Air effects on subharmonic bifurcations of impact in vertically vibrated granular beds

Abstract

Abstract. 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.