Mathematical Models of Fluttering Plates: Supersonic Flows

The flutter phenomenon is the principal concern in the field of aeroelasticity. In this paper we address the fundamental questions of well-posedness and long-time behavior of the primary mathematical model for a fluttering plate in a panel configuration. Such a system is known as a nonlinear flow-plate interaction. The flow is described by a perturbed wave equation. The plate is modeled by Kirchoff’s plate equation; we consider various configurations for the plate and focus on the primary physical configuration from large deflection theory utilizing the von Karman nonlinearity. Strong coupling between the two dynamics occurs in the acceleration potential for the plate and the down-wash for the flow (Neumann type flow condition). We provide a discussion of the most recent mathematical results pertaining to these issues in the principal case of interest (both mathematically and in application): supersonic flow velocities. Specifically, we provide a discussion and interpretation of results on semigroup well-posedness and existence of global attractors for flow-plate models, as well as a discussion of future directions for mathematical analysis for this broad class of models. Key Terms: aeroelasticity, flutter, fluidstructure interaction, nonlinear PDE, control theory, long-time behavior, dynamical sys-