On the occurrence of polygon-shaped patterns in vibrated cylindrical granular beds

We report experimental observations of polygon-shaped patterns formed in a vertically vibrated bed of circular cross-section. A phase map is determined, showing that the polygon pattern is established for Γ = A (2 πf ) 2 / g ≳ 10 . The sensitivity of the polygon structure to bed parameters was tested by studying beds of different particle sizes and fill levels. It was hypothesized that the polygon pattern observed in cylindrical beds is the corresponding pattern to the formation of arches in square-shaped beds. The close relationship between these two patterns was demonstrated by two observations: i) the radii of the arches of a corresponding square bed and the inner radius of the cylindrical bed were found to be very similar and ii) the boundary lengths of the two patterns were in good agreement.