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Subharmonic resonance of order ½ with an asymmetrical restoring force

Published online by Cambridge University Press:  04 July 2016

Z. F. Reif
Z. F. Reif*
Affiliation:
Department of Mechanical Engineering, University of Windsor
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Extract

Excitation of subharmonic resonances is one of the serious vibration problems which often have to be overcome in the development of high speed machinery. Such resonances have been observed, for example, in gas turbines(3), in rotor systems(4) and in the geared drive of a rotating kiln(5).

The subharmonic resonance of order 1/2, of a single degree of freedom system with viscous damping, is investigated for the case of a centrifugal disturbing force. The restoring force characteristic is of the non-odd form and its asymmetry is expressed in terms of the static deflection parameter. The Ritz averaging method, with a five term approximation, is used for the theoretical analysis. Numerical results are presented for the undamped case and are compared with analogue computer solutions.

The choice of the Ritz averaging method is determined mainly by its adequate accuracy at larger magnitudes of non-linearity. It is also more versatile than other methods and in a previous application(6) to a system with an asymmetrical restoring force it produced satisfactory results.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 77 , Issue 746 , February 1973 , pp. 98 - 101
Copyright
Copyright © Royal Aeronautical Society 1973 

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References

1. Jacobsen, S. J. and Ayre, R. S. Engineering Vibrations, p. 282, McGraw-Hill, 1958.Google Scholar
2. Klotter, K. Non-linear vibration problems treated by the averaging method of W. Ritz; Part 1, fundamentals of the method. Tech. Report No 17/1, Stanford University, 1951.Google Scholar
3. Schnitger, J. R. Development of a smooth running, double spool gas turbine rotor system, ASME paper No 58-A-197, 1958.Google Scholar
4. Tondl, A. Notes on the problem of self-excited vibrations and non-linear resonances of rotors supported in several journal bearings, Wear, 8, 349, 1965.Google Scholar
5. Chaloupka, V. On the initiation of subharmonic resonance in a torsional system with gears, Non-linear vibration problems, Warsaw, 5, 399, 1963.Google Scholar
6. Reif, Z. F. The effect of static deflection on the harmonic resonance of a system with a hardening non-linear spring. The Aeronautical Journal, 74, 59, 1970.Google Scholar