Free Vibrations of Transversely Isotropic Cylinders and Cylindrical Shells

[+] Author and Article Information
W. Q. Chen

Department of Civil Engineering, Zhejiang University, Hangzhou, 310027, P. R. China

J. Ying

The State Key Lab of CAD and CG, Zhejiang University, Hangzhou, 310027, P. R. China

Q. D. Yang

Department of Mechanics, Zhejiang University, Hangzhou, 310027, P. R. China

J. Pressure Vessel Technol 120(4), 321-324 (Nov 01, 1998) (4 pages) doi:10.1115/1.2842338 History: Received July 17, 1997; Revised February 27, 1998; Online February 11, 2008


Three displacement functions are introduced to decompose three displacement components so that the three-dimensional equations of motion of a transversely isotropic body are uncoupled. Expanding these functions in terms of orthogonal series, the equations of free vibration problem of a transversely isotropic cylindrical shell with ends simply supported are further simplified to be readily dealt with. As contrast to previous works, modified Bessel function solution with complex arguments is directly adopted for the case of complex eigenvalues. Moreover, for solid cylinders, (modified) Bessel functions of the first kind, even with pure imaginary arguments, are used because of their peculiar properties. Two numerical examples are given to check the correctness of the present method by comparing the results with those of others. Because no assumption is introduced in the paper, the method developed is completely three-dimensionally exact.

Copyright © 1998 by The American Society of Mechanical Engineers
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