Flutter analysis of a nonlinear airfoil using stochastic approach

Abstract

In this paper, the dynamic instability of a nonlinear system has been studied using the stochastic vibration analysis and employing statistical properties of the system response. In this method neither the time domain analysis nor limit cycle oscillations were used. A two degrees-of-freedom airfoil subjected to an aerodynamic quasi-steady flow with a nonlinear torsional spring was considered as the case study. The spring nonlinearity was examined in hardening and softening states. A random force in the form of the white noise with Gaussian function was added to the aerodynamic lift force. The statistical linearization and random vibration analysis were applied to the nonlinear system to obtain the equation of one-dimensional nonlinear map in terms of response variance and flow speed. Furthermore, the nonlinear map was solved to analyze the response variance of the system against the flow speed. The flow velocity of the maximum variance of the system response was regarded as the flutter speed. The bifurcation point and the approaching path to the chaos were determined by investigating the nonlinear map through the iteration process. In addition, a good vision of jump phenomenon in velocity-variance diagram was given through the current stochastic analysis using the chaos intermittency cascade and the tangent bifurcation point. The aforementioned result is new in the nonlinear aeroelastic dynamic instability field.