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 predictionand analysis of the dynamic characteristics of the casing is ofgreat significance for evaluating the safety of the structure andpreventing resonance. Based on Love shell theory, Donnell shelltheory and Soedel shell theory, the prediction model ofthree-layered thin-walled cylindrical shell is established by energymethod and solved and analyzed by Rayleigh Ritz method. This paperinvestigates nine classical boundary conditions including simplesupport–simple support (S–S), fixed support–fixed support(C–C), free–free (F–F), sliding–sliding (SL–SL), fixedsupport–simple support (C-S), fixed support–free (C–F), fixedsupport–sliding (C–SL), free–simple support (F–S),free–simple support \(\text{(F-)}\) $\text{(F-)}$ and free–sliding (F-SL). In this paper,the natural frequency values of the three models are solved underdifferent length–diameter ratio, thickness–diameter ratio andcircumferential wave number. The accuracy of the models establishedin this paper is verified by comparison with published papers, andthe differences and application ranges of the solution results ofdifferent models are given. The research of this paper providesuseful references for the design and optimization of aero-enginecylindrical shell.