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Nonlinear waves in disordered diatomic granular chains
Physics Review E
  • Laurent Ponson
  • Nicholas Boechler
  • Yi M Lai
  • Mason A Porter
  • PG Kevrekidis, University of Massachusetts - Amherst
Publication Date
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 spatiotemporal structure of the wave in both propagation regimes and propose a simple theoretical interpretation for a transition between the two regimes. 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.
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Citation Information
Laurent Ponson, Nicholas Boechler, Yi M Lai, Mason A Porter, et al.. "Nonlinear waves in disordered diatomic granular chains" Physics Review E Vol. 82 Iss. 2 (2010)
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