Limit Cycle Oscillation and Orbital Stability in Aeroelastic Systems with Torsional Nonlinearity

The paper treats the question of the existence of limit cycle oscillations of prototypical aeroelastic wing sections with structural nonlinearity using the describing function method. The chosen dynamic model describes the nonlinear plunge and pitch motion of a wing. The model includes an asymmetric structural nonlinearity in the pitch degree-of-freedom. The dual-input describing functions of the nonlinearity are derived for the limit cycle analysis. Analytical expressions for the average value, and the amplitude and frequency of oscillation of pitch and plunge responses are obtained. Based on an analytical approach as well as the Nyquist criterion, stability of the limit cycles is examined. Numerical results are presented for a set of values of the flow velocities and the locations of the elastic axis which show that the predicted limit cycle oscillation amplitude and frequency as well as the mean value are quite close to the actual values. Furthermore, for the chosen model with linear aerodynamics, it is seen that the amplitude of the pitch limit cycle oscillation does not always increase with the flow velocity for certain elastic axis locations