The aim of this study is to investigate the complex damping influences on the oscillatory/static instability characteristics of heated panels in supersonic airflow. Firstly, by assuming a constant, uniform thermal loading and adopting the piston theory, the panel aeroelastic governing equation is obtained. After deriving the panel buckling and vibration modes, the reduced order model can be built and adopted to investigate the system primary instability in the modal coordinates. Then, introducing the modal damping coefficients ratio $\eta >0$, the critical parameters of the panel flutter oscillation are theoretically evaluated based on the non-conservative energy balance principle, thus the system instability characteristics can be investigated. The results show that the system oscillatory and static buckling instability characteristics are significantly regulated by the thermal loading and modal damping. For the oscillatory instability, there exists the damping paradox, which is associated with the system energy dissipation efficiency, and can be quantitatively evaluated by the ratio $2\sqrt{\eta }/\left(1+\eta \right)$. The system static buckling instability characteristics is also affected by the modal damping, and this damping destabilization is clarified based on Hamiltonian energy conservation law. The results agree well with that obtained by Routh-Hurwitz criteria, and lead an in-depth understanding of the complex role played by the damping within the non-conservative dissipative systems.

本研究的目的是研究复杂阻尼对超音速气流中加热板的振荡/静态不稳定特性的影响。首先，假设一个恒定的、均匀的热载荷，采用活塞理论，得到面板气弹控制方程。在推导出面板屈曲和振动模式后，可以建立并采用降阶模型来研究系统在模态坐标中的初级不稳定性。然后，引入模态阻尼系数比$\eta >0$，基于非守恒能量平衡原理，对面板颤振的关键参数进行了理论评估，从而研究了系统的失稳特性。结果表明，热载荷和模态阻尼显着调节了系统的振荡和静态屈曲失稳特性。对于振荡不稳定性，存在阻尼悖论，它与系统能量耗散效率相关，可以通过比值来定量评价$2\sqrt{\eta }/\left(1+\eta \right)$. 系统静屈曲失稳特性也受模态阻尼影响，基于哈密顿能量守恒定律阐明了这种阻尼失稳。结果与 Routh-Hurwitz 准则获得的结果非常吻合，并引导人们深入了解非保守耗散系统中阻尼所起的复杂作用。