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Techical Notes

The Kron methodology and practical algorithms for eigenvalue, sensitivity and response analyses of large scale structural systems

Published online by Cambridge University Press:  04 July 2016

A. Simpson*
Affiliation:
University of Bristol

Extract

In this paper, the various facets of Kron’s eigenvalue method which have been developed over the past decade by the present writer are drawn together for review purposes and to provide solution algorithms for large scale eigenvalue and response problems which arise, for example, from the need to study large order finite element models in the frequency analysis of ship equipment raft structures. Also included are considerations of eigenvalue sensitivities which are found to be readily calculable by means of simple modification of the basic eigenvalue method. These sensitivities are of importance in the study of vibration transmission paths and hence in the design and positioning of optimum anti-vibration mountings (AVMs).

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society 1980 

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References

1. Kron, G. Diakoptics. MacDonald & Company, London, 1963.Google Scholar
2. Simpson, A. and Tabarrok, B. On Kron’s eigenvalue procedure and related methods of frequency analysis. QJ Mech App Math, XXI, pp 139, 1968.Google Scholar
3. Simpson, A. Kron’s method: A consequence of the minimisation of the primitive Lagrangian in the presence of displacement constraints. J Sound and Vibration, 27(3), pp 377386, 1973.Google Scholar
4. Simpson, A. A generalisation of Kron’s eigenvalue method. J Sound and Vibration, 26(1), pp 129139, 1973.Google Scholar
5. Simpson, A. Scanning Kron’s determinant. QJ Mech App Math, XXVII, pt 1, pp 2743, 1974.Google Scholar
6. Haywood, J. Private communication. September 1978.Google Scholar
7. Simpson, A. Eigenvalue and vector sensitivities in Kron’s method. J Sound and Vibration, 31(1), pp 7387, 1973.Google Scholar
8. Simpson, A. Kron’s method: an algorithm for the eigen value analysis of large-scale structural systems. ARC R & M No 3733, HMSO, London, 1973.Google Scholar
9. Wittrick, W. H. and Williams, F. W. A general algorithm for computing natural frequencies of elastic structures. QJ Mech App Math, XXIV, pt 3, pp 263284, 1971.Google Scholar
10. Lancaster, P. A generalised Rayleigh quotient iteration for Lambda matrices. Arch Rational Mech Anal, 8, pp 309322, 1961.Google Scholar
11. MacKenzie, I. W. Computational methods for the eigen value analysis of large structures by component synthesis. PhD Thesis, Dept of Aeronautics, Imperial College, London, 1974.Google Scholar