Dynamics of a grain-filled ball on a vibrating plate

We study experimentally how the bouncing dynamics of a hollow ball on a vibrating plate is modified when it is partially filled with liquid or grains. Whereas empty and liquid-filled balls display a dominant chaotic dynamics, a ball with grains exhibits a rich variety of stationary states, determined by the grain size and filling volume. In the collisional regime, i.e., when the energy injected to the system is mainly dissipated by interparticle collisions, an unexpected period-1 orbit appears independently of the vibration conditions, over a wide range. This is a self-regulated state driven by the formation and collapse of a granular gas within the ball during one cycle. In the frictional regime (dissipation dominated by friction), the grains move collectively and generate different patterns and steady modes: oscillons, waves, period doubling, etc. From a phase diagram and a geometrical analysis, we deduce that these modes are the result of a coupling (synchronization) between the vibrating plate frequency and the trajectory followed by the particles inside the cavity.