Bifurcation analysis of aircraft with structural nonlinearity and freeplay using numerical continuation

In recent years the aeroelastic research community has carried out substantial work on the characterization and prediction of nonlinear aeroelastic phenomena. Of particular interest is the calculation of Limit Cycle Oscillations (LCO), which cannot be accomplished using traditional linear methods. In this paper, the prediction of the bifurcation and post-bifurcation behavior of nonlinear subsonic aircraft is carried out using Numerical Continuation. The analysis does not make use of continuation packages such as AUTO or MatCont. Two different continuation techniques are detailed, specifically adapted for realistic aeroelastic models. The approaches are demonstrated on model of a simple pitch plunge airfoil with cubic stiffness and an aeroelastic model of a transport aircraft with two different types of nonlinearity in the control surface. It is shown that one of the techniques yields highly accurate predictions for LCO amplitudes and periods while the second method trades off some accuracy for computational efficiency.