Purpose and Intellectual Merit The objective of this research is the systematic development of a mathematical theory for Aeroelasticity drawing on Abstract Functional Analysis -- in particular nonlinear Aeroelasticity -- centered on the canonical problem of flutter: the instability endemic to aircraft at high enough air speed in the subsonic range, M < 1. In particular this would mean the development of mathematical models for aeroelastic phenomena of interest on their own and also explore analytically the design of feedback controllers -- including self-straining actuators, "intelligent controllers" for Flutter Boundary Expansion. Broader Impact We should point out that while aircraft wings (including UAV's) are the primary domain of the theory, there is a new emerging area of application: Alternate Sources of Energy such as Wind Turbines -- where the aeroelastic stabilization of the blades is an increasingly important issue. Longer blades are apparently more efficient but reducing weight implies higher flexibility, just as with UAV's. Specific Tasks: First Year Analytical study of the effect of nonzero angle of attack and nonzero camber on flutter speed as a function of Mach number, especially in the transonic range -- a currently unsettled problem. This would mean in particular studying the linearized version of the nonlinear aeroelastic equation, leading to generalization of the Possio Integral Equation. In turn we will need to study the root locus problem for the corresponding convolution-evolution equation, including the performance of self-straining actuator models -- still using the Goland cantilever beam model for the wing. Specific Tasks: Second Year Extend the theory to where the structure is a uniform thin plate rather than a beam so that we can consider controls on the leading and/or trailing edge of the wing. We could then investigate self-straining actuators -- piezo-strips chordwise as well as spanwise, eliminating ailerons. For a high-aspect-ratio wing we could still work with typical-section aerodynamics -- so that the nonlinear aerodynamic theory we have developed can be used without additional effort. Specific Tasks: Third Year Extend the aeroelastic theory to finite wings finally eliminating the high-aspect-ratio constraint.
