylor & Francis. A corrected version of the multipole solution for a thin plate perforated in a doubly periodic fashion is presented. It is assumed that free-edge boundary conditions are imposed at the edge of each cylindrical inclusion. The solution procedure given here exploits a well-known property of Bessel functions to obtain the solution directly, in contrast to the existing incorrect derivation. A series of band diagrams and an updated table of values are given for the resulting system (correcting known publications on the topic), which shows a spectral band at low frequency for the free-edge problem. This is in contrast to clamped-edge boundary conditions for the same biharmonic plate problem, which features a low-frequency band gap. The numerical solution procedure outlined here is also simplified relative to earlier publications, and exploits the spectral properties of complex-valued matrices to determine the band structure of the structured plate.	en_US
dc.relation.ispartof	Waves in Random and Complex Media	en_US
dc.relation.isbasedon	10.1080/17455030.2014.936534	en_US
dc.subject.classification	Optics	en_US
dc.title	A short remark on the band structure of free-edge platonic crystals	en_US
dc.type	Journal Article
utslib.citation.volume	4	en_US
utslib.citation.volume	24	en_US
utslib.for	0203 Classical Physics	en_US
utslib.for	0205 Optical Physics	en_US
utslib.for	0299 Other Physical Sciences	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	closed_access
pubs.issue	4	en_US
pubs.publication-status	Published	en_US
pubs.volume	24	en_US

Abstract:

© 2014 © 2014 Taylor & Francis. A corrected version of the multipole solution for a thin plate perforated in a doubly periodic fashion is presented. It is assumed that free-edge boundary conditions are imposed at the edge of each cylindrical inclusion. The solution procedure given here exploits a well-known property of Bessel functions to obtain the solution directly, in contrast to the existing incorrect derivation. A series of band diagrams and an updated table of values are given for the resulting system (correcting known publications on the topic), which shows a spectral band at low frequency for the free-edge problem. This is in contrast to clamped-edge boundary conditions for the same biharmonic plate problem, which features a low-frequency band gap. The numerical solution procedure outlined here is also simplified relative to earlier publications, and exploits the spectral properties of complex-valued matrices to determine the band structure of the structured plate.

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http://hdl.handle.net/10453/41261