Axisymmetric Free Vibrations of a Transversely Isotropic Finite Cylindrical Rod

[+] Author and Article Information
C. P. Lusher, W. N. Hardy

Department of Physics, University of British Columbia, Vancouver, B.C. V6T 2A6, Canada

J. Appl. Mech 55(4), 855-862 (Dec 01, 1988) (8 pages) doi:10.1115/1.3173733 History: Received September 14, 1987; Revised April 11, 1988; Online July 21, 2009


The frequencies of free vibration and mode shapes are calculated for axisymmetric modes of an elastic cylinder of finite length having hexagonal symmetry with the crystallographic c-axis coincident with the axis of the cylinder (a transversely isotropic finite cylindrical rod). A series solution is used which satisfies term-by-term the differential equations of linear elasticity and the boundary conditions on the shear stress; the boundary conditions on the normal stresses are satisfied by using an orthogonalization procedure. As an example, the method is applied to sapphire, with one of the six elastic constants (c14 ) taken to be zero. The other five elastic constants are those of the hexagonal system. The calculated acoustic vibration frequencies agree to better than 1 percent with measurements made on sapphire at room temperature, for a cylinder of half-height to radius ratio ∼ 1.

Copyright © 1988 by ASME
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