Shocks in non-loaded bead chains with impurities

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.