A Nonlinear Analysis of an Aeroelastic Three Degrees of Freedom Model

Abstract

The aeroelastic typical section, also known as the three degrees of freedom (3DoF) aeroelastic model, is a common way to start studying aeroelastic systems, especially when there are nonlinearities that can be isolated. There is a lack of research using cubic springs controlling aileron deflection and considering Peters’ unsteady loading acting on the model simultaneously. The model presented here have two linear springs (one commanding the vertical displacement and the other commanding the pitch angle) and one nonlinear cubic spring for aileron deflection. Peters’ unsteady model is used to define the lift and aerodynamic moment, forces used in the flutter analysis. In addition, this model is validated for very flexible surfaces, such as helicopter blades. With the numerical simulated time series, the 0–1 test is performed, as well as the Takens reconstruction and the determination of the Lyapunov exponent. The 0–1 test result is compared to the Lyapunov exponent, as part of their validation for aeroelastic systems subjected to structural nonlinearities. With this validation, in future work, these methodologies shall be applied in a more complex aeroelastic system, which will be a flat plate clamped at the root.