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.

在这项工作中，研究了反向传播的孤立波具有非互易特性的正面碰撞和传输，其中考虑了不同颗粒链之间的界面。由于两个周期性颗粒系统的不连续性，产生了透射和反射的孤立波。界面处出现正面碰撞，并应用还原微扰方法导出生成的孤立波。由推导和数值模拟可知，发射和反射的孤立波在位于同一链上时可以以相同的速度传播。此外，还讨论了布置和预应力的影响。发现由于预应力越大，孤立波的振幅和速度变大，这导致颗粒机械超材料中的非互易碰撞和传输。该研究有望对具有非线性孤立波的弹性波超材料和机械二极管的设计和应用有所帮助。