频域颤振μ分析的连续性及复摄动方法研究

On the continuity of frequency domain μ analysis and complex perturbation method for flutter solution

经典的线性颤振分析方法需要求解颤振特征值问题,并需要对特征值进行跟踪排序,以消除在确定颤振临界点时可能出现的颤振模态分支的"窜支"问题,从而影响了颤振分析的效率及自动化程度。为避免此类问题,根据现代鲁棒控制理论,提出了一种直接利用频域气动力的μ-ω方法;在气动弹性方程中,引入速压摄动,建立μ分析框架,从而可采用频域μ分析进行颤振临界点预测,无需求解颤振特征值问题。注意到速压摄动量必须为实参数的要求,使得结构奇异值μ可能存在不连续性;针对此问题,对一个二元机翼气动弹性系统,采用定常气动力模型,进行解析分析的结果表明,仅允许实数摄动时,μ不连续性的确存在;但若允许复数摄动,则可以解决该问题;且计算结果表明,提出的复摄动μ-ω方法是一种具有很好精度的频域颤振分析方法。

Classical linear flutter analysis is based on the solution of flutter eigenvalue problem,and needs to track the root loci to determine the correct flutter boundary but sometimes it may fail.To solve this problem,a new flutter solution called μ-ω method was presented by utilizing modern robust control theory.Based on the frequency-domain μ analysis,the method was established by applying dynamic pressure perturbation to the flutter equation with frequency domain unsteady aerodynamics.It is found that the continuity of the real μ analysis is crucial to the method,so a two dimensional wing model with steady aerodynamics was adopted to explore the continuity of real μ analysis.It is proven that the μ value obtained by real μ analysis is not a continuous function of frequency,but if complex perturbation is introduced,the complex μ analysis does guarantee the continuity of μ analysis.According to this conclusion,the algorithm of the μ-ω method was extended by use of complex μ analysis.Numerical results demonstrate that the complex perturbation μ-ω method is a useful frequency domain flutter solution with good convergence and accuracy.