HOPF BIFURCATION OF A TWO-DIMENSIONAL THIN PLATE IN SUPERSONIC AIRFLOW

The nonlinear dynamic equations of a simple supported two-dimensional thin plate in the supersonic airflow are established through the Hamiltonian variational principle. In the equation, the geometric nonlinear is expressed by the Von Karman’s thin plate theory and the aerodynamic pressure is expressed by the piston theory. The partial differential equation is turned into an ordinary differential equation by Galerkin method. A new algebraic criterion of Hopf bifurcation is utilized to achieve the analytic expression of critical flow velocity with the initial in-plane load, the flutter frequency with the initial in-plane load and the critical flow velocity. Finally, the Forth order Runge-Kutta numerical method was applied to certify the theories.