Buckling of a flat plate in a confined axial flow

Static instability of flexible structures forced by a parallel flow, a.k.a. divergence, has been the subject of a relatively small amount of studies, unlike flutter In order to prepare future studies of the collective behaviour of several slender structures coupled by the fluid in axial flow, the canonical case of a flat flexible plate clamped at both ends is investigated numerically and experimentally. The onset of divergence is determined throughout a series of calculation of the fluid forces generated by a prescribed deformation of the plate. Using the Galerkin method, these fluid forces are expanded in the basis of the natural modes; they exactly balance the mechanical forces when the fluid velocity reaches the instability threshold. The instability velocity can be determined by an eigenvalue calculation involving the fluid force expansion and the modal stiffnesses of the plate. Comparisons are provided with 2D analytical calculations and with an experiment performed with a 0.3m × 0.03m mylar plate at Reynolds numbers varying between 10⁴ and 10⁵. A fair agreement is observed between the 3D potential calculation and the experiments, whereas the 2D analytical solution underestimates the instability velocity by a factor higher than 2.