Dispersion characteristics of a nonlinear elastic metamaterial
We study wave dispersion in a one-dimensional nonlinear elastic metamaterial consisting of a thin rod with periodically attached local resonators. Our model is based on an exact finite-strain dispersion relation for a homogeneous solid, utilized in conjunction with the standard transfer matrix metho...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AIP Publishing LLC
2014-12-01
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| Series: | AIP Advances |
| Online Access: | http://dx.doi.org/10.1063/1.4905051 |
| _version_ | 1818857610949951488 |
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| author | R. Khajehtourian M. I. Hussein |
| author_facet | R. Khajehtourian M. I. Hussein |
| author_sort | R. Khajehtourian |
| collection | DOAJ |
| description | We study wave dispersion in a one-dimensional nonlinear elastic metamaterial consisting of a thin rod with periodically attached local resonators. Our model is based on an exact finite-strain dispersion relation for a homogeneous solid, utilized in conjunction with the standard transfer matrix method for a periodic medium. The nonlinearity considered stems from large elastic deformation in the thin rod, whereas the metamaterial behavior is associated with the dynamics of the local resonators. We derive an approximate dispersion relation for this system and provide an analytical prediction of band-gap characteristics. The results demonstrate the effect of the nonlinearity on the characteristics of the band structure, including the size, location, and character of the band gaps. For example, large deformation alone may cause a pair of isolated Bragg-scattering and local-resonance band gaps to coalesce. We show that for a wave amplitude on the order of one-eighth of the unit cell size, the effect of the nonlinearity in the structure considered is no longer negligible when the unit-cell size is one-fourteenth of the wavelength or larger. |
| first_indexed | 2024-12-19T08:43:08Z |
| format | Article |
| id | doaj.art-aecd0d30592745078a5368da75e5abec |
| institution | Directory Open Access Journal |
| issn | 2158-3226 |
| language | English |
| last_indexed | 2024-12-19T08:43:08Z |
| publishDate | 2014-12-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | AIP Advances |
| spelling | doaj.art-aecd0d30592745078a5368da75e5abec2022-12-21T20:28:52ZengAIP Publishing LLCAIP Advances2158-32262014-12-01412124308124308-1810.1063/1.4905051020497ADVDispersion characteristics of a nonlinear elastic metamaterialR. Khajehtourian0M. I. Hussein1Department of Aerospace Engineering Sciences, University of Colorado Boulder, Boulder, Colorado 80309, USADepartment of Aerospace Engineering Sciences, University of Colorado Boulder, Boulder, Colorado 80309, USAWe study wave dispersion in a one-dimensional nonlinear elastic metamaterial consisting of a thin rod with periodically attached local resonators. Our model is based on an exact finite-strain dispersion relation for a homogeneous solid, utilized in conjunction with the standard transfer matrix method for a periodic medium. The nonlinearity considered stems from large elastic deformation in the thin rod, whereas the metamaterial behavior is associated with the dynamics of the local resonators. We derive an approximate dispersion relation for this system and provide an analytical prediction of band-gap characteristics. The results demonstrate the effect of the nonlinearity on the characteristics of the band structure, including the size, location, and character of the band gaps. For example, large deformation alone may cause a pair of isolated Bragg-scattering and local-resonance band gaps to coalesce. We show that for a wave amplitude on the order of one-eighth of the unit cell size, the effect of the nonlinearity in the structure considered is no longer negligible when the unit-cell size is one-fourteenth of the wavelength or larger.http://dx.doi.org/10.1063/1.4905051 |
| spellingShingle | R. Khajehtourian M. I. Hussein Dispersion characteristics of a nonlinear elastic metamaterial AIP Advances |
| title | Dispersion characteristics of a nonlinear elastic metamaterial |
| title_full | Dispersion characteristics of a nonlinear elastic metamaterial |
| title_fullStr | Dispersion characteristics of a nonlinear elastic metamaterial |
| title_full_unstemmed | Dispersion characteristics of a nonlinear elastic metamaterial |
| title_short | Dispersion characteristics of a nonlinear elastic metamaterial |
| title_sort | dispersion characteristics of a nonlinear elastic metamaterial |
| url | http://dx.doi.org/10.1063/1.4905051 |
| work_keys_str_mv | AT rkhajehtourian dispersioncharacteristicsofanonlinearelasticmetamaterial AT mihussein dispersioncharacteristicsofanonlinearelasticmetamaterial |