Universal Relations for Solitary Waves in Granular Crystals under Finite Rise-decay Duration Shocks
arXiv:1502.04073 · doi:10.1103/PhysRevE.93.042905
Abstract
We focus on solitary waves generated in arrays of lightly contacting spherical elastic granules by shock forces of steep rise and slow decay durations, and establish a priori: (i) whether the peak value of the resulting solitary wave would be greater, equal, or less than the peak value of the input shock force; (ii) the magnitude of the peak value of the solitary waves; (iii) the magnitude of the linear momentum in each solitary wave; (iv) the magnitude of the linear momentum added to the remaining granules, if the first granule is ejected; and (v) a quantitative estimate of the effect of the granules' radius, density and stiffness on force amplification/mitigation. We have supported the analytical results by direct numerical simulations.
References in corpus (7)
- Tunability of solitary wave properties in one dimensional strongly nonlinear phononic crystals
- Energy trapping and shock disintegration in a composite granular medium
- How Hertzian solitary waves interact with boundaries in a 1-D granular medium
- Solitary wave trains in granular chains: Experiments, theory and simulations
- Experimental evidence of shock mitigation in a Hertzian tapered chain
- Pulse propagation in tapered granular chains: An analytic study
- Shock (Blast) Mitigation by "Soft" Condensed Matter