Hostname: page-component-7479d7b7d-m9pkr Total loading time: 0 Render date: 2024-07-11T16:19:33.667Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-Linear Vibrations of Rotating Cantilever Beams

Published online by Cambridge University Press:  04 July 2016

J. S. Rao  and
W. Carnegie
J. S. Rao
Affiliation:
Indian Institute of Technology, Kharagpur, India, at present Commonwealth Fellow, University of Surrey
W. Carnegie
Affiliation:
University of Surrey
Get access Rights & Permissions [Opens in a new window]

Extract

The problem of flexural vibration of a rotating cantilever blade is non-linear when the vibration takes place in a plane other than perpendicular to the plane of rotation. The non-linearity arises from the effects of Coriolis accelerations due to the rotation of the blade mounted on the periphery of a disc. Lo and Renbarger neglected the non-linear terms in their investigation and arrived at a simple relation for the frequency of vibration in terms of the stationary frequency of the beam, the rotating speed and the orientation of the plane of vibration. Lo in his analysis simplified the non-linear problem by assuming the blade to be rigid everywhere excepting at the root and presented the solution in a phase plane. Isakson and Eisley have considered a similar model to determine the natural frequencies in coupled bending and torsion of twisted rotating cantilever blades.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 74 , Issue 710 , February 1970 , pp. 161 - 165
Copyright
Copyright © Royal Aeronautical Society 1970 

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. Lo, H. and Renbarger, J. Bending Vibrations of a Rotating Beam. First US National Congress of Applied Mechanics, p 75, 1952.Google Scholar
2. Lo, H. A Non-Linear Problem in the Bending Vibration of a Rotating Beam. Journal of Applied Mechanics, Trans ASME, Vol 19, p 461, 1952.Google Scholar
3. Isakson, G. and Eisley, J. G. Natural Frequencies in Coupled Bending and Torsion of Twisted Rotating and Non-Rotating Blades. NASA Report prepared under Grant No NSG-27-59 by University of Michigan, Ann Arbor, Michigan.Google Scholar
4. Carnegie, W. Vibrations of Rotating Cantilever Blading: Theoretical Approaches to the Frequency Problem Based on Energy Methods. Journal of Mechanical Engineering Sciences, Vol 1, No 3, p 235, 1959.Google Scholar
5. Schilhansl, M. J. Bending Frequency of a Rotating Cantilever Beam. Journal of Applied Mechanics, Trans ASME, Vol 25, p 28, 1958.Google Scholar
6. Carnegie, W., Stirling, C. and Fleming, , —. Vibration Characteristics of Turbine Blading Under Rotation. Results of an Initial Investigation and Details of a High Speed Test Installation. IMechE, London. Paper No 32 of Applied Mechanics Convention held at Cambridge during 4th-6th April 1966.Google Scholar
7. Carnegie, W. The Application of the Variational Method to Derive the Equations of Motion of Vibrating Cantilever Blading under Rotation. Bull Mechanical Engineering Education, Vol 6, p 29, 1967.Google Scholar
8. Jacobsen, K. and Ayre, R. Engineering Vibrations, McGraw Hill Book Company, 1958.Google Scholar