Vibration of a circular cylindrical shell with elastic boundary restraints is of interest to both researchers and structural engineers. This class of problems, however, is far less attempted in the literature than its counterparts for beams and plates. In this paper, a general solution method is presented for the vibration analysis of cylindrical shells with elastic boundary supports. This method universally applies to shells with a wide variety of boundary conditions including all 136 classical (homogeneous) boundary conditions which represent the special cases when the stiffnesses for the restraining springs are set as either zero or infinity. The Rayleigh–Ritz procedure based on the Donnell–Mushtari theory is utilized to find the displacement solutions in the form of the modified Fourier series expansions. Numerical examples are given to demonstrate the accuracy and reliability of the current solution method. The modal characteristics of elastically restrained shells are discussed against different supporting stiffnesses and configurations.

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