Hostname: page-component-848d4c4894-pftt2 Total loading time: 0 Render date: 2024-05-17T18:17:40.931Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Integrals Relating to the Vibration of a Cantilever Beam and Approximation for the Effect of Taper on Overtone Frequencies

Published online by Cambridge University Press:  07 June 2016

A. I. Martin
Get access

Summary

In the investigation of approximate numerical values of overtone frequencies of a turbine blade it is desirable to know formulae for certain integrals of the modes of vibration of an ordinary cantilever beam. The first object of this paper is to obtain such formulae and to arrange them in tabulated form. By proceeding along the lines of the calculus of perturbations, these results may then be used to obtain new formulae which give second order approximations for the effects of uniform breadth and thickness tapers on the overtone frequencies. The theory gives good agreement with experiments for tapers which do not exceed about 0·5, which is present-day practice for turbine blading.

Type
Research Article
Information
Aeronautical Quarterly , Volume 7 , Issue 2 , May 1956 , pp. 109 - 124
Copyright
Copyright © Royal Aeronautical Society. 1955

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Biezeno, C. B. and Grammel, R. Engineering Dynamics, Blackie, Vol. III, 1954.Google Scholar
2. Kirchhoff, G. Uber die Transversalschwingungen eines Stabes von veränderlichen Querschnitt. Annalen der Physik und Chemie,Vol. X, p. 501, 1880.Google Scholar
3. Meyer, F. Mathematische Theorie der Transversalen Schwingungen eines Stabes von veränderlichen Querschnitt. Annalen der Physik und Chemie, Vol. XXXIII, p. 661, 1888.CrossRefGoogle Scholar
4. Ward, P. F. The Transverse Vibration of a Rod of Varying Cross Section. Phil. Mag. (6), Vol. 25, p. 85, 1913.CrossRefGoogle Scholar
5. Wrinch, D. M. The Lateral Vibrations of Bars of Conical Type. Proc. Roy. Soc. A, Vol. 101, p. 493, 1922.Google Scholar