Nonreciprocal Head-on Collision Between Two Nonlinear Solitary Waves in Granular Metamaterials with an Interface

In this work, the head-on collision and transmission with nonreciprocal properties of opposite propagating solitary waves are studied, in which the interface between different granular chains is considered. Due to the discontinuity of two periodic granular systems, the transmitted and reflected solitary waves are produced. The head-on collision appears at the interface and the reductive perturbation method is applied to derive the generated solitary waves. According to the derivation and numerical simulation, we can find that the transmitted and reflected solitary waves can propagate with the same speed when they locate at the same chain. Moreover, the influences of both the arrangement and prestress are discussed. It is found that the amplitude and velocity of solitary waves become larger because of a bigger prestress, which result in the nonreciprocal collision and transmission in the granular mechanical metamaterials. This study is expected to be helpful for the design and application of elastic wave metamaterials and mechanical diodes with nonlinear solitary waves.