Flutter-Type Oscillation Analysis of the Panel under Aerothermoelasticity Based on the Approximate Inertial Manifolds

摘要

For the hypersonic vehicle and aircraft, there is complicated aerodynamic force on the surface, and the aerodynamic heat induced by flow can’t be neglected. Not only the aerodynamic load, but also the thermal stress induced by the nonlinear temperature distribution, has great influence on the nonlinear oscillation of the surface panel. Consequently, in the mathematical model, it is absolutely necessary to couple the effects of aerodynamic, thermodynamic and elastic forces together. And then many nonlinear phenomena relevant to the panel oscillation will be discovered. In this study, the influence of the aerodynamic force and the thermal stress is added to the governing equation for a two-dimensional panel, and then the oscillation equation of the panel in hypersonic flow is obtained. According to the piston theory, aerodynamic load on the panel induced by supersonic flow is obtained, and then the unsteady temperature distribution is calculated due to the relationship of the pressure and the temperature of inviscid flow. Based on the laminar boundary layer theory of compressible viscid fluid, the steady temperature distribution is obtained. Using one-dimensional heat conduction equation, the exact temperature distribution in the panel is obtained by coupling thesteady and unsteady temperature distribution. And then thermal stress caused by nonlinear temperature distribution is calculated. Adding the thermal stress calculated above in the equilibrium equation of the panel, and then the non-dimensional PDE for the panel oscillation is obtained. Finally, some Nonlinear Galerkin methods combined with Approximate Inertial Manifolds, including traditional Approximate Inertial Manifolds, post-processed Galerkin method, are applied to the numerical solution of this equation, and a comparison between them are given further.The numerical results show that Hopf bifurcation, complicated periodic motion will appear as the Mach number increasing gradually. When only the steady temperature distribution is considered, setting the steady temperature recovery factor as a parameter, the buckling of the panel and complex bifurcations are discovered as steady temperature recovery factor is increased. Additionally, the numerical results show that the Approximate Inertial Manifolds and post-processed Galerkin method presented are efficient for the numerical analysis for the nonlinear dissipative dynamic systems, especially for the model reduction of the system.