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Air Effects on Subharmonic Bifurcations of Impact in Vertically Vibrated Granular Beds

机译:垂直振动颗粒床抗冲击性次谐分叉的空气影响

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Experiments have been performed to investigate the effects of interstitial air on the impact bifurcations in vertically vibrated granular beds. The impact of particles on the container bottom commonly undergoes a series of subharmonic bifurcations in the sequence of period-2, period-4, chaos, period-3, period-6, chaos, period-4, period-8, and so on. In the container with an air impermeable bottom, air flows are induced and air drag on the particles causes the bifurcations to be dependent on the particle size; the bifurcation point increases with the decreasing of particle size. This makes the higher-order bifurcations become unobservable when the particle size is sufficiently small. Meanwhile, such bifurcations are shown to be controlled by both the normalized vibration acceleration and the vibration frequency. However, in the container with an air permeable bottom the size dependence of bifurcations is cancelled, and the bifurcations turn to be controlled solely by the normalized vibration acceleration. The observed results are explained in terms of an inelastic bouncing ball model with air dragging terms involved.
机译:已经进行了实验以研究间质空气在垂直振动颗粒床中的冲击分叉上的影响。颗粒对容器底部的影响通常在时期-2,时期-4,混乱,时期-3,时期-6,混乱,时期-4,时期-8等序列中经历一系列次谐分叉分岔。在具有空气不可渗透的底部的容器中,诱导空气流量,并且在颗粒上的空气拖动导致分叉依赖于粒度;分叉点随着粒径的降低而增加。当粒径足够小时,这使得高阶分叉变得不可观察。同时,示出了这种分叉通过归一化振动加速度和振动频率来控制。然而,在具有透气底部的容器中,取消分叉的尺寸依赖性,并且分叉通过归一化的振动加速来控制。观察结果是根据涉及空中拖曳术语的非弹性弹跳球模型来解释。

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