In this paper, a general analysis method is developed for the free vibrations of cylindrical shells with general elastic supports. It is shown that the classical simple boundary conditions can be simply treated as the special cases when the stiffness constants for the restraining springs become either zero or infinity. The shell displacements are expanded as an improved Fourier series, which ensures the excellent accuracy and numerical stability of the solutions. This method is potentially advantageous for the mid-frequency vibration analysis because of its analytical forms of the solutions and involvement of much fewer degrees of freedom in comparison with the traditional grid-based methods.
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