Flutter analysis including structural uncertainties using a relaxed LMI-based approach

This paper proposes a new approach to investigate the flutter phenomenon considering structural frequencies as uncertain parameters. An affine parameter state space model is used to describe the aeroelastic system and linear matrix inequalities (LMI) are employed to solve the stability analysis with a relaxation on the inequalities. Uncertainties are present during the design phases of an aircraft as well as when considering an operational set of similar aircraft. In the first case, uncertain aeroelastic models have great potential to reduce computational costs during the design phases, and, in the second one, to provide robust aeroelastic predictions under uncertain operational quantities of a set of aircraft. In this work, uncertain aeroelastic predictions for a three-degrees-of-freedom typical section obtained from the relaxed approach are compared to predictions considering the quadratic Lyapunov approach. In the first case, the structural modal frequency of a single degree-of-freedom is considered uncertain. In the second one, all degrees-of-freedom are uncertain. In all cases, the numerical results show that the relaxed approach proposed in this work is less conservative than the quadratic Lyapunov approach, providing a useful tool for flutter analysis including structural uncertainties.