周期型二元颗粒链中孤波传播的二体碰撞近似分析

本文运用二体碰撞近似理论研究了孤波在周期型二元颗粒链中的传播. 周期型二元颗粒链由N个大球和一个小球交替排列而成, 球的材质都相同. 将小球和与之相邻的大球等效成一个球, 形成一条等效链. 采用二体碰撞近似理论, 推导了孤波在颗粒链中传播的速度、通过颗粒链时间以及小球的振荡频率. 理论分析得到小球振荡频率随着半径的增大而减小, 该结果与计算机模拟结果符合得相当好. 二体碰撞近似理论给出的波通过整条颗粒链时间, 在N ≤ 2时与计算机模拟结果符合得很好. 理论计算的误差随链长的变化不大. 但随着N的增大, 理论得到的结果相对误差变大.

Binary collision approximation for solitary wave in periodic dimer granular chains

We study solitary wave propagation in periodic dimer granular chains of beads with the same material but different sizes by binary collision approximation.This kind of chain which is called "N:1 dimer" consists of pairs of N big beads and one small bead.First we present a method to map the actual chain into an effective chain,then use the binary collision approximation to obtain the transmitted solitary wave speed,the total time taken by the pulse to pass through the chain,and the frequency of oscillation of the small particle. Frequency of oscillation,which increases with the decrease of the radius of the small particle,is analytically obtained.And the results are in excellent agreement with numerical results.For the total time of the pulse passing through the chain,the results of theoretical analysis is in good agreement with numerical results when N≤2.The relative error seems no change with the chain length but becomes larger with the increase of the value of N.