Comparative analysis and determination of applicable range for free vibration of laminated cylindrical shells considering multiple shell theories and nine boundary conditions

As the key structure of aero-engine, the prediction and analysis of the dynamic characteristics of the casing is of great significance for evaluating the safety of the structure and preventing resonance. Based on Love shell theory, Donnell shell theory and Soedel shell theory, the prediction model of three-layered thin-walled cylindrical shell is established by energy method and solved and analyzed by Rayleigh Ritz method. This paper investigates nine classical boundary conditions including simple support–simple support (S–S), fixed support–fixed support (C–C), free–free (F–F), sliding–sliding (SL–SL), fixed support–simple support (C-S), fixed support–free (C–F), fixed support–sliding (C–SL), free–simple support (F–S), free–simple support \(\text{(F-)}\) and free–sliding (F-SL). In this paper, the natural frequency values of the three models are solved under different length–diameter ratio, thickness–diameter ratio and circumferential wave number. The accuracy of the models established in this paper is verified by comparison with published papers, and the differences and application ranges of the solution results of different models are given. The research of this paper provides useful references for the design and optimization of aero-engine cylindrical shell.