Periodic Travelling Waves in Dimer Granular Chains

Abstract

We study bifurcations of periodic travelling waves in granular dimer chains from the anti-continuum limit, when the mass ratio between the light and heavy beads is zero. We show that every limiting periodic wave is uniquely continued with respect to the mass ratio parameter and the periodic waves with the wavelength larger than a certain critical value are spectrally stable. Numerical computations are developed to study how this solution family is continued to the limit of equal mass ratio between the beads, where periodic travelling waves of granular monomer chains exist.

References in corpus (7)

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• Breathers and surface modes in oscillator chains with Hertzian interactions
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Cited by in corpus (5)

• Nanopteron solutions of diatomic Fermi-Pasta-Ulam-Tsingou lattices with small mass-ratio
• Nonlinear Low-to-High Frequency Energy Cascades in Diatomic Granular Crystals
• Micropteron traveling waves in diatomic Fermi-Pasta-Ulam-Tsingou lattices under the equal mass limit
• High-energy waves in superpolynomial FPU-type chains
• Nonlinear instabilities of multi-site breathers in Klein-Gordon lattices