The coupled dynamics of two cantilevered flexible plates in axial flow

This paper studies the coupled dynamics of two cantilevered flexible plates aligned parallel to each other in axial flow. The nonlinear governing equation of the two-dimensional plate is developed using the inextensibility condition; and an unsteady lumped vortex model, taking into account the interactions between the two plates, is used to calculate the pressure difference across each plate. The analysis of the system dynamics is carried out in the time-domain; both the instability and the post-critical behaviour are investigated. It is found that the system loses stability through flutter when the flow velocity is sufficiently high, and the flutter threshold is a function of the separation between the two plates. It is also found that the two plates may oscillate both in the out-of-phase and in-phase modes; the former always has a lower critical point than the latter. Moreover, flutter of the two-plate system in the in-phase mode is proved to be associated with an unstable branch of the solution, which can be obtained through numerical simulations with the aid of so-called virtual spring connections.