Breathers in a locally resonant granular chain with precompression
arXiv:1603.06033 · doi:10.1016/j.physd.2016.05.007
Abstract
We study a locally resonant granular material in the form of a precompressed Hertzian chain with linear internal resonators. Using an asymptotic reduction, we derive an effective nonlinear Schrödinger (NLS) modulation equation. This, in turn, leads us to provide analytical evidence, subsequently corroborated numerically, for the existence of two distinct types of discrete breathers related to acoustic or optical modes: (a) traveling bright breathers with a strain profile exponentially vanishing at infinity and (b) stationary and traveling dark breathers, exponentially localized, time-periodic states mounted on top of a non-vanishing background. The stability and bifurcation structure of numerically computed exact stationary dark breathers is also examined. Stationary bright breathers cannot be identified using the NLS equation, which is defocusing at the upper edges of the phonon bands and becomes linear at the lower edge of the optical band.
arXiv comment40 pages, 25 figures
References in corpus (16)
- Discrete Breathers in One-Dimensional Diatomic Granular Crystals
- Shock Wave Structure in a Strongly Nonlinear Granular Lattice with Viscous Dissipation
- Highly Nonlinear Wave Propagation in Elastic Woodpile Periodic Structures
- Localized Breathing Modes in Granular Crystals with Defects
- Intrinsic Energy Localization through Discrete Gap Breathers in One-Dimensional Diatomic Granular Crystals
- Wave localization in strongly nonlinear Hertzian chains with mass defect
- Breathers and surface modes in oscillator chains with Hertzian interactions
- Wave propagation in single column woodpile phononic crystals: Formation of tunable band gaps
- Damped-Driven Granular Crystals: An Ideal Playground for Dark Breathers and Multibreathers
- Dark Breathers in Granular Crystals
- Mobile Localization in nonlinear Schrodinger lattices
- Interaction of Traveling Waves with Mass-With-Mass Defects within a Hertzian Chain
- Traveling Waves and their Tails in Locally Resonant Granular Systems
- Discrete breathers in honeycomb Fermi-Pasta-Ulam lattices
- Breathers In Periodic Granular Chains With Multiple Band Gaps
- Nonlinear waves in a strongly nonlinear resonant granular chain
Cited by in corpus (12)
- Nonlinear Coherent Structures in Granular Crystals
- Wave Propagation in a Strongly Nonlinear Locally Resonant Granular Crystal
- Effect of discrete breathers on the specific heat of a nonlinear chain
- Effect of discrete breathers on macroscopic properties of the Fermi-Pasta-Ulam chain
- Quasiperiodic granular chains and Hofstadter butterflies
- Nonlinear Excitations in Magnetic Lattices with Long-Range Interactions
- Discrete Breathers in a Mass-in-Mass Chain with Hertzian Local Resonators
- Nanoptera in nonlinear woodpile chains with zero precompression
- Breather modes of fully nonlinear mass-in-mass chains
- Elastic Wannier-Stark Ladders and Bloch Oscillations in 1D Granular Crystals
- Metamaterial two-sphere Newton's cradle
- Nanoptera in weakly nonlinear woodpile and diatomic granular chains