Defect modes in one-dimensional granular crystals
Name
Man-2012-Defect modes in one-dimensional granular crystals.pdf
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353.19 KB
Format
Adobe PDF
Checksum (MD5)
32e3d2611ec9f7ff8fbd1c611b49bc55
Author(s)
Boechler, Nicholas
Date Issued
March 2012
Journal
Physical Review E
Publisher
American Physical Society
Citation
Man, Y. et al. “Defect Modes in One-dimensional Granular Crystals.” Physical Review E 85.3 (2012). ©2012 American Physical Society
Version
Final published version
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.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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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.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1103/PhysRevE.85.037601
