Vibration of Stress-Free Hollow Cylinders of Arbitrary Cross Section

[+] Author and Article Information
K. M. Liew, K. C. Hung, M. K. Lim

School of Mechanical and Production Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798

J. Appl. Mech 62(3), 718-724 (Sep 01, 1995) (7 pages) doi:10.1115/1.2897005 History: Received November 15, 1993; Revised August 18, 1994; Online October 30, 2007


A three-dimensional elasticity solution to the vibrations of stress-free hollow cylinders of arbitrary cross section is presented. The natural frequencies and deformed mode shapes of these cylinders are obtained via a three-dimensional displacement-based energy formulation. The technique is applied specifically to the parametric investigation of hollow cylinders of different cross sections and sizes. It is found that the cross-sectional property of the cylinder has significant effects on the normal mode responses, particularly, on the transverse bending modes. By varying the length-to-width ratio of these elastic cylinders, interesting results demonstrating the dependence of frequencies on the length of the cylinder have been concluded.

Copyright © 1995 by The American Society of Mechanical Engineers
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