Insights on Aeroelastic Bifurcation Phenomena in Airfoils with Structural Nonlinearities

Abstract

This paper presents a study on aeroelastic response of airfoils with concentrated struc- tural nonlinearities. The analysis and identification of nonlinear phenomena leading to Hopf bifurcations, supercritical and subcritical responses, and harmonics interactions were performed numerically and experimentally for a typical aeroelastic section admitting hard- ening nonlinearities in pitching and free-play nonlinearities in the control surface hinge. Two experimental set-ups were considered, being the first one focussing on investigations with control surface free-play problems. A second apparatus was prepared to include a range of hardening nonlinearities in pitching. Both models have allowed inspecting on the combined effects of hardening and free-play nonlinearities in the Hopf bifurcations. The numerical model is based on potential unsteady aerodynamics and state space representa- tion of the resulting aeroelastic equations of motion. Model validation was performed and revealed to be adequate to predict complex bifurcations with respect to airspeed, as well as to infer on how flutter conditions are influenced by the nonlinearities. Other impor- tant phenomena such as the grazing bifurcation could also be investigated for the free-play cases. Moreover, subcritical bifurcations were also a common phenomena observed here, but studies have shown that a proper change in the systems parameters can lead to super- critical form of bifurcation. In order to identify internal couplings resulting in quadratic- or cubic-like nonlinearities, the higher-order spectral analysis was also performed for the respective models revealing the presence of both kinds of effects. The study aims to provide ways towards the mitigation of undesired nonlinear aeroelastic responses.