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Author:
Troeng, Tor (Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics) (Computational Mathematics Laboratory)
Title:
Frequency Response Analysis using Component Mode Synthesis
Department:
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics
Publication type:
Student thesis
Language:
English
Level:
Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE credits
Educational program:
Civilingenjörsprogrammet i teknisk fysik
Undergraduate subject:
Examensarbete i teknisk fysik
Uppsok:
Physics, Chemistry, Mathematics
Pages:
39
Year of publ.:
2010
URI:
urn:nbn:se:umu:diva-37809
Permanent link:
http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-37809
Keywords(sv) :
Component Mode Syntesis, model reduction, frequency response analysis
Abstract(en) :

Solutions to physical problems described by Differential Equationson complex domains are in except for special cases almost impossibleto find. This turns our interest toward numerical approaches. Sincethe size of the numerical models tends to be very large when handlingcomplex problems, the area of model reduction is always a hot topic. Inthis report we look into a model reduction method called ComponentMode Synthesis. This can be described as dividing a large and complexdomain into smaller and more manageable ones. On each of thesesubdomains, we solve an eigenvalue problem and use the eigenvectorsas a reduced basis. Depending on the required accuracy we mightwant to use many or few modes in each subdomain, this opens for anadaptive selection of which subdomains that affects the solution most.We cover two numerical examples where we solve Helmholtz equationin a linear elastic problem. The first example is a truss and the othera gear wheel. In both examples we use an adaptive algorithm to refinethe reduced basis and compare the results with a uniform refinementand with a classic model reduction method called Modal Analysis. Wealso introduce a new approach when computing the coupling modesonly on the adjacent subdomains.

Supervisor:
Larson, Mats, Professor (Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics)
Examiner:
Holme, Petter, Universitetslektor (Umeå University, Faculty of Science and Technology, Department of Physics)
Available from:
2010-11-15
Created:
2010-11-15
Last updated:
2010-11-15
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