Normal form representation of the aeroelastic response of the Goland wing

We follow two approaches to derive the normal form that represents the aeroelastic response of the Goland wing. Such a form constitutes an effective tool to model the main physical behaviors of aeroelastic systems and, as such, can be used for developing a phenomenological reduced-order model. In the first approach, an approximation of the wing's response near the Hopf bifurcation is constructed by directly applying the method of multiple scales to the two coupled partial-differential equations of motion. In the second approach, we apply the same method to a Galerkin discretized model that is based on the mode shapes of a cantilever beam. The perturbation results from both approaches are verified by comparison with results from numerical integration of the discretized equations.