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Shock and Vibration
Volume 10, Issue 1, Pages 27-35

A Combination of Modal Synthesis and Subspace Iteration for an Efficient Algorithm for Modal Analysis within a FE-Code

M.W. Zehn

Otto-von-Guericke-Universität Magdeburg, Institut für Mechanik, Magdeburg, Germany

Received 1 October 2001; Revised 24 May 2002

Copyright © 2003 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.


Various well-known modal synthesis methods exist in the literature, which are all based upon certain assumptions for the relation of generalised modal co-ordinates with internal modal co-ordinates. If employed in a dynamical FE substructure/superelement technique the generalised modal co-ordinates are represented by the master degrees of freedom (DOF) of the master nodes of the substructure. To conduct FE modal analysis the modal synthesis method can be integrated to reduce the number of necessary master nodes or to ease the process of defining additional master points within the structure. The paper presents such a combined method, which can be integrated very efficiently and seamless into a special subspace eigenvalue problem solver with no need to alter the FE system matrices within the FE code. Accordingly, the merits of using the new algorithm are the easy implementation into a FE code, the less effort to carry out modal synthesis, and the versatility in dealing with superelements. The paper presents examples to illustrate the proper work of the algorithm proposed.