Exact model reduction by a slow–fast decomposition of nonlinear mechanical systems
Open access
Datum
2017-10Typ
- Journal Article
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. Mehr anzeigen
Persistenter Link
https://doi.org/10.3929/ethz-b-000234714Publikationsstatus
publishedExterne Links
Zeitschrift / Serie
Nonlinear DynamicsBand
Seiten / Artikelnummer
Verlag
SpringerThema
Model reduction; Invariant manifolds; Slow–fast systemsOrganisationseinheit
03973 - Haller, George / Haller, George
Anmerkungen
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.