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Article Dans Une Revue Physica D: Nonlinear Phenomena Année : 2016

Breathers in a locally resonant granular chain with precompression

Résumé

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.

Dates et versions

hal-01417945 , version 1 (16-12-2016)

Identifiants

Citer

Lifeng Liu, Guillaume James, Panayotis Kevrekidis, Anna Vainchtein. Breathers in a locally resonant granular chain with precompression. Physica D: Nonlinear Phenomena, 2016, 331, pp.27-47. ⟨10.1016/j.physd.2016.05.007⟩. ⟨hal-01417945⟩
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