# Aerothermoelastic Analysis of Conical Shell in Supersonic Flow
## 1 Introduction  
Due to its beneficial aerodynamic shape and mechanical properties, the conical shell is widely used in the structural component of supersonic vehicles, such as the nose cones of supersonic missiles and aircraft radomes. During high-speed flight, these components, which are subjected to aerodynamic loads and aerodynamic heating, may experience aerothermoelastic instability, which can damage the structure. Therefore, it is necessary to investigate the aerothermoelastic behavior of the conical shell in supersonic flow. Many scholars have studied the vibration characteristics of shell of revolution, considering aerodynamic load and aerodynamic heating. Among them, the supersonic flutter and aerothermoelastic behavior of cylindrical shells has been studied extensively and carefully. Based on [PERSON]'s nonlinear shell theory and [PERSON]'s solution procedure, [PERSON] and [PERSON] [1,2] analyzed both the linear and nonlinear aeroelastic stability of circular cylindrical shells under supersonic airflow. [PERSON] [3] analyzed the supersonic flutter of a composite cylindrical shell under simply supported boundaries at both ends. The influence of temperature change on aeroelastic stability was explored with varied values of the power-law index. The aerothermoelastic characteristics of a composite cylindrical shell were studied by [PERSON] et al. [4], wherein the theory of the layer-wise displacement field was used for various damping treatments, and the post-buckling behaviors and aeroelastic characteristics were investigated with various damping treatments. Based on the frequency-domain and time-domain methods, [PERSON] and [PERSON] [5] conducted a study of the aerothermoelastic characteristics of a cylindrical shell made from laminated composite material. The effect of the direction of fiber laying on the flutter performance and buckling under heating conditions was studied. By combining the [PERSON] shell theory with a classical finite element method, [PERSON] and [PERSON] [6] proposed a hybrid finite element method to investigate the aerothermoelasticity of a functionally graded cylindrical shell, and analyzed the effects of internal pressure and temperature change on the aeroelastic stability. According to the virtual displacement principle, [PERSON] et al. [7] explored the aeroelasticbehavior of a heated cylindrical shell made from composite material under the combined action of internal and external air flows with clamped-clamped boundaries. The effects of material properties, aerodynamic loads and thermal loads on the flutter boundary were analyzed. [PERSON] [8] explored for the first time the aerothermoelastic stability of a cylindrical shell made from functionally graded carbon nanotube-reinforced composite material. The influence of various influential factors on the aerothermoelastic stability was investigated in detail. Additionally, taking a functionally graded carbon nanotube-reinforced composite cylindrical shell as the research object, [PERSON] et al. [9] analyzed the aerothermoelastic behavior of a cylindrical shell based on the frequency-domain method. In addition, the effect of varied control methods on active flutter control was also studied. [PERSON] et al. [10] adopted [PERSON]'s principle to establish a dynamic model of a composite laminated cylindrical shell. Based on the equation of motion, the aerothermoelastic behavior of the cylindrical shell with the elastic boundaries was studied. The effects of different directions of spring constant on thermal buckling and aeroelasticity stability were investigated in detail. [PERSON] et al. [11] explored the vibration behavior and flutter stability of a composite cylindrical shell under varied boundary conditions by using the same method as mentioned above. [PERSON] [12] decided to study the aerothermoelastic characteristics of a loaded functionally graded circular cylindrical shell under the action of supersonic airflow.