Phenomena and characterization of grazing-sliding bifurcations in aeroelastic systems with discontinuous impact effects

Abstract

Impacts are present in real aircraft movable surfaces, such as ailerons, flaps, rudder, elevators, trim tabs among other secondary control surfaces leading to complex, dangerous, and abrupt transitions. In this research study, we investigate the effects of discontinuous nonlinear stiffness simulating regions of freeplay, linear stiffness, and stoppers in the pitch degree of freedom on the response of a two-degree of freedom aeroelastic system. This system consists of a plunging and pitching rigid airfoil supported by a linear spring in the plunge degree of freedom and a nonlinear spring which includes the simulated stoppers at high angles in the pitch degree of freedom. The unsteady representation based on the Duhamel formulation is used to model the aerodynamic lift and moment. To characterize the system's response when subjected to impacts, we use modern methods of nonlinear dynamics including phase portraits, power spectra, and Poincaré sections. The results show that five main complex transitions are observed as the freestream velocity is increased. It is demonstrated that the observed transitions can be associated with grazing and/or grazing-sliding bifurcations.