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

Granular chain serves as a fundamental component for controlling the nonlinear solitary wave propagation in acoustic metamaterials. The understanding of the nonlinear scattering at the mismatched interface plays a crucial role in designing novel acoustic devices. In this study, numerical simulations are conducted to investigate the asymmetric scattering effect of solitary waves in a two-section composite granular chain. Building upon Nesterenko’s work on solitary waves in monodisperse granular chains and using 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 multipulse 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.