Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-27T09:49:39.389Z Has data issue: false hasContentIssue false
  • English
  • Français

Vibration Characteristics of Straight Blades of Asymmetrical Aerofoil Cross-Section

Published online by Cambridge University Press:  07 June 2016

W. Carnegie  and
B. Dawson
W. Carnegie
Affiliation:
University of Surrey
B. Dawson
Affiliation:
University of Surrey
Get access

Summary

Theoretical and experimental natural frequencies and modal shapes up to the fifth mode of vibration are given for a straight blade of asymmetrical aerofoil cross-section. The theoretical procedure consists essentially of transforming the differential equations of motion into a set of simultaneous first-order equations and solving them by a step-by-step finite difference procedure. The natural frequency values are compared with results obtained by an analytical solution and with standard solutions for certain special cases. Good agreement is shown to exist between the theoretical results for the various methods presented. The equations of motion are dependent upon the coordinates of the axis of the centre of flexure of the beam relative to the centroidal axis. The effect of variations of the centre of flexure coordinates upon the frequencies and modal shapes is shown for a limited range of coordinate values. Comparison is made between the theoretical natural frequencies and modal shapes and corresponding results obtained by experiment.

Type
Research Article
Information
Aeronautical Quarterly , Volume 20 , Issue 2 , May 1969 , pp. 178 - 190
Copyright
Copyright © Royal Aeronautical Society. 1969

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. Carnegie, W., Dawson, B. and Thomas, J. Vibration characteristics of cantilever blading. Proceedings, Institution of Mechanical Engineers, Vol. 180, Part 31, 1966.Google Scholar
2. Duncan, W. J. Torsion and flexure of cylinders and tubes. ARC R & M 1444, 1932.Google Scholar
3. Carnegie, W. Experimental determination of the centre of flexure and centre of torsion coordinates of an asymmetrical aerofoil cross-section. Journal of Mechanical Engineering Science, Vol. I, No. 3, 1959.Google Scholar
4. Lance, G. N. Numerical methods for high speed computers. Iliffe, London, 1960.Google Scholar
5. Carr, J. W. Error bounds for the Runge-Kutta single-step integration process. Journal, Association for Computer Machinery, Vol. V, p. 39, 1958.CrossRefGoogle Scholar
6. Diprima, R. C. and Handelman, G. H. Vibrations of twisted beams. Quarterly of Applied Mathematics, Vol. XII, No. 3, p. 241, 1954.CrossRefGoogle Scholar
7. Carnegie, W. Vibration of pre-twisted cantilever blading. Proceedings, Institution of Mechanical Engineers, Vol. 173, No. 12, 1959.CrossRefGoogle Scholar
8. Dawson, B. Ph.D. Thesis, University of London, 1967.Google Scholar