This paper considers the flexural vibrations of free thin circular cylinders. A frequency equation is derived using free-free characteristic beam functions to represent the variation of mid-surface shell displacement components, u, v and w, with respect to the axial direction. Timoshenko strain-displacement relations for thin cylinders are used to determine elastic vibratory strain energy. Energy methods are applied to obtain the frequency equation and associated amplitude ratios for each of its roots. This energy solution is checked experimentally using a vibration exciter and numerically using the SABOR IV finite element program. With minor modification, the frequency equation conforms to the one obtained in a similar way by Arnold and Warburton for cylinders with clamped ends and simply supported ends. Thus the proposed form of frequency equation, by accommodating a greater variety of boundary conditions, simplifies the task of determining cylinder vibration characteristics.

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