Universal Relations for Solitary Waves in Granular Crystals under Finite Rise-decay Duration Shocks

TL;DR

This paper derives universal relations for solitary waves in granular crystals subjected to shocks with finite rise and decay times, analyzing their peak values, momentum, and effects of granule properties through theory and simulations.

Contribution

It establishes new analytical relations for solitary wave characteristics in granular crystals under finite-duration shocks, supported by numerical validation.

Findings

Peak wave value depends on shock rise-decay profile.

Granule properties influence force amplification.

Analytical relations match numerical simulations.

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.