As the core structural component of aircraft engines, engine casings endure complex multiple mechanical loads. Accurate prediction of their dynamic characteristics is crucial for ensuring engine safety and reliability. Typically featuring cylindrical or conical shell geometries, the natural frequency represents a vital property of conical shells during free vibration, playing a significant role in assessing structural safety and preventing resonance. This paper establishes a free vibration prediction model for a three-layer thin-walled conical shell based on the Love first-order approximate shell theory, followed by detailed analysis. Using Lagrange polynomials as axial modal functions, the vibration differential equations under this theory are formulated and solved via the Rayleigh-Ritz method. The variation of the cone shell’s natural frequencies under different boundary conditions is examined. The accuracy of the proposed model is validated by comparing results with simulation data, and the differences in outcomes under various operating conditions are explored. The study demonstrates that the established prediction model effectively provides reference for the design and optimization of aeroengine cone shells, while also offering theoretical support for the application of multi-layer composite structures.
Pan et al. (Tue,) studied this question.