Asymmetric scattering effect of solitary wave in a two-section composite granular chain

Abstract

This study presents numerical simulations on the asymmetric scattering effect of solitary waves in a two$-$section composite granular chain. On the basis of Nesterenko's work on solitary waves in monodisperse granular chains and continuous acoustic wave theory in linear medium, we argue that the mismatches of acoustic velocity and acoustic impedance, because of the differences of mass density and elastic coefficient, dominate the asymmetric scattering effect at the mismatched interface. The simulation results confirm the occurrence of a multipusle structure for the transmitted solitary waves when the solitary wave passes through the mismatched interface with a small$-$large wave velocity. The overshooting effect occurs for the reflected solitary waves because of the mismatched interface with high$-$low acoustic impedance. The phase diagram in the space of the mass density and the elastic coefficient ratio of the right$-$section granular chain to the left$-$section granular chain further validates the predictions. The results are crucial for the fundamental understanding of the dynamic behavior of solitary waves in granular chains.