Nonlinear thermal flutter 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 modified piston theory appended with static aerodynamic loading are used in the formulation. The static deflection of a cylindrical curved panel is studied by numerical simulation using Newton iterative approach. Then the stability boundary curves under different temperature elevations are obtained by using Lyapunov indirect method. The motion equations of curved panel are solved by Runge-Kutta method, time history and phase plots of curved panel flutter responses are depicted and corresponding bifurcation diagrams are obtained for better understanding of the subcritical and supercritical flutter responses of curved panels with different initial height-rises under increasing dynamic pressure and static thermo-aerodynamic loading (STAL). The results demonstrate that the flutter boundary drops significantly with increasing temperature elevation for small curvature panel, whereas, the flutter boundary almost keeps the same value for large curvature panel. The flutter dynamic behaviors of curved panels differ from those of flat panels significantly. Curved panels may enter chaos from static stable point when considering temperature elevation effects, and static stable point and LCO motion also exist in the chaotic motion area. For larger curvatures, chaotic motions will not occur, however the supercritical flutter motions exhibit a limit strip oscillation in which the vibration amplitudes restrained in a limited range.