INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2007; 69:948–977 Published online 31 July 2006 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/nme.1795 The global modal parameterization for non-linear model-order reduction in flexible multibody dynamics Olivier Br¨ uls 1, ∗, † , Pierre Duysinx 2, ‡ and Jean-Claude Golinval 1, § 1 LTAS-Vibrations et Identification des Structures, University of Li` ege, Chemin des Chevreuils, 1, B52/3, B-4000 Li` ege, Belgium 2 LTAS-Ing´ enierie des v´ ehicules terrestres, University of Li` ege, Chemin des Chevreuils, 1, B52/3, B-4000 Li` ege, Belgium SUMMARY 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. Received 12 January 2006; Revised 6 May 2006; Accepted 7 May 2006 KEY WORDS: model reduction; component-mode technique; non-linear projection; flexible multibody dynamics; parallel mechanisms ∗ Correspondence to: Olivier Br¨ uls, LTAS-Vibrations et Identification des Structures, University of Li` ege, Chemin des Chevreuils, 1, B52/3, B-4000 Li` ege, Belgium. † E-mail: o.bruls@ulg.ac.be ‡ E-mail: p.duysinx@ulg.ac.be § E-mail: jc.golinval@ulg.ac.be Contract/grant sponsor: Belgian National Fund for Scientific Research Copyright 2006 John Wiley & Sons, Ltd.