This article studies the vibrational behavior of composite conical-cylindrical shells (CCSs) with functionally graded coatings (FGCs) in thermal environments using the first-order shear deformation theory. Firstly, the equivalent material parameters, fundamental frequency, and resonant displacement responses of the CCSs with FGCs are derived using the mixture principle, complex modulus method, and transfer function approach. Then, detailed thermal vibration tests are performed on CCS structures with and without coatings to assess the reliability of the proposed model, revealing that the current model accurately forecasts the thermal vibration behavior of the CCSs with FGCs. Finally, the effect of key parameters on the vibrational properties of the CCSs with FGCs is investigated. The results demonstrate that increasing the functionally graded index, coating thickness, and Young’s modulus ratio can greatly enhance the vibration suppression capability of the structure.

This study proposes a prediction method for ceramic matrix composite thin plates (CMCTPs) with protective coatings under high-temperature conditions, based on the first-order shear deformation theory and the energy principle while considering thermal effects. It can successfully predict the variations in natural frequencies and resonant responses of CMCTPs over the experimentally validated temperature range of 25 °C to 800 °C, using a thermo-vibrational platform with a maximum temperature capability of 1500 °C. In addition, a thorough investigation of multiple key parameter influences on the dynamic characteristics of CMCTPs with and without coating is performed, with special focus on the effect of the coating on enhancing the thermo-vibrational resistance of such structures. The analytical results demonstrate that the protective coating significantly enhances the thermo-vibrational resistance of the structure. Optimization of the coating-to-substrate thickness ratio, elastic modulus ratio, and thermal expansion coefficient ratio is recommended to maximize vibration suppression performance, providing critical guidance for the dynamic design of coated CMCTP components in aerospace.