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The global modal parameterization for non‐linear model‐order reduction in flexible multibody dynamics
Author(s) -
Brüls Olivier,
Duysinx Pierre,
Golinval JeanClaude
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1795
Subject(s) - reduction (mathematics) , multibody system , submanifold , modal , subspace topology , holonomic constraints , model order reduction , ordinary differential equation , ode , projection (relational algebra) , equations of motion , control theory (sociology) , mathematics , computer science , differential equation , mathematical analysis , classical mechanics , algorithm , physics , geometry , chemistry , control (management) , artificial intelligence , polymer chemistry
In flexible multibody dynamics, advanced modelling methods lead to high‐order non‐linear differential‐algebraic equations (DAEs). The development of model reduction techniques is motivated by control design problems, for which compact ordinary differential equations (ODEs) in closed‐form are desirable. In a linear framework, reduction techniques classically rely on a projection of the dynamics onto a linear subspace. In flexible multibody dynamics, we propose to project the dynamics onto a submanifold of the configuration space, which allows to eliminate the non‐linear holonomic constraints and to preserve the Lagrangian structure. The construction of this submanifold follows from the definition of a global modal parameterization (GMP): the motion of the assembled mechanism is described in terms of rigid and flexible modes, which are configuration‐dependent. The numerical reduction procedure is presented, and an approximation strategy is also implemented in order to build a closed‐form expression of the reduced model in the configuration space. Numerical and experimental results illustrate the relevance of this approach. Copyright © 2006 John Wiley & Sons, Ltd.