Polydispersed Granular Chains: From Long-lived Chaotic Anderson-like Localization to Energy Equipartition

TL;DR

This paper studies how polydispersed granular chains exhibit long-lived energy localization under moderate nonlinearities and transition to energy equipartition with chaos at higher nonlinearities, revealing the interplay between chaos and localization.

Contribution

It demonstrates the conditions under which granular chains maintain localization or reach equipartition, linking nonlinearity strength to dynamical regimes.

Findings

Long-lasting energy localization occurs at moderate nonlinearities.

Strong nonlinearities lead to energy equipartition and chaotic states.

Localization persists despite chaos for certain excitations.

Abstract

We investigate the dynamics of highly polydispersed finite granular chains. From the spatio-spectral properties of small vibrations, we identify which particular single-particle displacements lead to energy localization. Then, we address a fundamental question: Do granular nonlinearities lead to chaotic dynamics and if so, does chaos destroy this energy localization? Our numerical simulations show that for moderate nonlinearities, although the overall system behaves chaotically, it can exhibit long lasting energy localization for particular single particle excitations. On the other hand, for sufficiently strong nonlinearities, connected with contact breaking, the granular chain reaches energy equipartition and an equilibrium chaotic state, independent of the initial position excitation.