Mathematical Theory of Aeroelasticity

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Purpose and Intellectual MeritThe objective of this research is the systematic development of a mathematical theory forAeroelasticity drawing on Abstract Functional Analysis -- in particular nonlinear Aeroelasticity-- centered on the canonical problem of flutter: the instability endemic to aircraft at high enoughair speed in the subsonic range, M 1. In particular this would mean the development ofmathematical models for aeroelastic phenomena of interest on their own and also exploreanalytically the design of feedback controllers -- including self-straining actuators, "intelligentcontrollers" for Flutter Boundary Expansion.Broader ImpactWe should point out that while aircraft wings (including UAV's) are the primary domain of thetheory, there is a new emerging area of application: Alternate Sources of Energy such as WindTurbines -- 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 aswith UAV's.Specific Tasks: First YearAnalytical study of the effect of nonzero angle of attack and nonzero camber on flutter speed as afunction of Mach number, especially in the transonic range -- a currently unsettled problem. Thiswould 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 rootlocus problem for the corresponding convolution-evolution equation, including the performanceof self-straining actuator models -- still using the Goland cantilever beam model for the wing.Specific Tasks: Second YearExtend the theory to where the structure is a uniform thin plate rather than a beam so that we canconsider controls on the leading and/or trailing edge of the wing. We could then investigate self-strainingactuators -- piezo-strips chordwise as well as spanwise, eliminating ailerons. For ahigh-aspect-ratio wing we could still work with typical-section aerodynamics -- so that thenonlinear aerodynamic theory we have developed can be used without additional effort.Specific Tasks: Third YearExtend the aeroelastic theory to finite wings finally eliminating the high-aspect-ratio constraint.