Fuzzy uncertainty analysis in the flutter boundary of an aircraft wing subjected to a thrust force

In this study, flutter uncertainty analysis of an aircraft wing subjected to a thrust force is investigated using fuzzy method. The linear wing model contains bending and torsional flexibility and the engine is considered as a rigid external mass with thrust force. Peters' unsteady thin airfoil theory is used to model the aerodynamic loading. The aeroelastic governing equations are derived based on Hamilton's principle and converted to a set of ordinary differential equations using Galerkin method. In the flutter analysis, it is assumed that the wing static deflections do not have influence on the results. The wing bending and torsional rigidity, aerodynamic lift curve slope and air density are considered as uncertain parameters and modelled as triangle and trapezium membership functions. The eigenvalue problem with fuzzy input parameters is solved using fuzzy Taylor expansion method and a sensitivity analysis is performed. Also, the upper and lower bounds of flutter region at different alpha-cuts are extracted. Results show that this method is a low-cost method with reasonable accuracy to estimate the flutter speed and frequency in the presence of uncertainties.