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Tables of Characteristic Functions for Uniform Beams with Sliding Ends

Published online by Cambridge University Press:  28 July 2016

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

Tables of the characteristic functions of certain types of uniform beams were published by Young and Felgar in 1949. The functions concerned represent (to suitable scales) the principal modes of free flexural vibration, although their uses are far more extensive than is implied by this. Some of the uses to which they can be put are mentioned in Ref. 1 and others are discussed by Felgar and Bishop; they cover both statical and dynamical problems and relate to beams, plates and shells and include problems of elastic instability. In fact these functions can be used in series representations in the same way as circular functions are used in Fourier series.

One of the main uses to which these characteristic functions may be put does not appear to have been described in print, although the relevant formulae are quoted in Ref. 2. The functions can be used in vibration analysis to shorten calculations, sometimes leading to very considerable savings of labour.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 61 , Issue 559 , July 1957 , pp. 494 - 499
Copyright
Copyright © Royal Aeronautical Society 1957

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References

1. Young, Dana and Felgar, R. P. (1949). Tables of Characteristic Functions Representing Normal Modes of Vibration of a Beam. Engineering Research Bulletin No. 4913, Univ. of Texas, 1949.Google Scholar
2. Bishop, R. E. D. and Johnson, D. C. (1956). Vibration Analysis Tables. Cambridge University Press, 1956.Google Scholar
3. Felgar, R. P. (1950). Formulas for Integrals Containing Characteristic Functions of a Vibrating Beam. Circular No. 14, Bureau of Engineering Research, Univ. of Texas, 1950.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, 57, August, 1953.CrossRefGoogle Scholar
5. Bishop, R. E. D. (1956). The Vibration of Frames. Proceedings of the Institution of Mechanical Engineers 170, No. 29, 1956.Google Scholar
6. Duncan, W. J. (1947). Mechanical Admittances and their Applications to Oscillation Problems. R. & M. 2000, 1947.Google Scholar
7. Bishop, R. E. D. (1955). The Analysis of Vibrating Systems which Embody Beams in Flexure. Proceedings of the Institution of Mechanical Engineers 169, No. 51, 1955.Google Scholar