Determination of the Natural Frequencies of a Nearly Uniform System

[+] Author and Article Information
H. Bergkvist

Division of Strength of Materials, Lund Institute of Technology, Lund, Sweden

J. Appl. Mech 39(4), 918-922 (Dec 01, 1972) (5 pages) doi:10.1115/1.3422891 History: Received April 07, 1971; Online July 12, 2010


The equation giving the natural frequencies ωi of vibrations in a nearly uniform system is obtained from the knowledge of the natural frequencies of a uniform system and elementary determinant expansion. By inspection of the equation a sequence of frequency intervals is immediately found, each one containing one natural frequency. This fact makes the method superior to the classical Holzer method for this important type of vibratory system. A closer determination of the ωi :s, that sometimes could be needed, is easily performed by use of a simple desk-top calculator or even a slide rule, as is illustrated by some numerical examples in the Appendix.

Copyright © 1972 by ASME
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