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Which are the important modes of a subsystem?
Author(s) -
Givoli Dan,
Barbone Paul E.,
Patlashenko Igor
Publication year - 2004
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.935
Subject(s) - substructure , modal , discretization , reduction (mathematics) , degrees of freedom (physics and chemistry) , norm (philosophy) , coupling (piping) , simple (philosophy) , mathematics , computer science , physics , mathematical analysis , engineering , geometry , structural engineering , quantum mechanics , mechanical engineering , philosophy , chemistry , epistemology , political science , law , polymer chemistry
A linearly behaving vibrational substructure (or more generally a linear dynamic subsystem) attached to a main structure (or a main dynamic system) is considered. After discretization, the substructure is represented by a finite, typically large, number of degrees of freedom, N s and hence also by N S eigenmodes. In order to reduce the computational effort, it is common to apply ‘modal reduction’ to the subsystem such that only N r modes out of the total number of N S modes are retained, where N r ≪ N s . The following question then arises: ‘ Which N r modes should be retained?’ In structural dynamics, it is traditional to retain those modes associated with the lowest frequencies. In this paper, the question is answered by solving an appropriate optimization problem. The most important modes of the subsystem are shown to be those whose coupling matrices, which are defined in a particular way, have the highest norm. This leads to a simple and effective algorithm for optimal modal reduction. The new criterion for ‘modal importance’ is explained both mathematically and physically, and is demonstrated by numerical examples. Copyright © 2004 John Wiley & Sons, Ltd.