Using the Neumann series expansion for assembling Reduced Order Models
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Date issued
2014
Journal Title
Journal ISSN
Volume Title
Publisher
University of West Bohemia
Abstract
An efficient method to remove the limitation in selecting the master degrees of freedom in a finite element model
by means of a model order reduction is presented. A ma
jor difficulty of the Guyan reduction and IRS method
(Improved Reduced System) is represented by the need of
appropriately select the master and slave degrees of
freedom for the rate of convergence to be high. This study approaches the above limitation by using a particular arrangement of the rows and columns of the assembled matrices
K and M and employing a combination between
the IRS method and a variant of the analytical selection of masters presented in (Shah, V. N., Raymund, M., Analytical selection of masters for the reduced eigenvalue problem, International Journal for Numerical Methods in Engineering 18 (1) 1982) in case first lowest frequencies had to be sought. One of the most significant characteristics of the approach is the use of the Neumann series expansion that motivates this particular arrangement of the
matrices’ entries. The method shows a higher rate of convergence when compared to the standard IRS and very accurate results for the lowest reduced frequencies. To show the effectiveness of the proposed method two testing structures and the human vocal tract model employed in (Vampola, T., Horacek, J., Svec, J. G., FE modeling of human vocal tract acoustics. Part I: Prodution of Czech vowels, Acta Acustica United with Acustica 94 (3) 2008)
are presented.
Description
Subject(s)
numerické modelování, simulace dynamických soustav, Neumanova řada, model redukovaného řádu, analýza konečných prvků, lidský vokální trakt
Citation
Applied and Computational Mechanics. 2014, vol. 8, no. 1, p. 63-74.