Aeroelastic flutter analysis considering modeling uncertainties

A method for efficient flutter analysis of aeroelastic systems including modeling uncertainties is presented. The aerodynamic model is approximated by a piece-wise continuous rational polynomial function, allowing the flutter equation to be formulated as a set of piece-wise linear eigenproblems. Feasible sets for eigenvalue variations caused by combinations of modeling uncertainties are computed with an approach based on eigenvalue differentials and Minkowski sums. The method allows a general linear formulation for the nominal system model as well as for the uncertainty description and is thus straightforwardly applicable to linearized aeroelastic models including both structural and aerodynamic uncertainties. It has favorable computational properties and, for a wide range of uncertainty descriptions, feasible sets can be computed in output polynomial time. The method is applied to analyze the flutter characteristics of a delta wing model. It is found that both structural and aerodynamic uncertainties can have a considerable effect on the damping trends of the flutter modes and thus need to be accounted for in order to obtain reliable predictions of the flutter characteristics. This indicates that it can be beneficial to allow a flexible and detailed formulation for both aerodynamic and structural uncertainties, as is possible with the present system formulation.