器壁滑动摩擦力对受振颗粒体系中冲击力倍周期分岔过程的影响

颗粒物质由离散的固体颗粒组成, 受到周期性振动时可以表现出复杂的动力学行为. 这些行为往往受众多因素的影响, 如空气阻力和器壁摩擦力等. 针对受振颗粒体系中冲击力的倍周期分岔现象, 通过抽真空或将容器底镂空消除空气阻力, 单独研究器壁滑动摩擦力的影响. 结果表明在仅有器壁摩擦力作用的情况下, 倍周期分岔过程仅受约化振动加速度的控制, 与颗粒的尺寸、颗粒层数及振动频率无关. 将器壁摩擦力处理成一个大小恒定、方向与颗粒和器壁相对速度反向的阻力, 并包含到完全非弹性蹦球模型中, 能够对所观察到的现象给出很好的解释. 通过对倍周期分岔点测量平均值的拟合, 得到器壁滑动摩擦力的大小约为颗粒总重量的10%. 关键词： 颗粒物质 器壁摩擦力 倍周期分岔 冲击力

Effect of wall friction on subharmonic bifurcations of impact in vertically vibrated granular beds

Granular materials consist of a large number of discrete solid particles. When subjected to external vibrations, they exhibit various intricate dynamical behaviors, Which usually depend in a complicated way on many physical factors, such as air dragging, friction from the container wall and so forth. In this work, vertical vibrations are applied to a bed of stainless-steel spheres contained in a glass tube, and the subharmonic bifurcations of impact of particles on the container bottom are investigated. To eliminate the effects of air dragging, we evacuate the container or perforate the container bottom to make it quite permeable to the air. Experiments performed in such containers reveal that the impact bifurcations are controlled solely by the normalized vibration acceleration, but independent of the particle size, the filling height of particles, and the frequency of forced vibration. The sliding friction from the container wall is treated as a constant one with the direction opposite to the velocity relative to the container wall. By involving this damping term into the completely inelastic bouncing ball model, an explanation for the experimental results is made. Simulations on the averaged experimental bifurcation points indicate that the magnitude of wall friction is about 10% of the total weight of the particles.
Keywords： granular materials wall friction subharmonic bifurcations impact