Dynamic Pressure Perturbation Method for Flutter Solution: the Mu-Omega Method

Applying perturbation to dynamic pressure in the nominal aeroleastic equation of motion, a Mu-Omega method is presented for flutter solution. Utilizing structured singular value mu as stability margin indicator, the method simply uses frequency domain aerodynamics to solve nominal flutter and divergence margin through frequency domain mu analysis. The error of flutter reduced frequency is selected as convergence criterion during airspeed iteration. Detailed algorithm is given and three numerical examples are solved for demonstration. It is shown that the Mu-Omega method has good convergence and high accuracy, and the flutter and divergence result from the Mu-Omega method correlate well with that of the p-k or KE method. Nomenclature M = generalized mass matrix B = generalized damping matrix K = generalized stiffness matrix η = generalized displacement vector k = reduced frequency b = semi chord µ = structured singular value s = Laplace variable V = airspeed Q = generalized aerodynamic influence coefficient matrix ρ = air density q ∞ = dynamic pressure q0 = nominal dynamic pressure δq = perturbation operator to q0 Wq = weight value for ∆