摩擦力对非弹性蹦球倍周期运动的影响

分析了摩擦力对竖直振动台面上完全非弹性蹦球动力学行为的影响.当控制参数Γ由1逐渐增大时,作用在蹦球上的恒定摩擦力不会改变倍周期分岔的序列,但会使倍周期分岔点的数值变大.与无摩擦力时的情况相比,在飞行时间的分岔图中也存在倍周期分岔密集区,只是被横向拉伸纵向压缩,且具有不同的分形特性.与受振颗粒体系中的倍周期分岔过程做了比较,发现当摩擦力取值为颗粒总重量的20%—30%时两者符合很好.

Effect of frictional force on subharmonic bifurcations of a completely inelastic ball bouncing on a vibrating table

The behavior of a completely inelastic ball bouncing on a vertically vibrating table in the presence of frictional force is investigated. The frictional force is assumed to be constant. It is found that the sequence of bifurcation, controlled solely by the normalized vibration acceleration Γ, is the same as that in the absence of frictional force, but the value of each bifurcation point becomes larger. In the bifurcation diagram of ball flight time, the structure consisting of an infinity of bifurcation cascades in a narrow range of Γ is observed. Compared with that of no frictional force, it is longitudinally compressed and transversely stretched, and has a different fractal property. A comparison with the bifurcations observed in vertically vibrated granular beds is also made. When the fractional force is set to be 20%—30% of the whole weight of the particles, the results from the bouncing ball model are in good agreement with experimental observations.