Predicting tipping phenomenon in a conceptual airfoil structure under extreme flight environment

This paper investigates the tipping phenomenon in a conceptual airfoil system subjected to both periodic excitation and extreme random loads modeled by non-Gaussian Lévy noise. Firstly, the effects of main parameters of Lévy noise on the tipping phenomenon are uncovered. It is found that an increased noise intensity or a reduced stability index can induce the tipping phenomenon to take place before the bifurcation point of the corresponding deterministic system. Moreover, large rises and jumps in Lévy noise can more easily lead to catastrophic high-amplitude oscillations than the ideal Gaussian white noise. Then, the residence probability of the airfoil system remaining in high-amplitude oscillations is given to further quantify the likelihood of the tipping phenomenon induced by Lévy noise. To realize the prediction of these catastrophic high-amplitude oscillations, a concept of the high-risk region is defined based on the residence probability. Finally, the ranges of the related parameters, where Lévy noise-induced tipping phenomenon may occur, are approximately quantified. These findings may provide theoretical guidance for engineers in preventing catastrophic tipping phenomena in airfoil structures, thereby enhancing the safety of aircraft operations in extreme environments.