A new flutter speed analysis method using stochastic approach

In this study a new analytical method for analyzing flutter speed of aeroelastic systems is presented. In this method, apart from the aerodynamic lift and moment deduced from the aerodynamic theories, one Gaussian white noise force was also added to the lift force. Then the spectral density of response was calculated with respect to the frequency response of the system as well as the spectral density of the excitation. The variance of the response was determined with respect to the airspeed. The flutter speed was obtained by investigating the variation of the response-variance against the airspeed. The maximum of the variance of response represented the flutter speed. To verify this new approach, two case studies were considered. The first case study was a 2-D airfoil under unsteady subsonic flow and the second one was a slender wing in an unsteady incompressible flow with Goland wing properties. The results of the proposed method showed a good agreement with the results of the conventional flutter analysis. One of the major advantages of this approach over the other numerical methods such as the p–k method was that no convergence of reduced frequency was needed so the computational cost was reduced dramatically.