Asymptotic analysis of passive nonlinear suppression of aeroelastic instabilities of a rigid wing in subsonic flow

We study theoretically passive suppression of aeroelastic instabilities of a rigid wing in subsonic flow with an essentially nonlinear attachment. The analysis is performed by constructing a reduced-order model, applying complexification/averaging and slow-fast partition of the dynamics. The resulting slow-flow dynamics is then analyzed by singular perturbation. We fully recover computational and experimental results for this system reported in previous works and prove the existence of trivial/nontrivial stable attractors as well as relaxation oscillations in the slow-flow dynamics. These, in turn, correspond to complete/partial instability suppression, and (periodic or quasi-periodic) strongly modulated responses in the full-order dynamics. Moreover, we demonstrate the existence of Shilnikov bifurcations in the dynamics. The analysis of the slow-flow dynamics is confirmed by numerical simulations of the full-order system. The methodology developed in this work can be used in a predictive capacity when applying lightweight essentially nonlinear attachments to passive aeroelastic instability suppression of in-flow wings.