Nonlinear Waves in Disordered Diatomic Granular Chains

Abstract

We investigate the propagation and scattering of highly nonlinear waves in disordered granular chains composed of diatomic (two-mass) units of spheres that interact via Hertzian contact. Using ideas from statistical mechanics, we consider each diatomic unit to be a "spin", so that a granular chain can be viewed as a spin chain composed of units that are each oriented in one of two possible ways. Experiments and numerical simulations both reveal the existence of two different mechanisms of wave propagation: In low-disorder chains, we observe the propagation of a solitary pulse with exponentially decaying amplitude. Beyond a critical level of disorder, the wave amplitude instead decays as a power law, and the wave transmission becomes insensitive to the level of disorder. We characterize the spatio-temporal structure of the wave in both propagation regimes and propose a simple theoretical interpretation for such a transition. Our investigation suggests that an elastic spin chain can be used as a model system to investigate the role of heterogeneities in the propagation of highly nonlinear waves.

10 pages, 8 figures (some with multiple parts), to appear in Physical Review E; summary of changes: new title, one new figure, additional discussion of several points (including both background and results)

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• Nonlinear Low-to-High Frequency Energy Cascades in Diatomic Granular Crystals
• Supratransmission in a Disordered Nonlinear Periodic Structure
• Periodic Travelling Waves in Dimer Granular Chains
• Scattering of Waves by Impurities in Precompressed Granular Chains
• Chaos and Anderson Localisation in Disordered Classical Chains: Hertzian vs FPUT models
• Ill-posedness of degenerate dispersive equations
• Geometry-controlled phase transition in vibrated granular media
• Polydispersed Granular Chains: From Long-lived Chaotic Anderson-like Localization to Energy Equipartition
• Wave propagation across interfaces induced by different interaction exponents in ordered and disordered Hertz-like granular chains
• Wave propagation in a strongly disordered 1D phononic lattice supporting rotational waves
• Nanoptera in nonlinear woodpile chains with zero precompression
• Nanoptera in weakly nonlinear woodpile and diatomic granular chains
• Energy spreading, equipartition and chaos in lattices with non-central forces
• Wave-packet spreading in disordered soft architected structures