Abstract
An approximated formula representing the vibration characteristics of a shell structure with finite curvature is proposed. The model is based on the dynamic analogy between a cylinder and a flat plate. In order to derive the formula, the dynamics of a shell with and without the curvature effect is introduced. Then, resonance frequencies, constant frequency loci, and number of modes in a flat plate and in a cylinder are also examined. After that, a simplified driving point mobility function of a shell with the plate mobility is derived. An experimental verification is conducted in order to examine the proposed formula. Cylinders having two different ring frequencies of 5.9 and 13.8 kHz are used as test structures. Comparisons are done for the resonance frequency and for the mobility function. The accuracy of the analysis falls within 6% error when resonance frequencies are compared with those of experimental data. The results show that the proposed mobility function predicts the vibration behavior for the frequency bandwidth below and above the ring frequency. The model is simple to use and could be easily extended to various boundary conditions for vibration and noise prediction purposes.
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