Resonant phenomena and mechanism in vibrated granular systems.

We were motivated to perform this research by the investigation of Brownian motors in excited granular materials converting the chaotic motion of granules into the oriented motion of motors. We conducted experimental studies to explore the horizontal motion of granules in vertically vibrated annular granular systems, including mixed and pure granular systems with an asymmetrical periodic structure on the bottom. The variations of the horizontal granular flow caused by the height, vibrating parameters, and mixing ratio were described in detail. Our results revealed considerable changes in the horizontal flow of different granular systems. Most importantly, resonance was induced in the horizontal granular flow by the vertical vibration; that is, the horizontal flow reached its maximum at specific vibrating parameters. A collisional model of rigid objects was constructed to probe the flowing resonances in these granular systems and provided a qualitative agreement with the experimental results obtained. We conclude that when a flowing resonance occurs, the granular system oscillates horizontally with a natural frequency under periodic external excitation. The frequency matching between the external excitation and the horizontal oscillation is responsible for the flowing resonance. Our results could improve the current understanding of the dynamic properties of granular systems under external excitation.