Exact model reduction by a slow–fast decomposition of nonlinear mechanical systems
OPEN ACCESS
Loading...
Author / Producer
Date
2017-10
Publication Type
Journal Article
ETH Bibliography
yes
Citations
Altmetric
OPEN ACCESS
Data
Rights / License
Abstract
We derive conditions under which a general nonlinear mechanical system can be exactly reduced to a lower-dimensional model that involves only the softer degrees of freedom. This slow–fast decomposition (SFD) enslaves exponentially fast the stiffer degrees of freedom to the softer ones as all oscillations converge to the reduced model defined on a slow manifold. We obtain an expression for the domain boundary beyond which the reduced model ceases to be relevant due to a generic loss of stability of the slow manifold. We also find that near equilibria, the SFD gives a mathematical justification for two modal reduction methods used in structural dynamics: static condensation and modal derivatives. These formal reduction procedures, however, are also found to return incorrect results when the SFD conditions do not hold. We illustrate all these results on mechanical examples.
Permanent link
Publication status
published
External links
Editor
Book title
Journal / series
Volume
90 (1)
Pages / Article No.
617 - 647
Publisher
Springer
Event
Edition / version
Methods
Software
Geographic location
Date collected
Date created
Subject
Model reduction; Invariant manifolds; Slow–fast systems
Organisational unit
03973 - Haller, George / Haller, George
Notes
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.