A Unified Solution for Free Vibration Analysis of Cylindrical Shells with Arbitrary Boundary Conditions Comparing Different Thin Shell Theories

Thin shell theories have been widely used in the vibration analysis of cylindrical shells with small thickness-to-radius ratios, in which the rotary inertia and out-of-plane deformation are ignored. However, a variety of thin shell theories have been proposed according to different assumptions. It tends to cause controversy when researchers directly compare the results obtained based on different thin shell theories. In this paper, a unified solution including different thin shell theories is developed using the Rayleigh–Ritz method, via which the free vibration of cylindrical shells under arbitrary boundary conditions is investigated. The modified Fourier series are adopted as admissible functions for the axial modal shapes of cylindrical shells and artificial springs are introduced to simulate arbitrary boundary conditions. The unified solution is validated by comparing it with the finite element method (FEM) and the available literature data. On this basis, the influence of length-to-radius and thickness-to-radius ratios on the calculation accuracy of different thin shell theories under different boundary conditions is demonstrated, and the applicable scope of different thin shell theories is summarized. The thin shell theories discussed in this paper include the Donnell theory, the Reissner theory, the Sanders theory, and the Love theory. The results show that the calculation accuracy of the Love theory is the highest while the one of the Donnell theory is the lowest.