Abstract
In this paper, we analyze the axisymmetric vibrations of a cylindrical shell of which the thickness varies in the axial direction by using the thin cylindrical shell theory and an improved thick cylindrical shell theory. We solve the equations of vibration exactly by using a series solution. As numerical examples, we obtain the natural frequencies and the mode shapes of cylindrical shells with both ends clamped, simply supported and free and examine the variations of the natural frequencies and the mode shapes for the variations of the thickness. And also, we make clear the influences of the shear deformation and the rotatory inertia upon the natural frequencies and the mode shapes.
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