Acoustic measurement of a granular density of modes

TL;DR

This study introduces a new acoustic technique to measure the vibrational density of states in granular materials, revealing thermal-like features and pressure-dependent mode behavior in disordered and ordered packings.

Contribution

A novel method using acoustic excitations and embedded sensors to measure the density of modes in granular materials, extending thermal system analysis techniques to athermal granular systems.

Findings

Debye scaling observed in ordered packings

Low-frequency modes increase as pressure decreases

Characteristic frequency $f_c$ rises with pressure, but less than in frictionless simulations

Abstract

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 mimic thermal excitations 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. In spite of this deviation from a true thermal system, 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 $f_c$ increases with pressure, but more weakly than has been observed in simulations of frictionless packings.