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A Symmetry Property of Transfer Matrices

Published online by Cambridge University Press:  04 July 2016

D. S. Whitehead
D. S. Whitehead*
Affiliation:
Cambridge University Engineering Laboratory
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Extract

The transfer matrix method of vibration analysis is widely used for the calculation of the natural frequencies of turbo-generator rotors, and of propeller blades, axial compressor blades, turbine blades, and helicopter rotors. A comprehensive account of the method has been given by Pestel and Leckie. The basis of the method is to deine a state vector, which gives all the generalised displacements and forces at a given cross-section of the system. The state vector at one cross-section is then related to the state vector at a neighbouring cross-section by means of a transfer matrix. It is found that, by a suitable choice of the order and signs of the elements of the state vector, the transfer matrix can in many cases be made symmetrical about the secondary diagonal; that is the diagonal running from the top right corner to the bottom left corner of the matrix and is also often called the “cross diagonal”.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 73 , Issue 704 , August 1969 , pp. 686 - 688
Copyright
Copyright © Royal Aeronautical Society 1969 

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References

1. Pestel, E. C., and Leckie, F. A. Matrix Methods in Elastomechanics. McGraw-Hill, 1963.Google Scholar
2. Bishop, R. E. D. and Johnson, D. C. The Mechanics of Vibration. Cambridge University Press, 1960.Google Scholar