Supersonic Nonlinear Fluutre Analysis Of Dualistic Airfoil

This dissertation mainly presents a study on the aeroelastic flutter of a dualistic airfoil in the supersonic and hypersonic flow. The main contributions of this dissertation are as the follows:Chapter 1 surveys some recent achievements and developments of the study on the flutter of aerodynamic stretch system with nonlinearity.Chapter 2, the aerodynamical model of a dualistic airfoil in the supersonic flow is established by the Lagrange equation and the Piston theory. The V-G method and numerical simulation are used to receive the flutter velocity of the model.Chapter 3, a dualistic airfoil with free play nonlinear stiffness in pitch in the supersonic flow is considered and double state limit cycle flutter of the nonlinear aeroelastic system is investigated. By obtaining the expression of unsteady aerodynamic and moment by the piston theory in the second-order approximation, the equivalent linearization method based on the first order asymptotic solution of the KBM method is introduced into the qualitative analysis of flutter of nonlinear aeroelastic system, coupling figures about equivalent linearization stiffness, flutter velocity and the airfoilvibration amplitude is gotten. By the coupling figures the conclusion can be received: the system has one state limit cycle with smaller amplitude and the other state limit cycle with larger amplitude in the region of fluid velocity, viz. the system produce double state limit cycle flutter. To verify correctness of the conclusion, which is obtained by the qualitative method, numerical integration is used to integrate for the primary nonlinear equation. The results show that, the system arises double state limit cycle flutter.Chapter 4 considers the influence of cubic physical and aerodynamic non-linearity for flutter characteristic of aeroelastic system. The piston theory in the third-order approximation is proposed to get the expression of unsteady aerodynamic of the airfoil , and Center Manifold Method is used to reduce the flutter system to a two-dimensional one. Then type and stability of bifurcation points are analyzed by utilizing the method of succeeding function. With the Runge-Kutta method and the method based on the Second Liapunov Quantity the Hopf bifurcation of the system is judged, the results show that, when the mach number is lower the system yields super-critical Hopf bifurcation and the amplitude of flutter is raise slowly. When the mach number is raised the system yields sub-critical Hopf bifurcation. The airfoil yields strong vibration, which has very serious disserve when the air speed approach or exceed bifurcation points.