The polygon built-up structures are widely used in engineering applications, which consist of a few flat plates. This paper develops a unified solution for the vibration and flutter problems of heated arbitrary polygon built-up structures with general boundary conditions and in supersonic airflow. By using the first-order shear deformation theory (FSDT), thermo-elastic theory and supersonic piston theory, the dynamic model of heated arbitrary polygon built-up structures in supersonic airflow is established based on the energy method. The unified solution is obtained by means of a variational approach and several numerical cases are performed to validate the proposed model, showing the high efficiency and excellent accuracy. Finally, to reveal the effects of the constraint, thermal load, numbers of cross-section edge and cross-section shape of the arbitrary polygon built-up structure on the vibration and flutter characteristics of the structures, the parametric studies are carried out. The present study can be used as the reference for the dynamic design of the arbitrary polygon built-up structure to improve its aero-elastic stability characteristic.

多边形组合结构在工程应用中被广泛使用，它由几个平板组成。本文针对具有通用边界条件和超音速气流的加热的任意多边形组合结构的振动和颤振问题，提出了统一的解决方案。利用一阶剪切变形理论（FSDT），热弹性理论和超音速活塞理论，基于能量法，建立了超音速气流中任意多边形加热结构的动力学模型。通过变分方法获得统一的解决方案，并通过几个数值案例验证了所提出的模型，显示了高效率和出色的精度。最后，要揭示约束的影响，热负荷，对任意多边形组合结构的横截面边缘数和横截面形状的数量对结构的振动和颤动特性进行了参数研究。本研究可为任意多边形组合结构的动力学设计提供参考，以改善其气动弹性稳定性。