Intrinsic Energy Localization through Discrete Gap Breathers in One-Dimensional Diatomic Granular Crystals

Abstract

We present a systematic study of the existence and stability of discrete breathers that are spatially localized in the bulk of a one-dimensional chain of compressed elastic beads that interact via Hertzian contact. The chain is diatomic, consisting of a periodic arrangement of heavy and light spherical particles. We examine two families of discrete gap breathers: (1) an unstable discrete gap breather that is centered on a heavy particle and characterized by a symmetric spatial energy profile and (2) a potentially stable discrete gap breather that is centered on a light particle and is characterized by an asymmetric spatial energy profile. We investigate their existence, structure, and stability throughout the band gap of the linear spectrum and classify them into four regimes: a regime near the lower optical band edge of the linear spectrum, a moderately discrete regime, a strongly discrete regime that lies deep within the band gap of the linearized version of the system, and a regime near the upper acoustic band edge. We contrast discrete breathers in anharmonic FPU-type diatomic chains with those in diatomic granular crystals, which have a tensionless interaction potential between adjacent particles, and highlight in that the asymmetric nature of the latter interaction potential may lead to a form of hybrid bulk-surface localized solutions.

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• Damped-Driven Granular Crystals: An Ideal Playground for Dark Breathers and Multibreathers
• Experimental evidence of solitary wave interaction in Hertzian chains
• Discrete breathers in a nonlinear electric line: Modeling, Computation and Experiment
• Wave Propagation in a Strongly Nonlinear Locally Resonant Granular Crystal
• On the existence of solitary traveling waves for generalized Hertzian chains
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• Closed-form existence conditions for band-gap resonances in a finite periodic chain under general boundary conditions
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• Nonlinear waves in a strongly nonlinear resonant granular chain
• Breathers in lattices with alternating strain-hardening and strain-softening interactions
• Long-term behaviour of Hertzian chains between fixed walls is really equilibrium
• Kink Dynamics in a Non-Autonomous Sine-Gordon Model
• Nanoptera in weakly nonlinear woodpile and diatomic granular chains
• Parametric Resonance in the Non-Autonomous Sine-Gordon Model
• From Newton's cradle to the discrete p-Schrödinger equation