Abstract
This paper is concerned with a theoretical investigation of the free vibration of arbitrary shells of revolution by means of the classical bending theory of shells. A method is developed that is applicable to rotationally symmetric shells with meridional variations (including discontinuities) in Young's modulus, Poisson's ratio, radii of curvature, and thickness. By means of the method of this paper, the natural frequencies and the corresponding mode shapes of axisymmetric or nonsymmetric free vibration of rotationally symmetric shells can be obtained without a limitation on the length of the meridian of the shell. To illustrate the application of the method given in this paper to particular shells, stone results of free vibration of spherical and conical shells obtained earlier by means of the bending theory are reproduced by the general method of this paper, and a detailed comparison is made. In addition, paraboloidal shells and a sphere cone shell combination are considered, which have been previously analyzed by means of the inextensional theory of shells, and natural frequencies and mode shapes predicted by the bending theory are given.
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