Breather modes of fully nonlinear mass-in-mass chains

Abstract

We propose a model for a chain of particles coupled by nonlinear springs in which each mass has an internal mass and all interactions are assumed to be nonlinear. We show how to construct an asymptotic solution of this system using multiple timescales, the systematic solution of coupled equations by repeated application of a consistency condition. Our results show that for some combinations of nonlinearity the dynamics are governed by the NLS as in the more usual mass-in-mass chains with linear interactions between inner and outer masses. However, when both nonlinearities have quadratic components, we show that the asymptotic reduction results in a Ginzburg-Landau equation instead of NLS.

arXiv comment16pp, 17 figures, to appear in Phys Rev E

References in corpus (11)

• An introduction to the Ginzburg-Landau theory of phase transitions and nonequilibrium patterns
• Energy thresholds for discrete breathers in one-, two- and three-dimensional lattices
• Localized moving breathers in a 2-D hexagonal lattice
• Discrete breathers in a two-dimensional hexagonal Fermi-Pasta-Ulam lattice
• Nonlinear propagating localized modes in a 2D hexagonal crystal lattice
• Dark Breathers in Granular Crystals
• Interaction of Traveling Waves with Mass-With-Mass Defects within a Hertzian Chain
• Breathers in a locally resonant granular chain with precompression
• Traveling waves for the Mass in Mass model of granular chains
• Discrete Breathers in a Mass-in-Mass Chain with Hertzian Local Resonators
• Extreme waves and branching flows in optical media