求解二元机翼颤振方程的切比雪夫展式方法

Solution of Two-Dimensional Airfoil Flutter Equations Using Chebyshev Expansion Method

经典二元机翼颤振方程的建立基于结构正弦运动假设以及各种气动力理论。提出结构正弦运动假设是对真实运动的一种近似处理方法,事实上,颤振发生时结构运动形式完全可能更为复杂,结构的正弦运动假设的提出仅仅出于应用过程中的简单和容易。基于这样的假设,传统的谐波平衡法未必合适。常见的谐波平衡法由于忽略超过预估的高频项,可能会引发较大的误差。本文提出一种建立二元机翼颤振方程的新途径:切比雪夫多项式展式法。该方法适用于定量问题的分析和研究,精度优于标准的谐波平衡法,而且该方法也适用于处理非线性问题,更方便于对系统做定性分析。最后,通过一个算例说明如何利用切比雪夫多项式展式方法建立二元翼段的颤振方程,并结合V-g法获得了翼型的颤振速度。

The classical two-dimensional airfoil flutter equations can be established by using sinusoidal structure motion hypothesis and some kinds of aerodynamic theory. In fact, when flutter occurs, structure movement is likely to be more complex. Sinusoidal structure hypothesis is proposed merely because it is simple and easy to use. For this case, harmonic balance method cannot ap-propriate for all the higher order terms are ignored, which might lead to larger error. This paper presents a new way to establish the flutter equations: Chebyshev expansion method. This method which is suitable for quantitative questions has higher accuracy than harmonic balance, moreover, it is applicable to the analysis of those qualitative of nonlinear problems as well. Finally, an example is used to illustrate how to establish the flutter equations of two-dimension airfoil by using Chebyshev expansion method and how to find the flutter solution based on V-g method.