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On Running a Machine through its Resonant Frequency

Published online by Cambridge University Press:  28 July 2016

J. P. Ellington  and
H. McCallion
J. P. Ellington
Affiliation:
Departments of Civil and Mechanical Engineering, University of Nottingham
H. McCallion
Affiliation:
Departments of Civil and Mechanical Engineering, University of Nottingham
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Extract

A solution, in terms of known integrals, is obtained for the motion from rest of a machine, idealised as an undamped linear mass-spring system, when subjected to an exciting force whose frequency varies at a constant rate.

In many installations of modern high speed machinery the running speed of the machine is in excess of the resonant or natural frequency of the system, and consequently starting up or stopping the machine could result in vibrations of large amplitude. The problem of assessing the magnitude and duration of these vibrations is very complicated and has been solved analytically only for the case of a single degree of freedom system excited by an oscillating force whose frequency varies linearly with time. However, even this solution is not easy to evaluate, the integrals involved demanding either graphical construction and numerical integration or summation of series.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 60 , Issue 549 , September 1956 , pp. 620 - 621
Copyright
Copyright © Royal Aeronautical Society 1956

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References

1. Lewis, F. M. (1932). Vibration During Acceleration Through a Critical Speed. Trans. A.S.M.E., 54, p. 253, 1932.Google Scholar
2. Watson, G. N. (1922). Theory of Bessel Functions. Cambridge University Press, 1922.Google Scholar