On the instability and the post-critical behaviour of two-dimensional cantilevered flexible plates in axial flow

This paper deals with the dynamics of a cantilevered plate subject to axial flow on both surfaces, directed from the clamped to the free end. The system loses stability by flutter, a well known fact, but the mechanism of which is insufficiently well understood. In this paper, a relatively simple numerical model is constructed for examining the instability and the post-critical behaviour of this fluid–structure system: a nonlinear equation of motion of the plate is developed using the inextensibility condition; also, an unsteady lumped vortex model is used to calculate the pressure difference across the plate. The analysis of the system dynamics is carried out in the time-domain. Both the instability and the post-critical behaviour of the system are studied. Various factors that may influence the system dynamics such as material damping, the length of the rigid upstream segment and the viscous drag are discussed in detail. A model of the wake evolution is proposed to explain the hysteresis phenomenon observed in experiments. The flutter boundary and the vibration modes predicted by the current theory are found to be in good agreement with published experimental data.