Localized breathing modes in granular crystals with defects.
We study localized modes in uniform one-dimensional chains of tightly packed and uniaxially compressed elastic beads in the presence of one or two light-mass impurities. For chains composed of beads of the same type, the intrinsic nonlinearity, which is caused by the Hertzian interaction of the bead...
| Main Authors: | , , , , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
2009
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| _version_ | 1797101563929427968 |
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| author | Theocharis, G Kavousanakis, M Kevrekidis, P Daraio, C Porter, M Kevrekidis, I |
| author_facet | Theocharis, G Kavousanakis, M Kevrekidis, P Daraio, C Porter, M Kevrekidis, I |
| author_sort | Theocharis, G |
| collection | OXFORD |
| description | We study localized modes in uniform one-dimensional chains of tightly packed and uniaxially compressed elastic beads in the presence of one or two light-mass impurities. For chains composed of beads of the same type, the intrinsic nonlinearity, which is caused by the Hertzian interaction of the beads, appears not to support localized, breathing modes. Consequently, the inclusion of light-mass impurities is crucial for their appearance. By analyzing the problem's linear limit, we identify the system's eigenfrequencies and the linear defect modes. Using continuation techniques, we find the solutions that bifurcate from their linear counterparts and study their linear stability in detail. We observe that the nonlinearity leads to a frequency dependence in the amplitude of the oscillations, a static mutual displacement of the parts of the chain separated by a defect, and for chains with two defects that are not in contact, it induces symmetry-breaking bifurcations. |
| first_indexed | 2024-03-07T05:53:37Z |
| format | Journal article |
| id | oxford-uuid:e9c41ee8-1ada-4002-8c58-bc138d5a0068 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:53:37Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:e9c41ee8-1ada-4002-8c58-bc138d5a00682022-03-27T10:56:37ZLocalized breathing modes in granular crystals with defects.Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e9c41ee8-1ada-4002-8c58-bc138d5a0068EnglishSymplectic Elements at Oxford2009Theocharis, GKavousanakis, MKevrekidis, PDaraio, CPorter, MKevrekidis, IWe study localized modes in uniform one-dimensional chains of tightly packed and uniaxially compressed elastic beads in the presence of one or two light-mass impurities. For chains composed of beads of the same type, the intrinsic nonlinearity, which is caused by the Hertzian interaction of the beads, appears not to support localized, breathing modes. Consequently, the inclusion of light-mass impurities is crucial for their appearance. By analyzing the problem's linear limit, we identify the system's eigenfrequencies and the linear defect modes. Using continuation techniques, we find the solutions that bifurcate from their linear counterparts and study their linear stability in detail. We observe that the nonlinearity leads to a frequency dependence in the amplitude of the oscillations, a static mutual displacement of the parts of the chain separated by a defect, and for chains with two defects that are not in contact, it induces symmetry-breaking bifurcations. |
| spellingShingle | Theocharis, G Kavousanakis, M Kevrekidis, P Daraio, C Porter, M Kevrekidis, I Localized breathing modes in granular crystals with defects. |
| title | Localized breathing modes in granular crystals with defects. |
| title_full | Localized breathing modes in granular crystals with defects. |
| title_fullStr | Localized breathing modes in granular crystals with defects. |
| title_full_unstemmed | Localized breathing modes in granular crystals with defects. |
| title_short | Localized breathing modes in granular crystals with defects. |
| title_sort | localized breathing modes in granular crystals with defects |
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