Instability of a long ribbon hanging in axial air flow

A ribbon hanging in a vertical air stream experiences sudden vibrations by flutter when the flow velocity reaches a critical value. The experiments conducted here for strips made of different materials show two distinct behaviours depending on the length of the strip. For short strips, the critical flow velocity depends strongly on the length, whereas for longer strips the critical velocity becomes independent of the length. These behaviours are analysed using a model originally derived by Datta, based on a slender-body approximation and unsteady potential flow theory. This yields an equation of motion similar to that pertaining to a hanging pipe-conveying fluid. The corresponding critical velocities are in relatively good agreement with those of the experiments for a set of 12 different ribbons. An asymptotic critical velocity may thus be defined corresponding to the limit of very long ribbons. The model predicts that this velocity only depends on the ratio between the fluid added mass and the ribbon mass. This is compared with experiments using strips of various widths and materials, and relation is made to the case of a hanging fluid-conveying pipe, addressed in a recent paper, and with the case of long towed cylinders.