Match-Point Solutions for Robust Flutter Analysis

The computation of robust utter speeds presents a signi cant advancement over traditional types of utter analysis. In particular, -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 for-mulation 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 -method analysis is guaranteed to compute a match-point solution. The match-point solution is immediately realized by analyzing a single model so the com-putation 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.TheAerostructures Test Wing is used to demonstrate that the-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 QN = force model q = unscaled force vector Nq = dynamic pressure S = structural dynamic model V = velocity W = weighting matrix w = input from uncertainty z = output to uncertainty ¯ = lag pole 1 = uncertaintymatrix ± = uncertainty paramete