Nonlinear dynamics of a model of acoustic metamaterials with local resonators

Higashiyama, Naoki; Doi, Yusuke; Nakatani, Akihiro

Nonlinear Theory and Its Applications, IEICE, 2017, 8(2), 129-145

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Identifier to cite or link to this item: https://hdl.handle.net/11094/84552

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Title
Nonlinear dynamics of a model of acoustic metamaterials with local resonators
Creator
CreatorName
Higashiyama, Naoki
NRID
1000010403172 1000010403172
ORCID
0000-0003-3749-5353 0000-0003-3749-5353
researchmap permalink
yusuke_doi yusuke_doi
Scopus Author ID
36685120100 36685120100
CreatorName
Doi, Yusuke
NRID
1000050252606 1000050252606
ORCID
0000-0001-7212-9303 0000-0001-7212-9303
researchmap permalink
akihironakatani akihironakatani
Scopus Author ID
7005104428 7005104428
CreatorName
Nakatani, Akihiro
Subject
nonlinear vibration
stability
energy localization
Description
Higashiyama Naoki, Doi Yusuke, Nakatani Akihiro. Nonlinear dynamics of a model of acoustic metamaterials with local resonators. Nonlinear Theory and Its Applications, IEICE, 8(2), pp. 129-145, 2017. https://doi.org/10.1587/nolta.8.129.
Abstract
Nonlinear dynamics of a model of acoustic metamaterials with local resonators are investigated numerically and theoretically. We focus on dynamics of band edge modes (BEMs) and zone boundary modes (ZBMs) which are on the upper bounds of acoustic bands and optical bands of the phonon dispersion band. It is found that, in a region of weak anharmonicity, higher harmonics of a fundamental mode and static displacement are excited in both BEM and ZBM if the geometrical relation between the main lattice and the local resonators has even-order nonlinearity. Numerical solutions of nonlinear periodic orbits which are continued from vibrations in the small amplitude limit by the shooting method indicate that structure of the periodic orbits of the local resonators depends on the form of nonlinear terms of the geometrical relation. Moreover, the nonlinear periodic orbits become unstable when the amplitude of the periodic orbit becomes larger. Direct numerical simulations show that unstable dynamics occur due to modulational instability. After destabilization of the nonlinear periodic orbits, spatial energy localization is also observed.
Publisher
The Institute of Electronics, Information and Communication Engineers
Source Title
Nonlinear Theory and Its Applications, IEICE
Volume (Issue)
8(2)
Page
129-145
Date of Issued
2017
Language
English
Handle URL
https://hdl.handle.net/11094/84552
eISSN
21854106
Relation.isIdenticalTo
DOI (Publisher Version)
https://doi.org/10.1587/nolta.8.129
Access Rights
open access
CopyRight
Copyright(C)2017 IEICE
oaire:version
Version of Record
Category
学術雑誌論文 Journal Article