Damped-driven granular chains: An ideal playground for dark breathers and multibreathers

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. We demonstrate a remarkable control over the number of breathers within the multibreather pattern that can be "dialed in" by varying the frequency or amplitude of the actuation. The values of the frequency (or 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 and multibreather solutions. Moreover, we visualize detailed temporal and spatial profiles of breathers and, especially, of multibreathers using a full-field probing technology and enable a systematic favorable comparison among theory, computation, and experiments. A detailed bifurcation analysis reveals that the dark and multibreather families are connected in a "snaking" pattern, providing a roadmap for the identification of such fundamental states and their bistability in the laboratory.

Solitary waves propagation described by Korteweg-de Vries equation in the granular chain with initial prestress

“…[41][42][43][44][45][46] The dynamics of the bead chain is described by N coupled nonlinear equations,…”

Characterizing traveling-wave collisions in granular chains starting from integrable limits: The case of the Korteweg–de Vries equation and the Toda lattice

“…Geometry and/or material anisotropy between particles composing the systems allows for the observation of interesting dynamic phenomena deriving from the interplay of discreteness and nonlinearity of the problem (i.e. anomalous reflections, breathers, energy trapping and impulse fragmentation) [11,12,19,[24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. These findings open up a large parameter space for new materials design with unique properties sharply departing from classical engineering systems.…”

Nonlinear vibrational-state excitation and piezoelectric energy conversion in harmonically driven granular chains

“…Gap effects related to transient behavior of driven dissipative granular chains have also been studied [30]. Time-periodic solutions of damped-driven * cchong@bowdoin.edu granular chains (including, but not exclusively, breathers) have been explored in monomers [31], defect chains [10], dimers [32], and trimers [33].…”