Shocks in non-loaded bead chains with impurities

TL;DR

This study numerically explores shock wave propagation in non-loaded granular chains with varying bead interaction exponents, revealing different regimes and impurity interactions that affect wave behavior and solitonic features.

Contribution

It provides new insights into shock wave dynamics in granular chains with variable nonlinearity and impurity effects, combining numerical and analytical approaches.

Findings

Cross-over between nonlinearity-dominated and solitonic regimes near alpha=1

Different impurity interactions for light and heavy masses

Shock wave behavior varies with interaction exponent alpha

Abstract

We numerically investigate the problem of the propagation of a shock in an horizontal non-loaded granular chain with a bead interaction force exponent varying from unity to large values. When $\alpha$ is close to unity we observed a cross-over between a nonlinearity-dominated regime and a solitonic one, the latest being the final steady state of the propagating wave. In the case of large values of $\alpha$ the deformation field given by the numerical simulations is completely different from the one obtained by analytical calculation. In the following we studied the interaction of these shock waves with a mass impurity placed in the bead chain. Two different physical pictures emerge whether we consider a light or a heavy impurity mass. The scatter of the shock wave with a light impurity yields damped oscillations of the impurity which then behave as a solitary wave source. Differently an heavy impurity is just shifted by the shock and the transmitted wave loses its solitonic character being fragmented into waves of decreasing amplitudes.