Mathematical Theory of Aeroelasticity

气动弹性数学理论

• 批准号: 0400730
• 负责人: A Balakrishnan
• 金额: $ 19.39万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-09-01 至 2008-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0400730&HistoricalAwards=false
• 关键词: Mathematical; Theory; Aeroelasticity

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.

本研究的目的是在抽象泛函分析的基础上系统地发展气动弹性的数学理论，特别是非线性气动弹性，其中心是典型的颤振问题：飞机在亚音速范围内足够高的速度时特有的不稳定性。特别是，这将意味着发展自己感兴趣的气动弹性现象的数学模型，并分析地探索反馈控制器的设计——包括自应变致动器，颤振边界扩展的“智能控制器”。更广泛的影响我们应该指出，虽然飞机机翼（包括无人机）是该理论的主要领域，但有一个新兴的应用领域：替代能源，如风力涡轮机，其中叶片的气动弹性稳定是一个越来越重要的问题。更长的叶片显然效率更高，但减轻重量意味着更高的灵活性，就像无人机一样。分析研究非零攻角和非零弧度对颤振速度随马赫数变化的影响，特别是在跨声速范围内，这是一个目前尚未解决的问题。这将特别意味着研究非线性气动弹性方程的线性化版本，导致波西奥积分方程的推广。反过来，我们将需要研究相应的卷积进化方程的根轨迹问题，包括自应变致动器模型的性能-仍然使用戈兰悬臂梁模型的机翼。具体任务：第二年将理论扩展到结构是均匀薄板而不是梁的地方，这样我们就可以考虑对机翼前缘和/或后缘的控制。然后，我们可以研究自应变致动器——压电条弦向和展向，消除副翼。对于高展弦比的机翼，我们仍然可以使用典型截面空气动力学，这样我们开发的非线性空气动力学理论就可以在没有额外努力的情况下使用。具体任务：第三年将气动弹性理论扩展到有限翼，最终消除高展弦比约束。