Match-Point Solutions for Robust Flutter Analysis

Abstract

The computation of robust utter speeds presents a signi cant advancement over traditional types of utter analysis. In particular, ¹-method analysis is able to generate robust utter speeds that represent worst-case ight conditions with respect to potential modeling errors. Robust utter speeds may be computed using a model formulation that has been previously presented; however, that formulation has limitations in its ability to generate a match-point solution. A model formulation is introduced for which ¹-method analysis is guaranteed to compute a match-point solution. The match-point solution is immediately realized by analyzing a single model so the computation time is reduced from the previous approach that required iterations. Also, the solution is able to consider parametric uncertainty in any element, whereas the previous formulation did not consider mass uncertainty. The match-point formulation is derived by properly treating the nonlinear perturbations and uncertainties that affect the equation of motion. The Aerostructures Test Wing is used to demonstrate that the ¹-method analysis computes match-point utter speeds using this new formulation. Nomenclature A = aerodynamic force matrix a = scaled force vector C = damping matrix K = stiffness matrix L = aerodynamic force model M = mass matrix n = number of modes P = plant model p = coef cient in density approximation Q = aerodynamic force matrix Q N = force model q = unscaled force vector N q = dynamic pressure S = structural dynamic model V = velocity W = weighting matrix w = input from uncertainty z = output to uncertaintȳ = lag pole 1 = uncertainty matrix ± = uncertainty parameter

A method for flexible aircraft LFT modelling

“…1) modelling of aeroelastic (i.e. flexible) models was investigated in [1], [2] and [3] for flutter analysis. These methods are based upon the knowledge of the parametric structure of the aeroelastic equation of motion (1) to build the corresponding LFT with respect to flight parameters (e.g.…”

Comparison of Aeroelastic Modeling and Robust Flutter Analysis of a Typical Section**This work has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 636307, project FLEXOP

“…Considering now errors in the aerodynamic model, generally uncertainties in the values of the lag roots are contemplated (Lind (2002)). Although these terms have the same physical meaning for Roger and MS methods, the way they enter the equations is different, as previously seen.…”

Validation of a Robust Flutter Prediction by Optimization

“…In particular, it obtains a more conservative result compared to the nominal flutter boundary. Thus, the use of the mu method has been suggested as a predictor for robust aeroelastic systems [1,2]. Since then, many robust analysis results have been reported.…”

“…Recently, a new approach to aeroelastic analysis based on robust control theory and the mu method was used to determine the robust aeroelastic stability boundary [1,2]. The mu method is reported to be effective for the prediction of the stability boundary of an uncertain system.…”

“…Since then, many robust analysis results have been reported. A robust flutter boundary with varying dynamic pressures was investigated by Lind [1], who found out that the results of the robust flutter margin were about 4% more conservative than the nominal flutter boundary. A frequency domain analysis was performed by Borglund [3,4], who presented the mu value and reduced frequency results.…”