Title: Using the Neumann series expansion for assembling Reduced Order Models
Authors: Nasisi, Salvatore
Valášek, Michael
Vampola, Tomáš
Citation: Applied and Computational Mechanics. 2014, vol. 8, no. 1, p. 63-74.
Issue Date: 2014
Publisher: University of West Bohemia
Document type: článek
URI: http://www.kme.zcu.cz/acm/acm/article/view/246/276
ISSN: 2336-1182 (Online)
1802-680X (Print)
Keywords: numerické modelování;simulace dynamických soustav;Neumanova řada;model redukovaného řádu;analýza konečných prvků;lidský vokální trakt
Keywords in different language: numerical modelling;dynamic simulation;Neumann series;reduced order model;finite element analysis;human vocal tract
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.
Rights: © 2014 University of West Bohemia. All rights reserved.
Appears in Collections:Volume 8, number 1 (2014)
Volume 8, number 1 (2014)

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