Snap-through instability of a sheet with inclined clamping ends under fluid flow

Abstract

A buckled sheet, which is clamped at two ends with no inclination with respect to flow direction, is bistable under a uniform fluid flow. When the flow velocity exceeds a critical value, the sheet rapidly oscillates between two sides. In this work, we numerically investigate a new configuration in which the sheet is inclined by a certain angle at both clamped ends to reveal salient features in the instability and sheet deformation. With such an inclination, the two equilibria are asymmetric in the absence of a flow, leading to two separate instabilities under different conditions. At the lower flow-velocity threshold, the sheet transits from a bistable state to a monostable state, changing from an equilibrium with the higher bending energy to the other equilibrium with the lower bending energy through one-off snap-through. At the higher flow-velocity threshold, the sheet undergoes periodic snap-through. The critical flow velocity of one-off snap-through decreases with the inclination angle, while that of periodic snap-through increases. Considering changes in the bending energy and forces of the sheet with the inclination angle, dimensionless flow velocities are introduced to characterize the two transition conditions. In the periodic snap-through state, the temporal distribution of the bending energy changes dramatically with the inclination angle due to the asymmetric deformation of the sheet, and the peak-to-peak amplitude of the bending energy increases with the inclination angle, particularly in the low-flow-velocity regime.