Vibration characteristics analysis of multi-layer composite cylindrical shell casing with different layer thickness ratios under external pressure using energy method

Purpose Aero-engine casings commonly use composite cylindrical shell structures with excellent properties such as corrosion resistance and fatigue resistance. Still, their vibration behavior is relatively complex and may cause fatigue vibration damage, so it is essential to analyze the vibration characteristics of composite cylindrical shells. The purpose of this paper is to analyze the vibration characteristics of multilayer composite cylindrical shells subjected to external pressures and having different interlayer thickness ratios and provide some theoretical basis for the fatigue damage prediction of cylindrical shell casing to ensure the safety and stability of the engine during flight. Design/methodology/approach Firstly, the vibration differential equation with external pressure is established based on Soedel theory considering nonlinear effects, while four symmetric boundary conditions are chosen to constrain the cylindrical shell. Then the Rayleigh–Ritz method, which is more efficient and accurate in calculating large structural systems, is applied to solve the problem, and the theoretical model of three-layer cylindrical shell under external pressure is established. The accuracy of the model is verified by comparing the data with the specialized literature. Subsequently, the effects of different external pressures and different thickness-to-diameter ratios, different length-to-diameter ratios and different interlayer thickness percentages on the natural frequency of multilayer composite cylindrical shells were investigated by control variable analysis. Findings The conclusions obtained show that the external pressure increases the natural frequency of the cylindrical shell and that the frequency characteristics of the cylindrical shell vary for different boundary conditions. The effect of length-to-diameter ratio, thickness-to-diameter ratio and the percentage of the thickness of the intermediate layer on the natural frequency of the cylindrical shell are significantly increased under external pressure. Because the presence of external pressure increases the frequency of the cylindrical shell by about 70%, it has almost no effect on the frequency at the minimum number of circumferential waves, and the effect on the frequency at the maximum number of circumferential waves is reduced to about 50%. The frequencies in the SL-SL boundary condition are all in perfect agreement with the S-S boundary condition under the influence of different influencing factors. Originality/value In this paper, the effect of external pressure and the natural properties of the cylindrical shell under external pressure on the cylindrical shell’s frequency is considered, emphasizing the effect of different layer thickness ratios on the frequency. This paper aims to summarize the changing law between the natural frequency of the cylindrical shell itself and different design parameters during the flight pressure process. Reliable theoretical predictions are provided for analyzing the vibrational behavior of shells subjected to external pressures in aerospace, as well as a database for the practical production of cylindrical shells.