Frequency and amplitude prediction of limit cycle oscillations of an airfoil containing concentrated structural nonlinearities

The objective of the present work is to predict frequency and amplitude of limit cycle oscillations (LCO) of an airfoil containing concentrated structural nonlinearities which are represented by polynomial, freeplay and hysteresis springs. Mathematical analyses based on the centre manifold theory, the principle of normal form and the point transformation method are presented. These techniques are different from a numerical time-marching approach, not only do they not require any time-step, but they can be applied to accurately predict frequency and amplitude of LCO as well as other complex dynamical response phenomena including period doubling, coexistence of stable LCOs and chaotic motions. Moreover, the present approaches lead to a better understanding of the nonlinear behavior of the aeroelastic equations. The analytical predictions are verified by the numerical simulations using a time-integration method.