# Aerothermoelastic Analysis of Conical Shell in Supersonic Flow
## 1 Introduction
The influence of the different combination of mechanical, thermal and aerodynamic loads on the stability of the structure was analyzed. By using the improved differential quadrature method, which is a numerical approximation method, [PERSON] et al. [13] explored the aerothermo-elastic characteristics of functionally graded cylindrical curved panels under high supersonic airflow. The impact of temperature change, Mach number and other environmental factors on structure flutter response was emphasized. [PERSON] [14] used the Newton-Raphson method to study the aerothermoelastic stability of a composite cylindrical shell in a thermal environment. The effects of axisymmetric and asymmetric geometrical defects on aerothermoelastic stability were considered. Based on the first-order piston theory and the quasi-steady-state thermal stress theory, [PERSON] et al. [15] explored the post-buckling and flutter behavior of composite cylindrical panels in supersonic airflow in a thermal field, based on the least-square Ritz method. According to the literature review above, piston theory is an effective theory for calculating aerodynamic models in supersonic airflow. The scope and limitation of its application are studied in [16; 17; 18; 19]. For conical shells, numerous articles reported the vibration characteristics considering thermal load [20; 21; 22; 23] and aerodynamic load [24; 25; 26; 27; 28; 29; 30; 31; 32], individually. [PERSON] et al. [20] explored the thermal buckling of conical shells composed of advanced composite material by using a semi-analytic finite element method under the clamped-clamped boundary conditions. The influence of material performance and geometric parameters on thermal buckling behavior was studied. [PERSON] et al. [21] mainly investigated the thermal buckling characteristics of composite conical shells with simply supported boundaries at both ends. [PERSON] [22] explored the effect of thermal load on the vibration behavior of a ring-stiffened rotating conical shell composed of functionally graded material under a clamped-clamped boundary conditions. Based on the generalized differential quadrature method, [PERSON] [23] studied the vibration behavior of rotating conical shells in a thermal environment. Utilizing [PERSON]'s shell theory, [PERSON] and [PERSON] [24] investigated the flutter, vibration and buckling of a conical shell using the generalized [PERSON] method. In the modeling process, the in-plane inertias and structural damping were neglected, and the aerodynamic loading was established by inviscid two-dimensional quasi-steady approximation. [PERSON] and [PERSON] [25] first used the finite-element method to analyze the supersonic flutter of conical shells. According to a new formulation for calculating aerodynamic loads, considering quasi-static pressure and including the terms of added mass, rotational inertia and the forces in the midplane, [PERSON] [26] analyzed the flutter problem of the conical shell and discussed the effect degree of the terms on the critical Mach number. [PERSON] and [PERSON] [27] established an aeroelastic model of a conical shell according to the hybrid finite element method, and analyzed the flutter stability of the structure with different boundary conditions and a semi-vertex angle. With the differential quadrature method, the effects of the geometric parameters of conical shells, aerodynamic damping and the piston curvature correction term on the flutter stability of a conical shell were investigated by [PERSON] et al. [28]. [PERSON] et al. [29] mainly investigated the aeroelasticity of conical shells under yaw supersonic flow. The effects of material properties, geometric parameters, and aerodynamic loads on flutter boundaries have been explored in detail. [PERSON] et al. [30] investigated the linear and nonlinear flutter stability of truncated conical shells under the influence of supersonic airflow.