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Dynamic effective mass of granular media and the attenuation of structure-borne sound

John Valenza1, Chaur-Jian Hsu1, Rohit Ingale1,2, Nicolas Gland2, Hernán A. Makse2, and David Linton Johnson1

  • 1Schlumberger-Doll Research, One Hampshire Street, Cambridge, Massachusetts 02139, USA
  • 2Levich Institute and Physics Department, City College of New York, New York, New York 10031, USA

Phys. Rev. E 80, 051304 – Published 30 November, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.051304

Abstract

We report a theoretical and experimental investigation into the fundamental physics of why loose granular media are effective deadeners of structure-borne sound. Here, we demonstrate that a measurement of the effective mass, M̃(ω), of the granular medium is a sensitive and direct way to answer the question: what is the specific mechanism whereby acoustic energy is transformed into heat? Specifically, we apply this understanding to the case of the flexural resonances of a rectangular bar with a grain-filled cavity within it. The pore space in the granular medium is air of varying humidity. The dominant features of M̃(ω) are a sharp resonance and a broad background, which we analyze within the context of simple models. We find that: (a) on a fundamental level, dampening of acoustic modes is dominated by adsorbed films of water at grain-grain contacts, not by global viscous dampening or by attenuation within the grains. (b) These systems may be understood, qualitatively, in terms of a height-dependent and diameter-dependent effective sound speed [100300(ms1)] and an effective viscosity [5×104Poise]. (c) There is an acoustic Janssen effect in the sense that, at any frequency, and depending on the method of sample preparation, approximately one-half of the effective mass is borne by the side walls of the cavity and one-half by the bottom. (d) There is a monotonically increasing effect of humidity on the dampening of the fundamental resonance within the granular medium which translates to a nonmonotonic, but predictable, variation in dampening within the grain-loaded bar.

Corrections

3 December, 2009

Erratum

Publisher's Note: Dynamic effective mass of granular media and the attenuation of structure-borne sound [Phys. Rev. E 80, 051304 (2009)]

John Valenza, Chaur-Jian Hsu, Rohit Ingale, Nicolas Gland, Hernán A. Makse, and David Linton Johnson
Phys. Rev. E 80, 069901 (2009)

Article Text

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