Aeroelastic Stability and Nonlinear Flutter Analysis of Heated Panel with Temperature-Dependent Material Properties

Abstract

With the use of new structural materials and intelligent materials in aircraft panel manufacturing and flutter suppression, temperature-dependent material properties are increasingly outstanding. In this study, the effects of temperature-dependent material variation on the aeroelastic stability and nonlinear flutter behaviors of a heated flexible panel in supersonic flow are studied in detail. According to Hamilton’s principle, the aerothermoelastic governing equations are established with von Kármán’s nonlinear plate theory and piston theory. By applying the Lyapunov indirect method and Routh-Hurwitz criterion, the theoretical solutions for the static/dynamic (buckling/flutter) instability boundaries are derived. It is found that the temperature-dependent variation of the thermal expansion coefficient has a decisive impact on decreasing the critical buckling temperature elevation, and the temperature-dependent variation of the elastic modulus plays a decisive role in the parameter boundary cross by which the buckled modes are transformed into the flutter modes. Using the fourth-order Runge-Kutta numerical integration method to solve the aeroelastic equations directly, the nonlinear dynamic responses are obtained and then analyzed by phase portrait, Poincaré map, bifurcation diagram, and largest Lyapunov exponent. The results show that the concrete effects on dynamic responses are significant. More bifurcations and chaotic motions occur after considering the temperature-dependent material variation, and the route to the additional chaotic motions is via quasi-periodic motion.