维度和压强对颗粒体系振动态密度的影响

颗粒物质生产、储存和输送等研究已经有悠久的历史,近些年来,虽然开展了关于颗粒物质的多方面的实验和模拟计算,但对其运动规律研究还很肤浅,描述颗粒物质的基本理论尚未建立。基于离散元法(discrete element method, DEM),用PFC软件生成了压强分别为0.1、1、10、100、1 000、10 000 Pa的不同维度的无摩擦颗粒体系,基于Hessian矩阵的简正模式分析法,编写了计算不同维度和压强下颗粒体系态密度的程序,进一步分析了维度和压强对颗粒体系态密度的影响。结果表明：一维颗粒体系的态密度不受压强影响。在低频下态密度几乎不随频率变化,在高频下态密度曲线随频率呈现振荡上升趋势。二维颗粒体系态密度曲线在某个特征频率之上出现一个平台,且该平台随着压强的增加而增加。低于某个特征频率下,三维颗粒态密度随频率呈幂率标度,随着压强增加曲线向高频移动。

The effect of dimension and pressure on the vibrational density of states of particle system

In this paper, based on the discrete element method (DEM), the frictionless particle systems with different dimensions under pressure 0.1 Pa, 1 Pa, 10 Pa, 100 Pa, 1000 Pa, 10000 Pa are generated by PFC software. The procedure to calculate the density of states (DOS) of the particle system under different dimension and pressure is written based on the normal mode analysis of Hessian matrix, and the effect of dimension and pressure on the density of states of the particle system is further analyzed. It is found that the density of states of the one-dimensional particle system is not affected by the pressure. The density of states hardly varies with frequency at low frequencies, and the density of states curve shows an oscillating upward trend with frequency at high frequencies. The density of states curve of the two-dimensional particle system appears a plateau above a certain characteristic frequency, and the plateau increases with the increase of the pressure. Below a certain characteristic frequency, the density of states of the three-dimensional particles shows a power rate scale with frequency, and the curve shifts to high frequencies with increasing pressure.