竖直振动颗粒床中的倍周期运动

实验研究了竖直振动颗粒床中颗粒对容器底部的压力随振动强度的变化情况.发现压力随振动加速度的增加经历倍周期分岔，典型的分岔序列为：2P，4P，混沌，3P，6P，混沌，4P，8P，混沌.观察表明，伴随倍周期分岔现象，在颗粒床底部出现颗粒的聚集态.聚集态内颗粒密堆积在一起并作整体的上下运动.采用完全非弹性蹦球模型分析了颗粒对容器底的冲击力，并给出了倍周期分岔现象的一种解释. 关键词： 颗粒物质 混沌 倍周期分岔 非弹性碰撞

Period doubling motion in vertically vibrated granular beds

Experiments are performed to investigate the impact interaction between granular bed and container bottom, where the container is vertically vibrated. It is observed that the impact strength, controlled by the normalized vibration acceleration, undergoes a series of period doubling bifurcations, typically in the sequence of period-doubling, period-quadrupling, chaos, period-tripling, period-sextupling, chaos, period-quadrupling, period-octupling, and chaos. A condensed state of particles at the bottom of the container is observed, in which the particles are densely compacted and move as a bulk block in the vertical direction. Based on a completely inelastic bouncing ball model, a possible explanation for the bifurcation phenomena is presented.