Flow-induced vibration of an S-shaped bluff elastic sheet

The dynamics of an S-shaped elastic sheet, in which the inclination angles of two clamped ends are normal to the direction of uniform flow and opposite to each other, are experimentally investigated. Flow-induced vibrations are ensured in this novel configuration by the substantial area perpendicular to the flow and the bluff shape. The motions of the sheet can be divided into three modes depending on the trends of the oscillation amplitude and frequency with respect to the flow velocity. At low flow velocities, the sheet undergoes small-amplitude oscillations with a nearly constant frequency. Beyond a certain threshold of flow velocity, the amplitude increases rapidly while the frequency declines. The dimensionless critical flow velocity is almost independent of the ratio between the clamp distance and sheet length, as predicted by simple scaling analysis. As the flow velocity increases further, the amplitude becomes saturated, while the frequency becomes almost proportional to the flow velocity. The most notable features of the sheet are the temporal and spatial distributions of its bending energy. The bending energy exhibits negligible fluctuations over time, and despite changes in the flow velocity, the time-averaged bending energy remains almost constant. However, by dividing the sheet into front, center, and rear parts, significant variations in the bending energy are found, and these are intensified at higher flow velocities. The S-shaped sheet exhibits more pronounced variations in local bending energy at lower flow velocities compared with a snap-through sheet model clamped at both ends.