Hostname: page-component-7479d7b7d-767nl Total loading time: 0 Render date: 2024-07-11T16:21:59.552Z Has data issue: false hasContentIssue false
  • English
  • Français

An Improved Method of Matrix Displacement Analysis in Vibration Problems

Published online by Cambridge University Press:  07 June 2016

W. Carnegie ,
J. Thomas  and
E. Dokumaci
W. Carnegie
Affiliation:
University of Surrey
J. Thomas
Affiliation:
University of Surrey
E. Dokumaci
Affiliation:
University of Surrey
Get access

Summary

This paper presents a method with strong convergence characteristics for the determination of eigenvalues and eigenvectors of continuous systems. The limitation on the number of undetermined constants in the displacement functions introduced by the conditions at the ends of a segment is removed by the introduction of points of freedom within the segment.

This improves the convergence of eigenvalues and eigenvectors very rapidly with the number of segments, especially in torsional vibration problems where the convergence with the usual Matrix Displacement method is very poor. The continuous medium is successively approximated by the use of sub-systems with finite numbers of degrees of freedom. The principles upon which the method is based and the convergence of the results are discussed and illustrated by a series of examples.

Type
Research Article
Information
Aeronautical Quarterly , Volume 20 , Issue 4 , November 1969 , pp. 321 - 332
Copyright
Copyright © Royal Aeronautical Society. 1964

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. Pestel, E. C. and Leckie, F. A. Matrix methods in elastomechanics. McGraw-Hill, 1963.Google Scholar
2. Timoshenko, S. Vibration problems in engineering, 3rd Edition. Van Nostrand, 1955.Google Scholar
3. Fox, L. An introduction to numerical linear algebra. Monographs on Numerical Analysis, Clarendon Press, Oxford, 1964.Google Scholar
4. Aitken, A. C. Determinants and matrices. Oliver & Boyd, 1956.Google Scholar
5. Leckie, F. A. and Lindberg, G. M. The effect of lumped parameters on beam frequencies. Aeronautical Quarterly, p. 224, August 1963.Google Scholar
6. Lindberg, G. M. Vibration of non-uniform beams. Aeronautical Quarterly, p. 387, November 1963.Google Scholar
7. Huang, T. C. Tables of eigenvalues and charts of modifying quotients for frequencies and normal modes of beam vibration. Bulletin of the Florida Engineering and Industrial Experimental Station, University of Florida, 1964.Google Scholar