Research On Flutter Andactive Control For Two-dimensional Airfoil

The flutter phenomenon is one of the most important problems in dynamicaeroelastictiy. In this dissertation, by taking two-dimensional airfoil in subsonic flow as theresearch object, the flutter characteristics, the influence of structure nonlinearities onaeroelastic response, flutter active control method and its test verification aresystematically and thoroughly studied. The main contents are included as follows:(1) The aeroelastic characteristics of two-dimensional airfoil with flap and pitchdegrees of freedom is investigated. Applying strip theory, the expressions of unsteadyaerodynamic for lift and pitching moment acting on airfoil are derived, then aeroelasticequations of motion for two degrees of freedom rigid airfoil and four degrees of freedomflexible airfoil are established by using energy method. Eigenvalue method, graphicmethod and flutter conic method are employed to determine flutter frequencies and fluttervelocity. The effects of system parameters on aerodynamic characteristics are analyzed andsubsequently the trends of frequency and damping ratio for system are obtained.(2) The effect of cubic hard spring stiffness in pitching direction on fluttercharacteristic of two-dimensional rigid airfoil is studied. Firstly, with the help of describingfunction method, the equivalent linear flutter motion equations of airfoil system areestablished based on energy method. Then using the traditional linear analytical method topredict the flutter speed and limit circle amplitude of original nonlinear system.Furthermore, Hopf bifurcation theory is used to verify the accuracy of the above results,and the Routh-Hurwitz criterion to determine the stability of system. Finally, it isconcluded that cubic nonlinearity has no effects on flutter speed of the corresponding linearsystem, but the nonlinear airfoil system will generate limit circle oscillation behavior whenthe air speed beyond the flutter speed, moreover the system will converge to the same limitcircle under different initial value.(3) Considering the effects of freeplay in control surface, aeroelastic equations ofthree degrees of freedom two-dimensional airfoil system are constructed with Lagrangianequation. Similarly, by the use of describing function method to deal with the freeplaynonlinearity, then amplitude and frequency of limit circle could be deduced from thecharacteristic polynomial of system, thereafter the conditions for stabilization system arederived by perturbation technique. The numerical simulation shown that freeplaynonlinearity leads to the flutter phenomenon advanced, and the jumping behavior of limit circle amplitude for control surface deflection could be observed. In addition, the differentinitial condition of system will cause complex dynamic responses, such as period motionor divergence.(4) A two-dimensional airfoil with a control surface is studied, in which thenonlinearities are not included. A novel flutter active control method based on measuredreceptance is put forward, the close-loop control model of airfoil system is conducted, andcontrol gains can be derived by using its receptance, with the gains the poles can beassigned arbitrarily. It is conclude that the critical flutter speed is greatly increased underthe closed-loop system by way of numerical simulation. When cubic nonlinearity inpitching direction is considered, a robust control method based on measured receptance isproposed according to the difficulty of accurately assigning desired poles, where thecontrol gains can be obtained by solving the minimal norm least square solution fornonlinear airfoil system. With the proposed method, limit circle can be assigned accuratelyand the desired poles can be assigned around a range of values, the system has very goodrobustness.(5) Take a working section containing a NACA0018airfoil as the wind tunnel testobject, the test fig and control system are designed and built firstly. Then the verificationfor the above theoretical analysis including pole assignment and flutter active controlmethod is implemented through the wind tunnel test. The results shown that combing thesolved gains, the desired poles can be assigned conveniently based on the measuredreceptance. The flutter speed could be increased more efficiently by separating the flap andpitch frequencies method than increasing the mode damping ratio method. Experimentalresults validate the availability and accuracy of the receptance method in flutter activecontrol.