Stability analysis and vibration characteristics of an axially moving plate in aero-thermal environment

The stability and vibration characteristics of an axially moving plate in an aero-thermal environment subjected to transverse excitation are investigated. In the modeling of the equation of motion, the influences of the in-plane thermal load and the perturbation aerodynamic pressure on the transverse bending deflection of the axially moving plate are taken into account. The governing equation of the plate in aero-thermal environment is established applying the Hamilton’s principle based on the von Karman nonlinear plate theory and linear potential flow theory. For the linear equation, the natural frequencies of the moving plate are analyzed by solving the generalized eigenvalue problem. The critical parameters of the moving velocity, flow velocity and temperature change for the divergence of the plate are obtained. For the nonlinear equation, the displacement time responses of the plate in different stability states subjected to transverse excitation are analyzed by numerical simulations. From the study, it can be seen that with the moving velocity, flow velocity and temperature change increasing, the fundamental natural frequency of the plate decreases. When the fundamental natural frequency decreases to 0, the plate is in a divergence type of instability. The critical moving velocity decreases with increasing flow velocities and temperature changes. The vibration amplitude of the plate in divergence state is larger than that in the stable state. The vibration amplitude increases with the flow velocity and temperature change increasing, which illustrates that the aero-thermal environment has significant effects on the stability and vibration properties of the axially moving plate.