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Vibration Analysis Formulations for Optimisation

Published online by Cambridge University Press:  04 July 2016

M. C. C. Bampton
M. C. C. Bampton*
Affiliation:
The Boeing Company, Seattle, Wash
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Extract

In most dynamic analyses, it is customary to use a coarser mass idealisation than structural idealisation especially if stresses are to be involved. Compatibility between the stiffness matrix and the smaller mass matrix M is achieved by reduction of the stiffness matrix. Guyan has shown that the reduction is equivalent to a transformation of the original matrix K :

where KR is the reduced stiffness matrix and T is the transformation matrix which contains stiffness terms.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 74 , Issue 716 , August 1970 , pp. 676
Copyright
Copyright © Royal Aeronautical Society 1970 

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References

1. Guyan, R. J. Reduction of Stiffness and Mass Matrices. AIAA Journal, February 1965.Google Scholar
2. Scanlon, R. H. and Rosenbaum, R. Aircraft Vibration and Flutter. Macmillan, 1951.Google Scholar
3. Fox, R. L. and Kapoor, M. P. Rate of Change of Eigen values and Eigenvectors. AIAA Journal, December 1968.Google Scholar