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The Behaviour of Damped Linear Systems in Steady Oscillation

Published online by Cambridge University Press:  07 June 2016

R. E. D. Bishop
R. E. D. Bishop*
Affiliation:
University Engineering Laboratory, Cambridge
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Summary

The classical theory of small harmonic vibrations of a linear damped system embodies the notion of “ viscous damping.” The equations of motion which result are somewhat complicated and, when there are more than two degrees of freedom, they are usually too unwieldy to be of much practical value. When the damping is small, however, approximating assumptions may be made which permit the treatment of systems which are near resonance as if they possess but one degree of freedom. But the effects of making these assumptions are by no means easily assessed, and even their justification is tedious.

It is shown that these difficulties may be greatly diminished by postulating hysteretic damping instead of viscous damping; the concept of hysteretic damping has been dealt with in two previous papers. The equations then take a much simpler form and the justification for, and validity of, the foregoing approximations are more easily seen. Moreover, the effects of damping upon the principal modes which the system possesses in the absence of its damping may be elucidated in this way.

Type
Research Article
Information
Aeronautical Quarterly , Volume 7 , Issue 2 , May 1956 , pp. 156 - 168
Copyright
Copyright © Royal Aeronautical Society. 1955

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References

1. Yates, H. G. Vibration Diagnosis in Marine Geared Turbines. Transactions of the N.E. Coast Institution of Engineers and Shipbuilders, Vol. 65, 4, 225–261, 1949.Google Scholar
2. Bishop, R. E. D. The Treatment of Damping Forces in Vibration Theory. Journal of the Royal Aeronautical Society, November 1955.CrossRefGoogle Scholar
3. Bishop, R. E. D. The General Theory of “ Hysteretic Damping.” The Aeronautical Quarterly, February 1956.Google Scholar
4. Duncan, W. J. Mechanical Admittances and Their Applications to Oscillation Problems. R. & M. 2000, 1947.Google Scholar
5. Johnson, D. C. The Application of Admittance Methods to the Classical Theory of Small Oscillations. Engineering, Vol. 171, No. 4453, p. 650, 1951.Google Scholar
6. Bishop, R. E. D. The Analysis and Synthesis of Vibrating Systems. Journal of the Royal Aeronautical Society, October 1954.Google Scholar
7. Bishop, R. E. D. and Johnson, D. C. Some Properties of Nodes in Vibrating Systems. The Aeronautical Quarterly, February 1955.CrossRefGoogle Scholar