Abstract
In this paper, the axisymmetric free vibrations of truncated conical shells are analyzed by means of an improved shell theory. The equations of vibration and the boundary conditions are obtained from the stational condition of Lagrangian of the shells. The equations of vibration are solved exactly by a solution in series for a conical shell with linearly varied thickness along its axis and the effects of boundary conditions, thickness and semi-vertex angle on the natural frequencies are investigated. As a special case of the conical shell, we compare this theory with Mindlin's circular plate theory and with Mirsky's cylindrical shell theory.
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