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Defect modes in one-dimensional granular crystals

Man, Y. and Boechler, N. and Theocharis, G. and Kevrekidis, P. G. and Daraio, C. (2012) Defect modes in one-dimensional granular crystals. Physical Review E, 85 (3). Art. No. 037601. ISSN 1539-3755. doi:10.1103/PhysRevE.85.037601. https://resolver.caltech.edu/CaltechAUTHORS:20120501-132603317

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Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevE.85.037601 DOIArticle
http://link.aps.org/doi/10.1103/PhysRevE.85.037601PublisherArticle
http://arxiv.org/abs/1103.2483arXivDiscussion Paper
ORCID:
AuthorORCID
Kevrekidis, P. G.0000-0002-7714-3689
Daraio, C.0000-0001-5296-4440
Additional Information:© 2012 American Physical Society. Received 3 October 2011; published 29 March 2012. We thank Stéphane Job for help with the experimental setup. G.T. and P.G.K. acknowledge support from the A.S. Onassis Public Benefit Foundation through RZG 003/2010-2011 and PGK also through NSF-CMMI-1000337. C.D. acknowledges support from NSF-CMMI-969541 and NSF-CMMI-844540 (CAREER).
Funders:
Funding AgencyGrant Number
Alexander S. Onassis Public Benefit FoundationRZG 003/2010-2011
NSFCMMI-1000337
NSFCMMI-969541
NSFCMMI-844540
Issue or Number:3
Classification Code:PACS: 63.20.Ry, 63.20.Pw, 45.70.-n, 46.40.-f
DOI:10.1103/PhysRevE.85.037601
Record Number:CaltechAUTHORS:20120501-132603317
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20120501-132603317
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:31257
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:01 May 2012 20:34
Last Modified:09 Nov 2021 19:48

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