Solving for the Thermal Vibration Behaviors of Functionally Graded Stepped Conical Curved Plates with Point Connection Conditions

This paper proposed a degree-of-freedom reduction model for the rapid and unified solution of the modal and steady-state response behavior of functionally graded stepped conical curved plates with point connections under thermal environments. Within the framework of the first-order shear deformation theory, the two-dimensional spectral Chebyshev method and the fixed interface modal synthesis method were combined to derive the degree-of-freedom reduction model for functionally graded conical curved plates under thermal environments. Each reduction model was assembled considering external load excitations. Virtual springs were used to equivalently handle the coupling interface forces and point connection interface forces, further establishing a thermal vibration response analysis model for functionally graded stepped conical curved plates with point connections. In numerical examples, this degree-of-freedom reduction model was compared with experimental results and overall finite element results, validating the accuracy of the model and the advantages of rapid solution. Additionally, this degree-of-freedom reduction model was applied to quickly analyze the effects of material parameters and point connection parameters on the thermal steady-state response of the structure, providing a theoretical basis for the environmental adaptability design, verification, and evaluation of such structures.