Wall-bounded periodic snap-through and contact of a buckled sheet

Abstract

Fluid flow passing a post-buckled sheet placed between two close confining walls induces periodic snap-through oscillations and contacts that can be employed for triboelectric energy harvesting. The responses of a two-dimensional sheet to a uniform flow and wall confinement in both equilibrium and post-equilibrium states are numerically investigated by varying the distance between the two ends of the sheet, gap distance between the confining walls and flow velocity. Cases with strong interactions between the sheet and walls are of most interest for examining how contact with the walls affects the dynamics of the sheet and flow structure. At equilibrium, contact with the wall displaces the sheet to form a nadir on its front part, yielding a lower critical flow velocity for the transition to snap-through oscillations. However, reducing the gap distance between the walls below a certain threshold distinctly shifts the shape of the sheet, alters the pressure distribution and eventually leads to a notable delay in the instability. The contact between the oscillating sheet and the walls at post-equilibrium is divided into several distinct modes, changing from sliding/rolling contact to bouncing contact with increasing flow velocity. During this transition, the time-averaged contact force exerted on the sheet decreases with the flow velocity. The vortices generated at the extrema of the oscillating sheet are annihilated by direct contact with the walls and merging with the shear layers formed by the walls, resulting in a wake structure dominated by the unstable shear layers.