Vibration of a Free Rectangular Parallelepiped

[+] Author and Article Information
J. R. Hutchinson

University of California, Davis, Calif. 95616

S. D. Zillmer

Rockwell International, North American Aircraft Operations, 201 North Douglas, El Segundo, Calif. 90245

J. Appl. Mech 50(1), 123-130 (Mar 01, 1983) (8 pages) doi:10.1115/1.3166978 History: Received January 01, 1982; Revised August 01, 1982; Online July 21, 2009


A series solution of the general equations of linear elasticity is used to determine accurate natural frequencies for the vibrations of a rectangular parallelepiped with traction-free surfaces. The series solution is found to converge to accurate frequencies with the use of very few terms. Resulting frequences are tabulated for comparison with previous experimental results and are shown graphically for comparison with elementary rod, beam, and plate solutions. The comparisons with elementary solutions show good agreement, and comparisons with the experiment results shows excellent agreement.

Copyright © 1983 by ASME
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