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Defect modes in one-dimensional granular crystals

Y. Man1,2, N. Boechler1, G. Theocharis1, P. G. Kevrekidis3, and C. Daraio1

  • 1Graduate Aerospace Laboratories (GALCIT) California Institute of Technology, Pasadena, California 91125, USA
  • 2Keble College, University of Oxford, Oxford OX1 3PG, UK
  • 3Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA

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Phys. Rev. E 85, 037601 – Published 29 March, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.037601

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.

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Phys. Rev. E 85, 037601– Published 29 March, 2012
  • Received 3 October 2011

©2012 American Physical Society

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