Solitary wave trains in granular chains: Experiments, theory and simulations

Abstract

The features of solitary waves observed in horizontal monodisperse chain of barely touching beads not only depend on geometrical and material properties of the beads but also on the initial perturbation provided at the edge of the chain. An impact of a large striker on a monodisperse chain, and similarly a sharp decrease of bead radius in a stepped chain, generates a solitary wave train containing many single solitary waves ordered by decreasing amplitudes. We find, by simple analytical arguments, that the unloading of compression force at the chain edge has a nearly exponential decrease. The characteristic time is mainly a function involving the grains' masses and the striker mass. Numerical calculations and experiments corroborate these findings.

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References in corpus (4)

• Energy trapping and shock disintegration in a composite granular medium
• Anomalous wave reflection from the interface of two strongly nonlinear granular media
• How Hertzian solitary waves interact with boundaries in a 1-D granular medium
• Experimental evidence of shock mitigation in a Hertzian tapered chain

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• Gaussian solitary waves and compactons in Fermi-Pasta-Ulam lattices with Hertzian potentials
• Experimental evidence of solitary wave interaction in Hertzian chains
• Uniform Shock Waves in Disordered Granular Matter
• Wave mitigation in ordered networks of granular chains
• Traveling Waves and their Tails in Locally Resonant Granular Systems
• Nonlinear Low-to-High Frequency Energy Cascades in Diatomic Granular Crystals
• Localizing energy in granular materials
• Binary collision approximation for multi-decorated granular chains
• Travelling waves and conservation laws for highly nonlinear wave equations modelling Hertz chains
• The equilibrium phase in heterogeneous Hertzian chains
• Universal Relations for Solitary Waves in Granular Crystals under Finite Rise-decay Duration Shocks
• Long wavelength solitary waves in Hertzian chains and their properties in different nonlinearity regimes
• Localized energy absorbers in Hertzian chains
• Growth of Shock-Induced Solitary Waves in Granular Crystals
• Long-term behaviour of Hertzian chains between fixed walls is really equilibrium
• Solitons and thermal fluctuations in strongly nonlinear solids