Analysis of Effect of Freeplay on Flutter of an Airfoil in Incompressible Subsonic Flow

In this study the compatibility of nonlinear random vibration analysis is used and extended to the nonlinear aeroelastic systems to investigate the instability of these systems with using neither time domain analysis nor limit cycle oscillations. To this aim a 2-degree of freedom airfoil with freeplay nonlinearity under quasi steady flow is used. At first one random Gaussian white noise is added to the aerodynamic lift force then the statistical linearization and the random vibration analysis of the nonlinear systems are used to obtain a nonlinear map of variance of the response with flow velocity as the control parameter. This nonlinear map leads to a nonlinear algebraic equation which consists of two parameters as the flow velocity and variance of the response. Solving this nonlinear equation for various flow velocities، ultimate to calculate the flutter speed where maximum of variance of the response happens. Finally the jump phenomenon is investigated where tangent bifurcation point occurs.