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Shock and Vibration
Volume 3, Issue 4, Pages 287-292

Accelerated Solutions for Transcendental Stiffness Matrix Eigenproblems

F.W. Williams and D. Kennedy

Cardiff School of Engineering, University of Wales Cardiff, P.O. Box 917, Cardiff CF2 1XH, UK

Received 16 January 1995; Accepted 2 January 1996

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This article outlines many existing and forthcoming methods that can be used alone, or in various combinations, to accelerate the solutions of the transcendental stiffness matrix eigenproblems that arise when the stiffness matrix is assembled from exact member stiffnesses, which are obtained by solving the member differential equations exactly. Thus distributed member mass and/or the flexural effect of axial loading are incorporated exactly, and the solutions are the natural frequencies for vibration problems or the critical load factors for buckling problems.