Abstract: Based on Theodorsen’s theory and Wagner’s function , the expressions of unsteady aerodynamic forces forarbitrary motions of a two-dimensional airfoil with three degrees of freedom are presented. It is assumed that the airfoil is subjected to an incompressible flow. The non-dimensional piecewise linear equations of motion for the two-dimensional airfoil with control surface freeplay nonlinearity are established. The phase trajectories , non-dimensionalamplitudes and frequencies of limit cycle oscillation are predicted through numerical simulation. Simulation resultsdemonstrate that the freeplay nonlinearity in the control surface hinge moment can result in limit cycle oscillations ofthe whole system. With the increase of air speed , the jump phenomenon appears in the amplitudes and frequenciesof limit cycle oscillations.

Key words: aeroelasticity, two-dimensional airfoil with 3-DOF, unsteady aerodynamic forces, freeplay nonlinearity, limit cycle oscillations