Straightforward Free Vibration Solutions of Open Cylindrical Shells by the Finite Integral Transform Method

Straightforward analytical free vibration solutions of non-Lévy-type open cylindrical shells are obtained in this study by the finite integral transform method, which was not achieved by conventional semi-inverse methods. Three double finite integral transforms are imposed on the high-order partial differential equations (PDEs) for the problems, with some boundary conditions input, by which the relations between the transformed quantities and specific unknowns are given. Substituting the corresponding inverse transforms into the other boundary conditions provides systems of linear algebraic equations for determining the final analytical solutions. Comprehensive benchmark results for representative open cylindrical shells under different boundary conditions are shown. The results are well verified by other solution methods. With the present solutions, the effects of geometric parameters and boundary conditions on the vibration behaviors are quantitatively revealed by a parametric study. Due to its rigorous and straightforward solution procedure, this study presents a solid easy-to-implement way to explore new analytical solutions of similar problems.