Title: Dynamic Effective Mass of Granular Media

Author (Talk): David Johnson, Schlumberger-Doll Research

Abstract:

We report an experimental and theoretical investigation of the frequency-dependent effective mass, $\tilde{M}(\omega)$, of a rigid cavity filled with loose granular particles. We demonstrate the transferability of $\tilde{M}(\omega)$ to predict the changes in resonant frequency and in attenuation for general situations of structure-borne sound. The dominant features of $\tilde{M}(\omega)$ are a sharp resonance and a broad background, which we analyze within the context of simple models as well as with molecular dynamic simulations. We find that: a) These systems may be understood in terms of a height-dependent effective sound speed ($\sim 150$ m/s) and an effective viscosity ($\sim 2\times 10^4$ Poise). b) There is a dynamic 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. c) On a fundamental level, dissipation is dominated by that at grain-grain contacts, not by global viscous damping.

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