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On the Iterative Solution of Semidefinite Eigenvalue Problems

Published online by Cambridge University Press:  04 July 2016

R. Craig Jr.  and
M. C. C. Bampton
R. Craig Jr.
Affiliation:
The Boeing Company, Seattle, Washington
M. C. C. Bampton
Affiliation:
The Boeing Company, Seattle, Washington
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Extract

The free vibration of an elastic system represented by a finite number of degrees of freedom leads to the problem of determining the eigenvectors and eigenvalues of the equation

where K and M are symmetric matrices of order n, and x is an n-dimensional vector of generalised co-ordinates. Under certain circumstances as, for example, when the matrices are of large order and only a few eigenvalues and eigenvectors are required, it is preferable to use an iterative procedure for solving eqn. (1) or an equation equivalent to it. However, when the system has one or more rigid-body degrees of freedom the stiffness matrix K is singular. This precludes an iterative solution.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 75 , Issue 724 , April 1971 , pp. 287 - 290
Copyright
Copyright © Royal Aeronautical Society 1971 

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