Mathematical Theory of Aeroelasticity

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ECCS-0722750Balakrishnan An instability endemic to aircraft, resulting in possible catastrophic destruction, is 'Wing Flutter', which sets a limit to attainable speed at any altitude known as the Flutter Boundary. The FAA mandates a 15% Flutter safety margin. Our primary objective is to study control design for Flutter Boundary Expansion based on mathematical models not available hitherto because of the level of mathematics required. Intellectual Merit: The precise dependence of the Flutter Boundary on the altitude is naturally of great interest While the flutter speed generally decreases with altitude, it was recently discovered in computation that this need not be the case if the 'angle of attack' (the angle made by the aircraft velocity (vector) with the wing) is taken into account and can in fact start to increase at a high enough altitude, known as the 'Transonic Dip' which is taken advantage for instance in the design of the Air Bus 380. The analytical theory we are developing is able to predict this phenomenon. Such a theory is essential for studying a novel control concept of current interest: Morphing -- changing the shape of the wing dynamically.At normal altitudes the air-friction (viscosity) is small enough to be neglected, so that the aerodynamic flow model is much simpler. But the effect of viscosity is little understood and one of our objectives is to extend the theory to include viscosity and explore phenomena unique to it.Broader Impact:Although flutter phenomena were observed as early as the 1930's (by stunt pilots), many basic questions still remain unanswered. Remarkable progress has been made in numerical computational schemes, but these require approximations for specific parameters, provide little insight into phenomena, and above all are inadequate for Control Design. The PI plans to educate students and transition the research results to aerospace companies for the design of high performance aircrafts.