Control and Stabilization Problems for Aircraft Wing Models in Subsonic Air Flow

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The first main objective of this project is to carry out a detailed mathematical analysis of several control and stabilization problems for four increasingly more complete and complicated models of an aircraft wing in a surrounding air flow, and to apply the results to flutter control. The first of these models describes a long slender wing (which bends and twists) in an incompressible, subsonic, inviscid air flow. The second model is a generalization of the first one to the case of a compressible air flow. The remaining two models are the generalizations of the first two models to a wing with a movable flap (a trailing edge wing section whose angle with the main part of a wing is changing during take off and landing). The second objective of the project is to extend asymptotic and spectral analysis carried out by the investigator for the first of the above models to the other three models. The asymptotic and spectral results form the necessary basis for the solutions of all suggested control and stabilization problems. The broad goal of the entire project is to contribute to the theoretical foundations of aeroelasticity by analytical investigation of a new generation of physically realistic wing models and by analysis of the related control and stability problems.This theoretical research has practical applications to the design of mechanisms that would control and suppress flutter in aircraft wings. Flutter is the development of sudden violent vibrations of a wing, which occur in certain airspeed-altitude combinations. Flutter most commonly results in severe damage or total destruction of a wing, often leading to catastrophic failure. A significant amount of research is devoted to experimental and numerical analysis of flutter. However, theoretical analysis is essential for finding ways to design efficient methods of controlling flutter and this work develops the theoretical foundations for this problem.