Vibrations of Jammed Disk Packings with Hertzian Interactions

TL;DR

This study investigates how Hertzian interactions influence the vibrational behavior of jammed disk packings, revealing that contact breaking dominates the nonlinear response even with Hertzian potentials.

Contribution

It provides a detailed comparison of vibrational responses in granular packings with Hertzian versus linear interactions, highlighting the role of contact breaking in nonlinearities.

Findings

Hertzian interactions cause weak nonlinearities like harmonic generation.

Contact breaking dominates the vibrational response in Hertzian packings.

Linear response breaks down above a certain energy threshold.

Abstract

Contact breaking and Hertzian interactions between grains can both give rise to nonlinear vibrational response of static granular packings. We perform molecular dynamics simulations at constant energy in 2D of frictionless bidisperse disks that interact via Hertzian spring potentials as a function of energy and measure directly the vibrational response from the Fourier transform of the velocity autocorrelation function. We compare the measured vibrational response of static packings near jamming onset to that obtained from the eigenvalues of the dynamical matrix to determine the temperature above which the linear response breaks down. We compare packings that interact via single-sided (purely repulsive) and double-sided Hertzian spring interactions to disentangle the effects of the shape of the potential from contact breaking. Our studies show that while Hertzian interactions lead to weak nonlinearities in the vibrational behavior (e.g. the generation of harmonics of the eigenfrequencies of the dynamical matrix), the vibrational response of static packings with Hertzian contact interactions is dominated by contact breaking as found for systems with repulsive linear spring interactions.