Abstract
A technique is presented for obtaining estimates for the natural frequencies of axisymmetric free vibration for anisotropic cylinders of finite length. The weak forms of the governing differential equations are solved by using the Ritz method with terms of power series in the co-ordinate directions as the approximating functions. The dimensions of the cylinder are arbitrary, and a wide range of geometries can be considered. The solution technique is applied to the example problems of an isotropic cylinder and a cylinder composed of a material with hexagonal symmetry. The method gives natural frequencies and mode shapes that are in excellent agreement with existing solutions. The condition of traction-free faces of the cylinder is also accurately satisfied.
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