The Complex Response Of The Two Degrees Freedom Airfoil Flutter

With the flourishing development of the aerospace industry, the aeroelastical problems are more and more concerned widely. Flutter not only cause fatigue damage of the parts and components, but also can make catastrophic accidents. In classical theory, we usually assume that the structure of system is linear, but in fact, there are a large number of nonlinear factors in the aeroelastical systems, which can bring great effects on the dynamic characteristics. In this paper, the two degree of freedom airfoil is studied as a model. The problem of the bifurcations and complex dynamical responses of the systems are studied used eigenvalue theory and by numerical simulation method. The main work of this paper is as follows:1. Summarized the research status and achievements of nonlinear aeroelastical systems.2.The flutter of the two degree of freedom airfoil in steady flow aerodynamics is analysed. Firstly, equations of motion are established by Lagrange equations. Secondly, eigenvalues method is used to get the flutter velocity of the model and then numerical simulation method is used to check the calculated results above. Lastly, the influence of the structural parameters of the linear velocity are discussed.3.An airfoil flutter with cubic nonlinear stiffness in pitch is studied. Firstly, the flow velocity-equivalent stiffness diagram and the flow velocity-amplitude diagram are studied by equivalent linearization method. Secondly, stable limit cycle regions are determined and the results of the qualitative analysis are simulated by numerical integration. Finally, stability of limit cycle in the different velocity of flow regions is analysed by numerical integration.4.Firstly, the second order differential equations of motion of the two degree of freedom airfoil are rewritten as four dimensional first-order differential equations. Secondly, the velocity of bifurcation is obtained through Jacobian matrix of the equilibrium points of system. Finally, the numbers of limit cycle, stability and complex response in different velocity of flow regions are analysed by numerieal simulation.