Mathematical Analysis of Aircraft Wing Models and Application to Flutter Control

本建议的主要目标是发展的频谱，渐近和稳定性分析的三个越来越完整的模型的飞机机翼在周围的气流，这是由复杂的系统的演变型积分微分方程。前两个模型（分别为1-dim和2-dim）是由加州大学洛杉矶分校的飞行系统研究中心与美国宇航局德莱登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的四次飞行实验。 结果表明，与理论预测的模型，至少在较低频率的气动弹性模式的一个很好的协议。 整个机翼建模项目的最终目标是为从事飞机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。 本项目的目标包括完成一维模型的分析，即，获得连续谱的特征函数的渐近性并导出主要方程的解的时空域表示; 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（项目中最具挑战性的部分）; d）为数学和工程专业的学生开发一个关于飞机工程数学方法的新研究生课程

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