Stability and Bifurcation of a Nonlinear Aero-thermo-elastic Panel in Supersonic Flow

Abstract

Stability and bifurcation of a nonlinear supersonic panel under aerothermal loads are analyzed numerically in the present study. In the structural model, von Karman’s large deformation theory is taken into account for the geometric nonlinearity of the panel. In light of Hamilton’s principle, the governing equation of motion of a twodimensional aero-thermo-elastic panel is established. Coupling with the panel vibration, aerodynamic pressure is evaluated by first order supersonic piston theory and aerothermal load is approximated by quasi-steady theory of thermal stress. By transforming the partial differential equation to a series of ordinary differential equations via Galerkin method, fixed points and their stabilities of the system are studied using nonlinear dynamic theory. The complex dynamic responses regions are discussed with temperature loads as a bifurcation parameter. The results show that the thermal stress has a significant influence in the stability of the panel. The panel system undergoes Hopf bifurcation, period doubling, quasi-period and chaos with the increase of the temperature.