Effect of wall friction on subharmonic bifurcations of impact in vertically vibrated granular beds

Abstract

Granular materials consist of a large number of discrete solid particles. When subjected to external vibrations, they exhibit various intricate dynamical behaviors, Which usually depend in a complicated way on many physical factors, such as air dragging, friction from the container wall and so forth. In this work, vertical vibrations are applied to a bed of stainless-steel spheres contained in a glass tube, and the subharmonic bifurcations of impact of particles on the container bottom are investigated. To eliminate the effects of air dragging, we evacuate the container or perforate the container bottom to make it quite permeable to the air. Experiments performed in such containers reveal that the impact bifurcations are controlled solely by the normalized vibration acceleration, but independent of the particle size, the filling height of particles, and the frequency of forced vibration. The sliding friction from the container wall is treated as a constant one with the direction opposite to the velocity relative to the container wall. By involving this damping term into the completely inelastic bouncing ball model, an explanation for the experimental results is made. Simulations on the averaged experimental bifurcation points indicate that the magnitude of wall friction is about 10% of the total weight of the particles.