On grazing bifurcations in an aeroelastic system with multi-segmented nonlinearity in the pitch degree of freedom

Abstract

A nonlinear characterization based on modern methods of nonlinear dynamics is performed to identify the effects of a multisegmented nonlinearity on the response of an 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 in the pitch degree of freedom. The multisegmented nonlinearity is associated with the pitch degree of freedom and contains two different boundaries. The results show that the presence of this multi-segmented nonlinearity results in the presence of a subcritical instability. It is also shown that there are four main transitions or sudden jumps in the system's response when increasing the freestream velocity. It is demonstrated that the first and second sudden jumps are accompanied by the appearance and disappearance of quadratic nonlinearity induced by discontinuity and static positions. The results show that the first transition is due to a near grazing bifurcation that occurs near the first boundary of the multi-segmented nonlinearity. As for the second transition, it is demonstrated that the sudden jump at this transition is associated with a tangential contact between the trajectory and the first boundary of the multisegmented nonlinearity and with a zero-pitch velocity incidence which is a characteristic of a grazing bifurcation. In the third and fourth transitions, it is demonstrated that there are changes in the response of the system from simply periodic to two periods having the main oscillating frequency and its superharmonic of order 3 and from chaotic to two periods having the main oscillating frequency and its superharmonic of order 3. Using modern methods of nonlinear dynamics, it is shown that this transition is due to a grazing bifurcation at the second boundary of the multisegmented nonlinearity.