二维颗粒结构中非线性波的传播和脉冲衰减

Nonlinear wave propagation and pulse mitigation in 2D granular chains

有序颗粒介质在冲击振动缓解、能量捕获和吸收等领域具有重要的研究价值。本文运用赫兹接触理论建立二维颗粒链数学模型,在冲击激励作用下,研究二维颗粒系统中脉冲波的传播特性、能量传递规律和传递力的降低机理。二维均匀颗粒系统嵌入了耦合颗粒以传递动能,初始脉冲激励在2列颗粒链间发生能量交换和脉冲等分现象,脉冲波在激励施加点附近发生强能量散射,激发出混合型的非线性波,即纵向传播的近零频率孤立波与横向高频剪切波。与一维均匀颗粒链相比,二维颗粒系统的末端传递力峰值得到了大幅度降低。通过改变颗粒间的质量比,在二维均匀颗粒链中引入轻珠链构成非均匀结构,沿纵向传播的孤立波在轻-重颗粒交界面发生反射,能量被局部约束在轻珠链中,使得一系列低幅值脉冲波按照不同的波速,延时释放到颗粒链末端,导致末端传递力峰值的进一步降低。

Ordered granular media have important research value in fields such as shock and vibration mitigation,and shock energy trapping and absorption.In this paper,Hertzian contact theory is used to establish a mathematical model of two two-dimensional(2D)granular chains,and the nonlinear wave propagation characteristics,energy transfer,and reduction of transmitted force in two impulsively excited systems are investigated.The two-dimensional homogeneous granular chain includes embedded coupling beads,leading to energy exchange and eventual equipartition of energy between the directly excited chain and the absorbing chain.Strong energy scattering occurs in the vicinity of the point of application of the impulsive load,and mixed nonlinear waves are excited,involving coupled longitudinal propagatory solitary waves of near-zero frequency and higher-frequency transverse oscillatory shear waves.Compared with that found in the one-dimensional homogeneous granular chain,the transmitted force peak at the end of the two-dimensional granular chains is substantially reduced.By changing the mass ratio between particles and introducing light beads into the two-dimensional homogeneous granular chain to form a non-homogeneous structure,the longitudinally propagating solitary waves are reflected at the light-heavy interface,and energy is temporarily spatially confined in the light beads.This results in a series of low-amplitude pulse waves being released to the end of the granular chain with different wave speeds and time delays,leading to a further reduction of peak transmitted force.