73:
The types of platonic structures that have been examined include arrays of perforations, arrays of pins, arrays of point masses, as well as periodic variations in the plate material itself. Platonic crystals have been shown to exhibit a number of behaviours similar to photonic crystals, including
82:
where wave propagation is not possible through the crystal, as well as cloaking near degenerate band surfaces. Investigations into defective platonic crystals has also revealed strong energy localization effects within the defects, with high
572:
355:
S.G. Haslinger; N.V. Movchan; A.B. Movchan; R.C. McPhedran (2012), "Transmission, trapping and filtering of waves in periodically constrained elastic plates",
236:
D.V. Evans; R. Porter (2007), "Penetration of flexural waves through a periodically constrained thin elastic plate in vacuo and floating on water",
194:
M. Farhat; S. Guenneau; S. Enoch (2010), "High directivity and confinement of flexural waves through ultra-refraction in thin perforated plates",
669:
M. Dubois; M. Farhat; E. Bossy; S. Enoch; S. Guenneau; P. Sebbah (2013), "Flat lens for time-domain focusing of elastic waves in thin plates",
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C.G. Poulton; A.B. Movchan; N.V. Movchan; R.C. McPhedran (2012), "Analytic theory of defects in periodically structured elastic plates",
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111:
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M.J.A. Smith; R.C. McPhedran; C.G. Poulton; M.H. Meylan (2012), "Negative refraction and dispersion phenomena in platonic clusters",
20:
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Experimental work in platonics to date has shown promising results in cloaking and flat lens focusing of flexural wave energy.
39:
477:
T. Antonakakis; R.V. Craster (2012), "High-frequency asymptotics for microstructured thin elastic plates and platonics",
65:. The term is now in common usage by multiple research groups in Australia, New Zealand, France, and the United Kingdom.
718:
278:
N.V. Movchan; R.C. McPhedran; A.B. Movchan; C.G. Poulton (2009), "Wave scattering by platonic grating stacks",
545:
R. C. McPhedran; A.B. Movchan; N.V. Movchan (2009), "Platonic crystals: Bloch bands, neutrality and defects",
109:
A.B. Movchan; N.V. Movchan; R.C. McPhedran (2007), "Bloch-Floquet bending waves in perforated thin plates",
314:
M. H. Meylan; R.C. McPhedran (2011), "Fast and slow interaction of elastic waves with platonic clusters",
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which governs other types of crystals. There are also strong connections between platonic crystals and
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N. Stenger; M. Wilhelm; M. Wegener (2012), "Experiments on elastic cloaking in thin plates",
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are periodic structures which are designed to guide flexural wave energy through thin
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Moulding flexural waves in elastic plates lying atop a Faqir's bed of nails
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158:"Focussing bending waves via negative refraction in perforated thin plates"
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M. Farhat; S. Guenneau; S. Enoch; A.B. Movchan; G.G. Petursson (2010),
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573:"The effect on bending waves by defects in pinned elastic plates"
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26:The term platonic crystal is formed by analogy to
53:The study of platonic crystals is referred to as
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571:M.J.A. Smith; R. Porter; T.D. Williams (2012),
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606:1983/d65f8bc3-1d33-44b7-b3e3-f75aa60d1a01
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7:
480:Proceedings of the Royal Society A
442:Proceedings of the Royal Society A
358:Proceedings of the Royal Society A
317:Proceedings of the Royal Society A
281:Proceedings of the Royal Society A
238:Journal of Engineering Mathematics
112:Proceedings of the Royal Society A
14:
396:Waves in Random and Complex Media
641:10.1103/physrevlett.108.014301
577:Journal of Sound and Vibration
1:
559:10.1016/j.mechmat.2009.01.005
40:partial differential equation
416:10.1080/17455030.2012.711495
735:
216:10.1209/0295-5075/91/54003
597:10.1016/j.jsv.2012.06.013
258:10.1007/s10665-006-9128-0
671:Applied Physics Letters
621:Physical Review Letters
162:Applied Physics Letters
547:Mechanics of Materials
501:10.1098/rspa.2011.0652
464:10.1098/rspa.2011.0609
379:10.1098/rspa.2011.0318
339:10.1098/rspa.2011.0234
302:10.1098/rspa.2009.0301
133:10.1098/rspa.2007.1886
44:second order equation
693:2013ApPhL.103g1915D
633:2012PhRvL.108a4301S
589:2012JSV...331.5087S
533:2013arXiv1301.7653A
493:2012RSPSA.468.1408A
487:(2141): 1408–1427,
455:2012RSPSA.468.1196P
449:(2140): 1196–1216,
408:2012WRCM...22..435S
371:2012RSPSA.468...76H
330:2011RSPSA.467.3509M
324:(2136): 3509–3529,
294:2009RSPSA.465.3383M
288:(2111): 3383–3400,
250:2007JEnMa..58..317E
208:2010EL.....9154003F
174:2010ApPhL..96h1909F
125:2007RSPSA.463.2505M
119:(2086): 2505–2518,
76:negative refraction
42:, as opposed to a
36:plasmonic crystals
701:10.1063/1.4818716
583:(23): 5087–5106,
182:10.1063/1.3327813
32:phononic crystals
28:photonic crystals
17:Platonic crystals
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69:Applications
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94:References
684:1303.3022
524:1301.7653
424:119831638
224:120154590
141:111291430
80:stopbands
61:, or the
55:platonics
713:Category
657:35264750
649:22304261
266:52238485
689:Bibcode
629:Bibcode
585:Bibcode
529:Bibcode
489:Bibcode
451:Bibcode
404:Bibcode
367:Bibcode
326:Bibcode
290:Bibcode
246:Bibcode
204:Bibcode
170:Bibcode
121:Bibcode
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34:, and
679:arXiv
653:S2CID
519:arXiv
420:S2CID
262:S2CID
220:S2CID
137:S2CID
59:Plato
645:PMID
697:doi
675:103
637:doi
625:108
601:hdl
593:doi
581:331
555:doi
497:doi
485:468
459:doi
447:468
412:doi
375:doi
363:468
334:doi
322:467
298:doi
286:465
254:doi
212:doi
196:EPL
178:doi
129:doi
117:463
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