Aeroelastic analysis of two-dimensional airfoil with control surface free play nonlinearity

Based on the Theodorsen's theory and the Wagner's function, the expressions of unsteady aerodynamic forces for arbitrary motions of a two-dimensional airfoil with three degrees of freedom, which is subjected to an incompressible flow, are presented. The non-dimensional piecewise linear equations of motion for the two-dimensional airfoil with control surface free play nonlinearity are established. The phase trajectories, non-dimensional amplitudes and frequencies of limit cycle oscillation are predicted through numerical simulation. Simulation results demonstrate that the free play nonlinearity in the control surface hinge moment can result in the limit cycle oscillation of the whole system. With the increase of air speed, the jump phenomenon appears in the amplitude and frequency of the limit cycle oscillation.