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

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.