Formulation of a complete structural uncertainty model for robust flutter prediction

Flutter is a dynamic instability that aerodynamic vehicles encounter in atmospheric flight. The interaction between structural elastic, structural inertial and aerodynamic forces may cause the flexible vehicle to undergo divergent oscillations, at which point flutter is encountered. Undesirable effects of this behavior include difficult controllability, structural fatigue and even catastrophic structural failure. This point of instability is dependant on many factors including the structural properties, structural geometry, aerodynamic shape and the flight condition. Since these factors may influence the flutter point in a sensitive manner investigation of uncertainty in these properties is warranted. A modern method to investigate system uncertainty is with the use of robust stability, namely [mu] analysis. These modern technologies are used to analyze the uncertainty in structural properties (mass and stiffness properties) of a wing in flight and the effect these uncertainties have on the flutter point. Recent use of these robust stability techniques on the flutter problem have focused on uncertainty in the natural structural modal frequencies. The uncertainties in the modal frequencies are also typically assumed independent. Uncertainties in the natural structural mode shapes have not been explored in complete detail. By including uncertainty in the structural mode shapes the robust flutter margins will be much less conservative. A complete structural uncertainty model for robust flutter prediction is constructed. Robust flutter margins are found for a fictitious wing with uncertainties in wing mass and stiffness properties, using the structured singular value ([mu]). Since the robust flutter margins include uncertainty in the structural mode shapes, as well as the structural mode frequencies, they are least conservative estimates. The uncertainties in many structural properties on the wing are investigated and the effect that they have on the flutter point is determined. The formulation presented herein can be applied to a wide array of problems concerning the sensitivity of the flutter solution