Active Control Strategy For The Nonlinear Flutter Of Airfoil And Panel In The Supersonic Flow

The aerodynamic problem of flight vehicle structures plays an important role inmodern vehicle design. Structures with light character and high flexibility arewidely used in modern vehicles for the purpose of high flight performance. It makesthe aerodynamic problem becoming more important. Nonlinearities in structures andaerodyamic loads especially produce more difficulties in analysis. In thisdissertation, the nonlinear aerodynamic flutter of2-D airfoil and panel model arestudied in a systematic way. Then active control methods are designed according todifferent structures with different flutter stability features. The present study devotesto flutter are in following aspects.The2-D airfoil with soft and hard cubic nonlinear stiffness is studied byapplying the nonlinear third order piston theory. Both the nonlinear aerodynamicdamping and stiffiness are considered. Linear critical speed is obtained by checkingthe real part of eigenvalues in the linearized system. Nonlinear critical speed can beobtained by using the numerical simulation method. Subcritical Hopf bifurcationswill happen when the flight speed reaches the nonlinear critical speed. Nonlinearstiffness plays a key role in this kind of nonlinear flutter. When the soft nonlinearstiffness in pitching displacement is changed to be hard nonlinear stiffness, thesubcritical flutter can be changed into supercritical flutter. While increase thenonlinear cubic stiffness with hard characteristics in plunging, the LCOs amplitudeand nonlinear critical speed can both be improved.The analysis of nonlinear aerodynamic response gives a clue to designnonlinear flutter active control. With LQR control the linear critical speed of airfoilcan be increased by53%. The LQR control method can enhance the nonlinearcritical speed compared to velocity feedback control method. It can also work wellin high flight speed. In the demand of further suppression of flutter LCOs, cubicnonlinear feedback control are designed according to the influence of nonlinearcoefficients on flutter. Numerical results show that the nonlinear feedback controlcan reduce the LCOs amplitude and enhance the nonlinear critical speed efficiently.The von Karman nonlinear displacement-strain relationship is employed toestablish the model of2-D panel and3-D panel with piezoelectric pieces. Hamiltonprinciple is adopted to get the equation of motion. Ordinary differential equationsare derived in terms of the assumed mode method and used to study the dynamicalresponse character. Critical speeds of panel with different ratio of length to widthare calculated for3-D panel. The results obtained can be used to judge whether a2-D panel model can be adopted or not. Piezoelectric actuators and sensors are deployed according to the distribution of stress and strain respectively. The outputfeedback control is designed on account of the output voltage of piezoelectricsensors and input voltage of piezoelectric actuators. The MIMO LQR control isvalid in panel flutter suppression which can both improve the critical speed andreduce the flutter amplitude. Nonlinear LQR combined control method based onLQR control can further reduce the flutter amplitude in a certain speed region.Updated feedback gain based on LQR control can enhance linear flutter criticalspeed step by step. Regarding the efficiency of input control energy, the ProgressiveLQR control method is proposed. By adding different feedback gain to the updatingsystem, the flutter is suppressed efficiently and control energy is reduced to a certainextent. Results show that this control strategy can improve linear critical speed ofboth the airfoil model and panel model in significantly.The research on nonlinear aeroelastic flutter and suppression of vehiclestructures in this dissertation can offer an theoretical criterion for vehicle design.Meanwhile, it establishes an academic foundation of prevention and elimination forunstable aerodynamics.