Nonlinear Aeroelastic Analysis of Heated Curved Panels in Supersonic Air Flow

A nonlinear aeroelastic model for a two-dimensional heated curved panel in supersonic air flow is established by using Galerkin method. The von Karman large deflection theory and the third-order piston theory appended with the static aerodynamic loading are used in the governing equations. The static aero-thermal deflection of the curved panel is firstly obtained by using Newton iterative approach. Then the stability boundary under different temperature elevations is achieved by using Lyapunov’s indirect method. Lastly, the motion equations of a heated curved panel in supersonic air flow are solved by a fourth-order Runge–Kutta numerical scheme. Time history responses, phase plots, Poincare maps and bifurcation diagrams are used for better understanding of the pre/post-flutter responses of a curved panel by varying parameters, including curvatures, dynamic pressures and temperature elevations. The results demonstrate that the flutter boundary drops significantly with increasing temperature elevation for panels with small curvatures. However, the flutter boundary almost keeps the same for panels with large curvatures. The nonlinear flutter characteristics of the curved panel differs from those of flat panels significantly, the nonlinear flutter response of heated curved panels changes from static equilibrium point or LCO to chaos with the increase of temperature elevation or dynamic pressure and the static, LCO motions also exist in the chaotic area. For panels with large curvatures, the chaotic motions cannot occur, and the amplitude of LCO is limited in a certain range.