Damped-Driven Granular Crystals: An Ideal Playground for Dark Breathers and Multibreathers

TL;DR

This study demonstrates the experimental creation and control of dark breathers in granular chains through boundary actuation, supported by theoretical modeling and detailed stability analysis, advancing understanding of nonlinear localized structures.

Contribution

The paper introduces a method to generate and control dark breathers in granular crystals using boundary actuation, supported by a comprehensive theoretical and experimental framework.

Findings

Dark breathers can be experimentally generated with boundary actuation.

The number of breathers can be tuned by adjusting actuation parameters.

Theoretical predictions match experimental and numerical results.

Abstract

By applying an out-of-phase actuation at the boundaries of a uniform chain of granular particles, we demonstrate experimentally that time-periodic and spatially localized structures with a nonzero background (so-called dark breathers) emerge for a wide range of parameter values and initial conditions. Importantly, the number of ensuing breathers within the multibreather pattern produced can be "dialed in" by varying the frequency or amplitude of the actuation. The values of the frequency (resp. amplitude) where the transition between different multibreather states occurs are predicted accurately by the proposed theoretical model, which is numerically shown to support exact dark breather solutions. The existence, linear stability, and bifurcation structure of the theoretical dark breathers are also studied in detail. Moreover, the distributed sensing technologies developed herein enable a detailed space-time probing of the system and a systematic favorable comparison between theory, computation and experiments.