The influence of air on period doubling motion in vertically vibrated grains beds

We investigated the effects of interstitial air on the impact bifurcations of period doubling motion in vertically vibrated grains beds. The impact of grains on the container bottom undergoes a series of subharmonic bifurcations as the vibration intensity increases. With the presence of air, the vibration acceleration of the bifurcation points caused by the air drag on grains increases as the size of grains decreases. Especially, for grains with sufficiently small diameters, higher-order bifurcations become unobservable. We also found that with the decrease of the grains size, the dependence of the bifurcation points on the size of grains and vibrating frequency becomes more obvious due to the air drag, and such a dependence disappears when a vacuumed or porous-bottomed container is used.