The global modal parameterization for non-linear model-order reduction in flexible multibody dynamics

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 (c) 2006 John Wiley & Sons, Ltd.