Vertical oscillation of a bed of granular material

The vertical vibrations in a bed of granular material cause at least one sudden bed expansion for a critical acceleration amplitude. A bifurcation in bed dynamics, having an effective coefficient of restitution greater than zero, causes the sudden expansion in the case of shallow beds. Deeper beds show heaping when the coefficient is equal to zero and exhibit a period doubling bifurcation instead of the sudden expansion. Results of a study using beads are compared with a model based on a ball bouncing on a vibrating plate.