Mathematical Theory of Aeroelasticity

ECCS-0722750 Balakrishnan 飞机特有的一种不稳定性，可能导致灾难性的破坏，是“机翼颤振”，它设定了一个限制，可达到的速度在任何高度被称为颤振边界。FAA规定了15%的Flutter安全裕度。我们的主要目标是研究颤振边界扩展的控制设计的数学模型的基础上没有迄今为止，因为所需的数学水平。智力优势：颤振边界对高度的精确依赖性自然引起人们极大的兴趣。虽然颤振速度一般随高度而减小，但最近在计算中发现，如果"迎角"（由飞机速度（矢量）与机翼形成的角度）被考虑并且实际上可以在足够高的高度开始增加，被称为"跨音速下降"，例如在空中客车380的设计中就利用了这一点。我们正在发展的分析理论能够预测这种现象。这样的理论对于研究一种新的控制概念是必不可少的，这种控制概念是当前感兴趣的：变形--动态地改变机翼的形状。在正常高度，空气摩擦（粘性）小到可以忽略，因此空气动力学流动模型要简单得多。但粘度的影响是很少了解和我们的目标之一是扩展理论，包括粘度和探索独特的现象。更广泛的影响：虽然颤振现象早在20世纪30年代（特技飞行员）观察到，许多基本的问题仍然没有答案。在数值计算方案方面已经取得了显着的进展，但是这些方案需要对特定参数进行近似，对现象的了解很少，而且最重要的是不适合于控制设计。PI计划教育学生，并将研究成果转移到航空航天公司，用于设计高性能飞机。

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.