Controlling flutter for nonlinear panels in subsonic flows via structural velocity feedback

Abstract

Mechanical control of flutter for a thin panel immersed in an inviscid flow is considered. The model arises in aeroelasticity and comprises the interaction between a clamped von Karman plate a surrounding potential flow of gas. Recent results show that the plate dynamics of the model converge to a global compact attracting set of finite dimension [6]. This result was obtained in the absence of mechanical damping of any type. Here, we incorporate a sufficiently large velocity feedback control applied to the structure to show that the full flow-plate system exhibits strong convergence to a stationary state (when flows are subsonic and a “good” energy identity is available). Our method is based on first showing the desired convergence properties when the plate dynamics exhibit additional regularity. We then show a dichotomy for the plate dynamics: they are either asymptotically regular or the plate velocities decay uniformly exponentially. In the case when no additional plate regularity is available, we utilize an approximation by smooth initial data; this requires propagation of initial regularity on the infinite time horizon. The final result complements results previous obtained (for this model and similar models), as we show that there is a strong convergence for the entire dynamics and that the limiting behavior of the flow-plate system is, in fact, stationary. Physically, this implies that flutter (a non-static end behavior) can be eliminated by a velocity feedback control in subsonic flows.