A non-linear theory of torsional divergence

In recent years, research on aerofoil morphing is increasingly focusing on innovative ideas such as the use of compliant systems and the exploitation of aeroelastic servo-effects. If brought to their limit, these concepts would allow operating aerofoils in aeroelastically marginally stable or even unstable conditions. In this view, a non-linear approach to aeroelastic torsional divergence becomes relevant. This article presents an extension of the well-known linear theory of divergence, which takes into account non-linear effects of structural as well as aerodynamic nature. The non-linear theory is applied to the case of a thin aerofoil and the pre-critical as well as post-critical response is computed for selected values of the flow parameters. Instability curves are also included, which show the aerofoil's torsional deformation as a function of the dynamic pressure, for selected values of an imposed disturbance.