Defect modes in one-dimensional granular crystals
We study the vibrational spectra of one-dimensional statically compressed granular crystals (arrays of elastic particles in contact) containing light-mass defects. We focus on the prototypical settings of one or two spherical defects (particles of smaller radii) interspersed in a chain of larger uni...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
American Physical Society
2012
|
| Online Access: | http://hdl.handle.net/1721.1/71900 |
| _version_ | 1826195528348598272 |
|---|---|
| author | Boechler, Nicholas |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Boechler, Nicholas |
| author_sort | Boechler, Nicholas |
| collection | MIT |
| description | We study the vibrational spectra of one-dimensional statically compressed granular crystals (arrays of elastic particles in contact) containing light-mass defects. We focus on the prototypical settings of one or two spherical defects (particles of smaller radii) interspersed in a chain of larger uniform spherical particles. We present a systematic measurement, using continuous noise, of the near-linear frequency spectrum within the spatial vicinity of the defect(s). Using this technique, we identify the frequencies of the localized defect modes as a function of the defect size and the position of the defects relative to each other. We also compare the experimentally determined frequencies with those obtained by numerical eigenanalysis and by analytical expressions based on few-site considerations. These approximate analytical expressions, based on normal-mode analysis, are found to be in excellent agreement with numerics for a wide range of mass ratios. We also observe that the experimentally measured frequencies of the localized defect modes are uniformly upshifted, compared to the numerically and theoretically predicted values. |
| first_indexed | 2024-09-23T10:14:09Z |
| format | Article |
| id | mit-1721.1/71900 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:14:09Z |
| publishDate | 2012 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/719002022-09-30T19:48:21Z Defect modes in one-dimensional granular crystals Boechler, Nicholas Massachusetts Institute of Technology. Department of Mechanical Engineering Boechler, Nicholas Boechler, Nicholas We study the vibrational spectra of one-dimensional statically compressed granular crystals (arrays of elastic particles in contact) containing light-mass defects. We focus on the prototypical settings of one or two spherical defects (particles of smaller radii) interspersed in a chain of larger uniform spherical particles. We present a systematic measurement, using continuous noise, of the near-linear frequency spectrum within the spatial vicinity of the defect(s). Using this technique, we identify the frequencies of the localized defect modes as a function of the defect size and the position of the defects relative to each other. We also compare the experimentally determined frequencies with those obtained by numerical eigenanalysis and by analytical expressions based on few-site considerations. These approximate analytical expressions, based on normal-mode analysis, are found to be in excellent agreement with numerics for a wide range of mass ratios. We also observe that the experimentally measured frequencies of the localized defect modes are uniformly upshifted, compared to the numerically and theoretically predicted values. 2012-07-30T20:09:50Z 2012-07-30T20:09:50Z 2012-03 2011-10 Article http://purl.org/eprint/type/JournalArticle 1539-3755 1550-2376 http://hdl.handle.net/1721.1/71900 Man, Y. et al. “Defect Modes in One-dimensional Granular Crystals.” Physical Review E 85.3 (2012). ©2012 American Physical Society en_US http://dx.doi.org/10.1103/PhysRevE.85.037601 Physical Review E Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society APS |
| spellingShingle | Boechler, Nicholas Defect modes in one-dimensional granular crystals |
| title | Defect modes in one-dimensional granular crystals |
| title_full | Defect modes in one-dimensional granular crystals |
| title_fullStr | Defect modes in one-dimensional granular crystals |
| title_full_unstemmed | Defect modes in one-dimensional granular crystals |
| title_short | Defect modes in one-dimensional granular crystals |
| title_sort | defect modes in one dimensional granular crystals |
| url | http://hdl.handle.net/1721.1/71900 |
| work_keys_str_mv | AT boechlernicholas defectmodesinonedimensionalgranularcrystals |