Mathematical Analysis of Aircraft Wing Models and Application to Flutter Control

这一建议的主要目标是发展三个越来越完整的飞机机翼模型在周围气流中的频谱、渐近和稳定性分析，这些模型由复杂的进化型积分-微分方程组控制。前两个模型(分别为1维和2维)是由加州大学洛杉矶分校的飞行系统研究中心与NASA Dryden飞行研究中心合作开发的。三维模型的设计正在进行中。一维模型最近在爱德华兹空军基地进行了一系列四次飞行试验。计算结果与理论计算结果吻合较好，至少在较低频率的气动弹性振型上是如此。整个机翼建模项目的最终目的是为从事机翼颤振抑制工作的飞机工业工程师提供具体的实用建议。这个项目的目标包括完成一维模型的分析，即获得连续谱特征函数的渐近性，并推导出主要方程解的时空表示；b)将结果应用于颤振抑制问题；c)将分析扩展到二维和即将到来的三维模型(该项目最具挑战性的部分)；d)为数学和工程专业的学生开发一个新的飞机工程数学方法研究生课程。

The primary goal of this proposal is to develop the spectral, asymptotic, and stability analysis for three increasingly more complete models of an aircraft wing in a surrounding airflow, which are governed by complicated systems of evolution-type integro -differential equations. The first two of these models (1-dim and 2-dim respectively) have been developed at the Flight Systems Research Center at UCLA in collaboration with NASA Dryden Flight Research Center. The designing of the 3-dim model is in progress. The 1-dim model has recently been tested in a series of four flight experiments at Edwards Airforce Base. The results have shown an excellent agreement with theoretical predictions of the model, at least, for lower frequency aeroelastic modes. The ultimate goal of the entire wing modeling projects is to give specific practical recommendations to aircraft industry engineers working on flutter suppression in aircraft wings. The objective of this project include completion of the analysis of 1-dim model, i.e., obtaining the asymptotics for the eigenfunctions of the continuous spectrum and deriving the space-time domain representation for the solution of the main equations; b) applying the results to the flutter suppression problem; c) extension of the analysis to 2-dim and forthcoming 3-dim models (the most challenging part of the project); d) developing of a new graduate program on mathematical methods in aircraft engineering for both mathematics and engineering students