Motion Modes Of Granular Particles In A Vibrating Narrow Tube

This work gives a survey of the static property and dynamical behaviors of granular materials that vertically vibrated, and then presents our research on the phenomena of period doubling bifurcations observed in vibrated granular beds. When subjected to vertical vibrations, granular materials exhibit behaviors of heaping, convection, and surface standing waves. Our observations show that, accompanying with these phenomena, there exist serials of subharmonic bifurcations of the impact of the granular bed and container base. It is shown that the bifurcations are controlled solely by the normalized vibration acceleration. The serial of bifurcations and corresponding bifurcation points have been experimentally determined, and their dependence on the particle size, vibration frequency, material of particles, lateral size of container, and bed thickness has been investigated. Also it is found that in narrow cylindrical vessels the particles in the lower part of the bed are in a condensed state, as which in an ordered packing that consists of a concentric array of cylindrical"shells"of particles. Here a completely inelastic bouncing ball model is employed to analyze the bifurcation phenomena in granular materials bed of vertically vibrating. Due to the dissipative of the particles by inelastic collisions, the particle system move as an inelastic bulk block in the vertical direction, just like an inelastic bouncing ball on the vibrating platform. It is found that the motion modes of particles strongly depend on the bed thickness. When the condensed state formed, the particles perform the phenomena as which the concentric array of cylindrical"shells"in the lower part of the bed, and moving all together. In a"shell", the particles are arrayed hexagonally. There will be appeared point or line difect sometimes, but the particles always transform to the most compactness structure.