- Title
- A short remark on the band structure of free-edge platonic crystals
- Creator
- Smith, Michael J. A.; Meylan, Michael H.; McPhedran, Ross C.; Poulton, Chris G.
- Relation
- Waves in Random and Complex Media Vol. 24, Issue 4, p. 421-430
- Publisher Link
- http://dx.doi.org/10.1080/17455030.2014.936534
- Publisher
- Taylor & Francis
- Resource Type
- journal article
- Date
- 2014
- Description
- 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.
- Identifier
- http://hdl.handle.net/1959.13/1293835
- Identifier
- uon:18691
- Identifier
- ISSN:1745-5030
- Language
- eng
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