A comparative study of nonlinear aeroelastic models for high aspect ratio wings

Abstract

Linear and nonlinear aeroelastic analyses and results for a cantilevered beam subjected to an unsteady subsonic airflow are presented as a model of a high aspect ratio wing. A third-order nonlinear beam model is used as the structural model. This model includes nonlinear inertial and damping terms as well as nonlinear stiffness terms. To model aerodynamic loads a Wagner model based on a state-space model along with 2D and 3D Peters’ aerodynamic models are used and the results are compared. The Galerkin method is used to transform partial differential equations to ordinary differential equations. For aeroelastic analysis of a high aspect ratio wing, using a state-space Wagner model reduces the number of degrees of freedom. The distribution of the lift and inflow derived using 2D and 3D Peters aerodynamic models are compared and the range of aspect ratios has been determined for which a 2D aerodynamic model is sufficient. There is a good agreement between the flutter speed obtained in this study and those reported in the literature. Beside nonlinear stiffness terms, the effects of nonlinear inertial and damping terms may be significant for flow velocities above the flutter speed. As the flow velocity increases further the oscillations lose their periodicity and become chaotic. Using the different number of structural modes, the convergence of the results is shown.