Prediction of Free-Boundary Cylindrical Shell Vibrations Based on Supported-State Modal Parameters

Free-boundary cylindrical shells are widely applied in various engineering fields. However, direct measurement of their vibration responses under actual operating conditions is technically infeasible. To address this limitation, this study proposes a prediction method for the vibration response of free-boundary cylindrical shells based on modal parameters and frequency-response data obtained from cylindrical shells under supported boundary conditions. First, a mapping relationship between the modal parameters of supported- and free-boundary cylindrical shells is established, enabling transformation of supported-boundary modal parameters into their free-boundary counterparts. Second, the variation of the equipment excitation force with the structural receiving impedance is taken into account. By exploiting the invariance of the free velocity of mechanical equipment, a relationship between the excitation force in the supported state and that under free-boundary conditions is derived. Based on the transformed modal parameters and the corresponding excitation force, the vibration response of the free-boundary cylindrical shell subjected to equipment excitation is subsequently predicted. The proposed theoretical approach is validated through finite element simulations. Results indicate that boundary conditions significantly influence the vibration characteristics of cylindrical shells. Support springs modify the natural frequencies and mode shapes by altering the shell’s modal parameters, while simultaneously affecting the excitation force through impedance changes at the excitation point. The combined effect of these mechanisms leads to substantial variations in vibration responses under different boundary conditions. As direct measurement under free-boundary conditions is impractical, the proposed method provides an effective means for accurately predicting the vibration behavior of freeboundary structures subjected to equipment excitation.