Characterization of grazing bifurcation in airfoils with control surface freeplay nonlinearity

A variety of nonlinear features is obtained from aeroelastic systems with discontinuous nonlinearity motivates investigations that may support future applications in controls design, flutter prediction problems, and energy harvesting exploration. The freeplay nonlinearity leads to bifurcations and abrupt response changes which can result in undesirable or catastrophic responses. Grazing bifurcations of limit cycles are one of the most commonly found discontinuity-induced bifurcations (DIBs) and are caused by a limit cycle that becomes tangent to the discontinuity boundary of the available piecewise-smooth function. The abrupt transition from periodic to aperiodic is directly related with the discontinuous nature of freeplay nonlinearity. In fact, recent studies in different areas discussed the presence of grazing bifurcations and the associated behavior changes. These abrupt transitions caused by grazing bifurcations are different from the well-known routes to chaos. In this work, a nonlinear analysis based on modern methods of nonlinear dynamics, such as power spectra and phase portraits is performed to characterize the sudden transitions in a three-degree of freedom aeroelastic system with freeplay nonlinearity in the flap degree of freedom. The results show that the main transition is due to a grazing bifurcation.