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The Acceleration of a Single Degree of Freedom System Through its Resonant Frequency

Published online by Cambridge University Press:  04 July 2016

S. Hother-Lushington  and
D. C. Johnson
S. Hother-Lushington
Affiliation:
Mechanical Engineering Department, University of Leeds.
D. C. Johnson
Affiliation:
Mechanical Engineering Department, University of Leeds.
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Extract

It is Sometimes required to find the maximum amplitudes of vibration attained and the speeds at which they occur when a machine is run through its critical speed with different accelerations. The solution of this problem for single degree of freedom systems has been obtained by Lewis and by Ellington and McCallion for mechanical vibrations and by Hok for the equivalent electrical case. These solutions require higher mathematics (contour integration, Fresnel's integrals or series solutions leading to Bessel functions). The purpose of this note is to show how, by using simple integration only, an alternative method of solution can be obtained for both zero and small values of damping.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 62 , Issue 574 , October 1958 , pp. 752 - 757
Copyright
Copyright © Royal Aeronautical Society 1958

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References

1.Lewis, F. M. (1932). Vibration During Acceleration Through a Critical Speed. Transactions of the American Society of Mechanical Engineers, Vol. 54, A-P-M-54-24, 1932.Google Scholar
2.Ellington, J. P. and McCallion, H. (1956). On Running a Machine Through its Resonant Frequency. Journal of the Royal Aeronautical Society, Vol. 60, p. 620, Sept. 1956.Google Scholar
3.Gunnar, Hok (1948). Response of a Linear Resonant System to Excitation of a Frequency Varying Linearly with Time. Journal of Applied Physics, Vol. 19, 1948.Google Scholar