Vibration analysis of functionally graded conical shells in thermal environment

Based on the spectro-geometric method, the prediction model for vibration characteristics of the functionally graded material (FGM) conical shell under thermal environment was established. In the current model, temperature-dependent material characteristics, which change with the shell thickness direction, were considered. Firstly, the boundary conditions for the shell were simulated by using the artificial spring theory. The energy equation of the FGM conical shell in thermal environment was derived based on the framework of the first-order shear deformation theory. Then, an efficient and accurate spectro-geometric method and the form of the sum of the products of the circumferential Fourier harmonic functions were employed to express the displacement admissible function. On the basis, the displacement admissible functions were substituted into the energy equation. Also the Rayleigh - Ritz method was utilized to perform variational operations on the unknown coefficients of the displacement admissible function and the free and transient thermal vibration characteristics were solved with the standard dynamic equation. By comparing the calculation results with those obtained from the existing literatures and finite element analysis, the accuracy and reliability of the current model was demonstrated. Finally, the effects of the boundary conditions, material properties, geometric properties and temperature field on the transient vibration characteristics of FGM conical shells were investigated. © 2022 Chinese Vibration Engineering Society. All rights reserved.