Breathers in a locally resonant granular chain with precompression

Liu, Lifeng; James, Guillaume; Kevrekidis, Panayotis; Vainchtein, Anna

doi:10.1016/j.physd.2016.05.007

Title: Breathers in a locally resonant granular chain with precompression

Journal Article · Thu Sep 01 00:00:00 EDT 2016 · Physica. D, Nonlinear Phenomena

DOI:https://doi.org/10.1016/j.physd.2016.05.007· OSTI ID:1258012

Liu, Lifeng ^[1]; James, Guillaume ^[2]; Kevrekidis, Panayotis ^[3]; Vainchtein, Anna ^[1]

Univ. of Pittsburgh, PA (United States)
INRIA Grenoble-Rhone Alpes, Montbonnot-Saint-Martin (France)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Here 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. In turn, this 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. Moreover, 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.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: DMS-1007908; DMS-1506904; FA9550-12-1-0332; W911NF-15-1-0604; AC52-06NA25396

OSTI ID:: 1258012

Alternate ID(s):: OSTI ID: 1359742

Report Number(s):: LA-UR-15-25012

Journal Information:: Physica. D, Nonlinear Phenomena, Vol. 331, Issue C; ISSN 0167-2789

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 22 works

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Elastic Wannier-Stark ladders and Bloch oscillations in 1D granular crystals Shi, Xiaotian; Chaunsali, Rajesh; Wu, Ying Journal of Applied Physics, Vol. 123, Issue 10 https://doi.org/10.1063/1.5011664	journal	March 2018
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Nonlinear mechanisms of two-dimensional wave-wave transformations in the initially coupled acoustic structure Vorotnikov, K.; Starosvetsky, Y. Journal of Applied Physics, Vol. 123, Issue 2 https://doi.org/10.1063/1.4986282	journal	January 2018
Nonlinear excitations in magnetic lattices with long-range interactions Molerón, Miguel; Chong, C.; Martínez, Alejandro J. New Journal of Physics, Vol. 21, Issue 6 https://doi.org/10.1088/1367-2630/ab0118	journal	June 2019
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Nonlinear Coherent Structures in Granular Crystals Chong, C.; Porter, Mason A.; Kevrekidis, P. G. arXiv https://doi.org/10.48550/arxiv.1612.03977	text	January 2016
Elastic Wannier-Stark Ladders and Bloch Oscillations in 1D Granular Crystals Shi, Xiaotian; Chaunsali, Rajesh; Wu, Ying arXiv https://doi.org/10.48550/arxiv.1711.00511	text	January 2017
Nonlinear Excitations in Magnetic Lattices with Long-Range Interactions Molerón, Miguel; Chong, C.; Martínez, Alejandro J. arXiv https://doi.org/10.48550/arxiv.1801.09560	text	January 2018

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