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Receptance Series for Systems Possessing “Rigid Body” Modes

Published online by Cambridge University Press:  04 July 2016

G. M. L. Gladwell ,
R. E. D. Bishop  and
D. C. Johnson
G. M. L. Gladwell
Affiliation:
On secondment to University College of the West Indies, Jamaica
R. E. D. Bishop
Affiliation:
Department of Mechanical Engineering, University College, London
D. C. Johnson
Affiliation:
University of Cambridge
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Summary

Certain elastic systems may not only vibrate freely at proper (non-zero) natural frequencies, but may also move as rigid bodies. Such systems have “rigid body” modes which behave like principal modes corresponding to zero natural frequencies. These modes may be disregarded in the series representation of static distortions of such systems but must be taken into account in the representation of forced vibrations.

This note is concerned with the series representation of receptances of certain simple systems of this type, namely strings, bars, shafts and beams. These systems were discussed in reference 1, but there the rigid body modes were omitted. As the matter appears to raise some points of interest, a discussion of it seems to be called for. A similar analysis to that presented here may be applied to other unsupported, or partially supported systems, such as an unsupported plate.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 66 , Issue 618 , June 1962 , pp. 394 - 397
Copyright
Copyright © Royal Aeronautical Society 1962

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References

1.Bishop, R. E. D. and Johnson, D. C. (1960). The Mechanics of Vibration. 1st Edition, Cambridge University Press; see also Vibration Analysis Tables (1956).Google Scholar
2.Ker Wilson, W.Torsional Vibration Amplitudes at Non-Resonant Speeds, with Special Reference to the Interpretation of Trosiograph Records. Proc. Inst. Mech. Eng., Vol. 153, p. 83, 1945.Google Scholar
3.Bromwich, T. J. I'A (1926). An Introduction to the Theory of Infinite Series. 2nd Edition, Macmillan, London.Google Scholar
4.Bishop, R. E. D. (1953). The Normal Functions of Beam Vibration in Series Solutions of Static Problems. Journal of the Royal Aeronautical Society, p. 527, Vol. 57, August 1953.Google Scholar
5.Springfield, J. F. (1960). The Normal Rigid Body Functions of Free-Free and Free-Pinned Beams. Report No. EP-4422-116-60U. Research Laboratories for the Engineering Sciences, University of Virginia, August 1960.Google Scholar