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Oil Damped Free Vibration with Particular Reference to Systems having Nearly-Equal Natural Frequencies

Published online by Cambridge University Press:  07 June 2016

R. E. D. Bishop  and
D. C. Johnson
R. E. D. Bishop
Affiliation:
Department of Mechanical Engineering, University College, London
D. C. Johnson
Affiliation:
Department of Mechanical Enginering, Leeds University
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Summary

This paper concerns the free vibration of linear systems which are subject to damping. The general theory for a system having n degrees of freedom is recalled and illustrated by means of a simple example. Using an analytical method, the approximate theory for small damping is derived, showing the nature of the entrainment of the principal modes; the results are found to confirm those of Southwell (who uses a physical argument) and they are illustrated by an example. The approximate theory is shown to need modification when there are two nearly-equal natural frequencies and the appropriate corrections are found. The analysis is made somewhat complicated by the existence of two criteria of “ smallness ” instead of one; these are the difference between the close natural frequencies and the amount of the damping.

Type
Research Article
Information
Aeronautical Quarterly , Volume 9 , Issue 1 , February 1958 , pp. 71 - 95
Copyright
Copyright © Royal Aeronautical Society. 1958

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References

1. Southwell, R. V. Relaxation Methods in Engineering Science. First Edition, Oxford University Press, Arts. 174-6, 1940.Google Scholar
2. Rayleigh, Lord The Theory of Sound. Macmillan, London, Art. 102, 1894.Google Scholar
3. Lamb, H. Higher Mechanics. First Edition. Cambridge University Press, Art. 97, 1920.Google Scholar
4. Duncan, W. J. The Principles of the Control and Stability of Aircraft. Cambridge University Press, Chap. 4, 1952.Google Scholar