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Published March 2012 | Published + Submitted
Journal Article Open

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 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.

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).

Attached Files

Published - Man2012p17893Phys_Rev_E.pdf

Submitted - 1103.2483.pdf


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August 19, 2023
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