Analysis and Control of Nonlinear Flow-structure Interactions

We consider an aeroelastic model known as a nonlinear flow-structure interaction, which describes the oscillations of a thin, flexible plate immersed in a potential flow. This model is used to study the phenomenon known as flutter, which involves the coupling of the plate’s vibrational modes with the aerodynamic load. Here, we treat this problem from a partial differential equations point of view and state results on well-posedness and long-time behavior of the system. The flow is described by a wave equation perturbed by a term which is proportional to the flow velocity. The plate is modeled by Kirchoff’s equation; various boundary conditions and the physical (Berger and von Karman) nonlinearities are considered for the plate. Strong coupling between the two equations occurs in the acceleration potential (plate forcing term) and the down-wash (Neumann type boundary condition on the flow). The key parameters in this analysis correspond to the laminar flow velocity and the thickness of the plate. Key Terms: aeroelasticity, flutter, fluidstructure interaction, nonlinear PDE, PDE control, long-time behavior, dynamical sys-