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Issue 4, 2013
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Acoustic measurement of a granular density of modes

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In glasses and other disordered materials, measurements of the vibrational density of states reveal that an excess number of long-wavelength (low-frequency) modes, as compared to the Debye scaling seen in crystalline materials, is associated with a loss of mechanical rigidity. In this paper, we present a novel technique for measuring the density of modes (DOM) in a real granular material, in which we excite vibrational modes using white noise acoustic waves. The resulting vibrations are detected with piezoelectric sensors embedded inside a subset of the particles, from which we are able to compute the DOM via the spectrum of the velocity autocorrelation function, a technique previously applied in thermal systems. The velocity distribution for individual particles is observed to be Gaussian, but the ensemble distribution is non-Gaussian due to varying widths of the individual distributions. We find that the DOM exhibits several thermal-like features, including Debye scaling in a compressed hexagonally ordered packing, and an increase in low-frequency modes as the confining pressure is decreased. In disordered packings, we find that a characteristic frequency fc increases with pressure, but more weakly than has been observed in simulations of frictionless packings.

Graphical abstract: Acoustic measurement of a granular density of modes

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Publication details

The article was received on 13 Sep 2012, accepted on 16 Nov 2012 and first published on 27 Nov 2012

Article type: Paper
DOI: 10.1039/C2SM27122B
Soft Matter, 2013,9, 1214-1219

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    Acoustic measurement of a granular density of modes

    E. T. Owens and K. E. Daniels, Soft Matter, 2013, 9, 1214
    DOI: 10.1039/C2SM27122B

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