Nonlinear Infinite Dimensional Model for a Two Degree-of-Freedom Flexible Wing

Aninfinite-dimensional nonlinear model for a two-degree-of-freedom highly flexible wing is presented in this paper. The model describes the coupled dynamics of bending and torsion in terms of a set of nonlinear partial differential equations. When torsion is ignored, the resulting transverse bending equations are identical to those for the well-known elastica. The in vacuo response and the flutter onset characteristics of the model are compared with standard aeroelastic models using numerical simulation. The nonlinear model presented here could potentially serve as a benchmark for PDE-based control design methods, providing an intermediate step between low-fidelity linear models and nonlinear simulation models whose high fidelity is usually accompanied by large computational times.