Study On Flutter And Control Of Airfoil With Physical And Aerodynamic Nonlinearities

In airplane design, structural nonlinearities cannot be avoided. The structuralnonlinearities arise from worn hinges of control surfaces, loose control linkages,material behavior and various other sources. In the flighting, the aerodynamicnonlinearities also cannot be avoided. The aerodynamic nonlinearities can benegligible when the speed of the plan is not very high;but when the speed of the planis supersonic or highly supersonic, it cannot be negligible.This paper studies theflutter of a two-dimensional airfoil with the cubic physical nonlinearty and with thecubic physical and aerodynamic nonlinearities coupling. Furthermore the activecontrol is introduced for the flutter of a two-dimensional airfoil with the cubicphysical nonlinearty in the incompressible flow. The following are our main work:Part one, the flutter of the airfoil with the physical nonlinearty is study and theactive control is introduce for itFirstly, the equation of the flutter of a two-dimensional airfoil with the cubicphysical nonlinearty in the incompressible flow is obtained. Let the airspeed Q asthe bifurcation parameters. The normal form and the diagram of the Hopf bifurcationare deduced with the Maple procedure of the Normal Form Direct Method. Theinfluence of the parameter of the system on the flutter is analyed. The flutter may besub-critical or super-critical Hopf bifurcation with the different parameter, and theseare certified by numerical analysis. The sub-critical Hopf bifurcation must be avoidedbecause it is jeopardy. So we introduce the active control on the flutter of the airfoilwith the wash-out filter method, in order to avoid the sub-critical Hopf bifurcation.Part two, studing the flutter of the airfoil with the physical and aerodynamicnonlinearity coupling.Firstly, the kinetic equation of a two-dimensional airfoil in the supersonic orhighly supersonic flow is builted from the piston theory. Not only the physical butalso the aerodynamic nonlinearity is taken into account. Also the normal form and thediagram of the Hopf bifurcation are deduced with the normal form direct method.Secondly, the influences of the physical and aerodynamic parameter on the type of theHopf bifurcation are analyzed. Study shows that the "hard" structural non-linearitiesand the longer distance of the suspension point and the center of mass render theairfoil safer, whereas the "soft" ones render the airfoil more unsafe.In this paper, further and detailed investigations are given from theory, method andapplication. Some qualitative and quantitative rules are obtained, which benefit airfoildesign and dynamics analysis.