A Novel Grazing Bifurcation Inducing Quasi-Periodic Response Directly From Equilibrium in a Piecewise-Linear Aeroelastic System

Abstract

Abstract. Grazing bifurcation is commonly encountered in nonsmooth dynamical systems, which usually results in periodic response featured with grazing on the nonsmooth border. This study reports a novel grazing bifurcation arising in the piecewise-linear aeroelastic system of an airfoil with a control surface. Interestingly, quasi-periodic (QP) rather than periodic response appears immediately after the controlling parameter (the flow velocity) varies through the bifurcation point. The equilibrium point at the origin loses stability when the flow velocity reaches the linear critical threshold, forming a sequence of concentric phase trajectories with the maximum amplitude grazing the border. This sequence of concentric trajectories diverges as the flow velocity increases further, producing the QP response. To the best of our knowledge, this type of bifurcation has never been reported within the category featured by grazing behaviors. The time history, phase diagram, and frequency spectra are utilized to analyze some fundamental features of the grazing bifurcation and induced QP response, showing much difference compared to some routine bifurcations and responses. We believe this finding could enrich the grazing bifurcation research in nonsmooth dynamics by revealing a nonconventional transition mechanism from stability to quasi-periodicity, with implications for predicting nonlinear phenomena in piecewise aeroelastic systems.