Aeroelastic stability analysis of heated flexible panel subjected to an oblique shock

The critical conditions for aeroelastic stability and the stability boundaries of a flexible two-dimensional heated panel subjected to an impinging oblique shock are considered using theoretical analysis and numerical computations, respectively. The von-Karman large deflection theory of isotropic flat plates is used to account for the geometrical nonlinearity of the heated panel, and local first-order piston theory is employed in the region before and after shock waves to estimate the aerodynamic pressure. The coupled partial differential governing equations, according to the Hamilton principle, are established with thermal effect based on quasi-steady thermal stress theory. The Galerkin discrete method is employed to truncate the partial differential equations into a set of ordinary differential equations, which are then solved by the fourth-order Runge-Kutta numerical integration method. Lyapunov indirect method is applied to evaluate the stability of the heated panel. The results show that a new aeroelastic instability (distinct from regular panel flutter) arises from the complex interaction of the incident and reflected wave system with the panel flexural modes and thermal loads. What's more, stability of the panel is reduced in the presence of the oblique shock. In other words, the heated panel becomes aeroelastically unstable at relatively small flight aerodynamic pressure.