Stabilization of a nonlinear flow-plate interaction via component-wise decomposition

Abstract

Asymptotic-in-time interior feedback control of a panel interacting with an inviscid, subsonic flow is considered. The classical model [8] is given by a clamped nonlinear plate strongly coupled to a convected wave equation on the half space. In the absence of energy dissipation the plate dynamics converge to a compact and finite dimensional set [6, 7]. With a sufficiently large velocity feedback control on the structure we show that the full flow-plate system exhibits strong convergence to the set of stationary states in the natural energy topology. We show a decomposition of the dynamics into “smooth” component and global-in-timeHadamard continuous component, thus permitting approximation by smooth data. That the flows are subsonic is critical for our approach. Our result implies that flutter (a periodic or chaotic end behavior) is not present in subsonic flows with sufficient viscous damping in the structure.