Destabilization of a rectangular membrane in axial flow through compression of its lateral edges

The flutter of rectangular sheets in axial flow ("flags") is a canonical problem of fluid structure interaction. As such, it has been studied in many variations and for various applications ranging from energy harvesting to biomedical. The flow speed required to initiate the dynamic instability is a basic quantity of interest. In conventional flag flutter, among the contributing factors the tension induced by viscous drag is known to have a stabilizing effect. Conversely, the effects of compression remain unexplored to date. As a first step towards filling this knowledge gap, here we study the effect of axial compression induced at the lateral edges of a membrane on its stability. A rectangular rubber sheet is mounted in a fixture that clamps the leading edge and allows for adjustable compression along the lateral edges. The fixture is placed in a water tunnel and the sheet's motion is studied under quasi-static variations of axial flow speed, for a range of compression ratios. The experiment is repeated with multiple sheets of different thicknesses. Even in the absence of flow, axial compression induces waves in the sheet whose spatial frequency depends on thickness. Tendentially, axial compression drastically reduces the flow speed beyond which a traveling wave instability is observed in the sheet. To the author's knowledge, this is the first study on the dynamic instability of a membrane under compression.