Numerical Analysis On A Two-degree-of-freedom Self-excited Airfoil With Asymmetry Freeplay Model

In airplane design, structural nonlinearities cannot be avoided．The structural nonlinearities arise from worn hinges of control surfaces, loose control linkages, material behavior and various other sources. In this paper, the nonlinear behavior of a two-degree-of-freedom airfoil with pitch freeplay nonlinearity stiffness in incompressible flow is investigated. The aeroelastic equations-of-motion for the self-excited system can be formulated into a system of eight first-order ordinary differential equations. Taking the ratio of non-dimentional stream velocity to non-dimentional linear flutter speed as the bifurcation parameter, numerical analysis are presented for the asymmetry freeplay model with and without preload using a fourth-order Runge-Kutta method. The time history of some kinds of periodic motions, bifurcation, chaos, the influence by the initial conditions and some aspects affecting the flutter amplitude of airfoil are studied. In this paper, further and detailed investigations are given from theory. Some conclusions are obtained, which are benefit to airfoil design and dynamics analysis. Globe and local bifurcation diagrams are given after a great deal of numerical computation. Complicated motions are found in the system without preload. When U*/U*L increases from zero to 1 gradually, there are chaos, double-bifurcations from P-1 to P-2, inverse bifurcations from P-4 to P-2 and from P-2 to P-1. The responded motions are changed with the initial value. The LCO (Limit Cycle Oscillation) region is decreased and chaos region is increased when is decreased while other conditions are not changed. Some conclusions are attained for the system with preload.①The solution of system is converged to an equilibrium point or period-one LCO without chaos and the responded motions are not changed with the initial value；②The LCO region is decreased when increasing or decreasing and the amplitude of equilibrium point or LCO is reduced for a same speed ratio.③The LCO region is decreased and the linear flutter speed is raised when increasing. The amplitude of pitch motion isn't changed withμ,but is found to increase withμincreasing；④The amplitude of pitch motion is doubled whenand initial conditions are all doubled. ⑤The solution of system is not increasing with increasing speed ratio but converged to an equilibrium point in some speed ratio region in some cases.