One-Dimensional Mass-Spring Chains Supporting Elastic Waves with Non-Conventional Topology

Persistent Link:
http://hdl.handle.net/10150/615109
Title:
One-Dimensional Mass-Spring Chains Supporting Elastic Waves with Non-Conventional Topology
Author:
Deymier, Pierre; Runge, Keith
Affiliation:
Univ Arizona, Dept Mat Sci & Engn
Issue Date:
2016-04-16
Publisher:
MDPI AG
Citation:
One-Dimensional Mass-Spring Chains Supporting Elastic Waves with Non-Conventional Topology 2016, 6 (4):44 Crystals
Journal:
Crystals
Rights:
© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).
Collection Information:
This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.
Abstract:
There are two classes of phononic structures that can support elastic waves with non-conventional topology, namely intrinsic and extrinsic systems. The non-conventional topology of elastic wave results from breaking time reversal symmetry (T-symmetry) of wave propagation. In extrinsic systems, energy is injected into the phononic structure to break T-symmetry. In intrinsic systems symmetry is broken through the medium microstructure that may lead to internal resonances. Mass-spring composite structures are introduced as metaphors for more complex phononic crystals with non-conventional topology. The elastic wave equation of motion of an intrinsic phononic structure composed of two coupled one-dimensional (1D) harmonic chains can be factored into a Dirac-like equation, leading to antisymmetric modes that have spinor character and therefore non-conventional topology in wave number space. The topology of the elastic waves can be further modified by subjecting phononic structures to externally-induced spatio-temporal modulation of their elastic properties. Such modulations can be actuated through photo-elastic effects, magneto-elastic effects, piezo-electric effects or external mechanical effects. We also uncover an analogy between a combined intrinsic-extrinsic systems composed of a simple one-dimensional harmonic chain coupled to a rigid substrate subjected to a spatio-temporal modulation of the side spring stiffness and the Dirac equation in the presence of an electromagnetic field. The modulation is shown to be able to tune the spinor part of the elastic wave function and therefore its topology. This analogy between classical mechanics and quantum phenomena offers new modalities for developing more complex functions of phononic crystals and acoustic metamaterials.
ISSN:
2073-4352
DOI:
10.3390/cryst6040044
Keywords:
phononic structures; topological elastic waves; time-reversal symmetry breaking
Version:
Final published version
Sponsors:
This research was supported in part by the University of Arizona.
Additional Links:
http://www.mdpi.com/2073-4352/6/4/44

Full metadata record

DC FieldValue Language
dc.contributor.authorDeymier, Pierreen
dc.contributor.authorRunge, Keithen
dc.date.accessioned2016-06-30T02:00:41Z-
dc.date.available2016-06-30T02:00:41Z-
dc.date.issued2016-04-16-
dc.identifier.citationOne-Dimensional Mass-Spring Chains Supporting Elastic Waves with Non-Conventional Topology 2016, 6 (4):44 Crystalsen
dc.identifier.issn2073-4352-
dc.identifier.doi10.3390/cryst6040044-
dc.identifier.urihttp://hdl.handle.net/10150/615109-
dc.description.abstractThere are two classes of phononic structures that can support elastic waves with non-conventional topology, namely intrinsic and extrinsic systems. The non-conventional topology of elastic wave results from breaking time reversal symmetry (T-symmetry) of wave propagation. In extrinsic systems, energy is injected into the phononic structure to break T-symmetry. In intrinsic systems symmetry is broken through the medium microstructure that may lead to internal resonances. Mass-spring composite structures are introduced as metaphors for more complex phononic crystals with non-conventional topology. The elastic wave equation of motion of an intrinsic phononic structure composed of two coupled one-dimensional (1D) harmonic chains can be factored into a Dirac-like equation, leading to antisymmetric modes that have spinor character and therefore non-conventional topology in wave number space. The topology of the elastic waves can be further modified by subjecting phononic structures to externally-induced spatio-temporal modulation of their elastic properties. Such modulations can be actuated through photo-elastic effects, magneto-elastic effects, piezo-electric effects or external mechanical effects. We also uncover an analogy between a combined intrinsic-extrinsic systems composed of a simple one-dimensional harmonic chain coupled to a rigid substrate subjected to a spatio-temporal modulation of the side spring stiffness and the Dirac equation in the presence of an electromagnetic field. The modulation is shown to be able to tune the spinor part of the elastic wave function and therefore its topology. This analogy between classical mechanics and quantum phenomena offers new modalities for developing more complex functions of phononic crystals and acoustic metamaterials.en
dc.description.sponsorshipThis research was supported in part by the University of Arizona.en
dc.language.isoenen
dc.publisherMDPI AGen
dc.relation.urlhttp://www.mdpi.com/2073-4352/6/4/44en
dc.rights© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).en
dc.subjectphononic structuresen
dc.subjecttopological elastic wavesen
dc.subjecttime-reversal symmetry breakingen
dc.titleOne-Dimensional Mass-Spring Chains Supporting Elastic Waves with Non-Conventional Topologyen
dc.typeArticleen
dc.contributor.departmentUniv Arizona, Dept Mat Sci & Engnen
dc.identifier.journalCrystalsen
dc.description.collectioninformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.en
dc.eprint.versionFinal published versionen
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