Proceedings of ACOMEN2008 Fourth International Conference on Advanced Computational Methods in Engineering
Advanced Computational Methods in Engineering edition:4 location:Liège, Belgium date:26-28 May 2008
The equations of motion for a mechanical system generally take the form of a set of differentialalgebraic
equations. The algebraic constraints and the often non-linear character of this mathematical
description generally lead to high ratios of simulation time over simulated time. However, in
applications such as real-time simulation, model predictive control or condition monitoring the simulation
should be performed real-time. Current simulation techniques cannot meet this demand for today’s
The Global Modal Parametrization is a systematic model order reduction technique with promising
prospects to reduce simulation times considerably. By performing an eigenvector analysis at strategically
chosen points in the configuration space, i.e. the space of possible configurations, before actual
simulation, the computational workload during simulation can be reduced considerably.
The nature of the degrees of freedom left used in the reduced model is vital for the stability and the
accuracy of the simulation. One can choose to use modal coordinates, or to retain physical coordinates.
The use of modal coordinates is hindered by the non-linear character of the set of equations. Possibilities
to circumvent this problem are considered. In case of retaining physical degrees of freedom, the choice
of these degrees of freedom is crucial for the conditioning of the reduced set of equations. In the limit
case, a change in the set of retained degrees of freedom is necessary to avoid singularities. A systematic
strategy to change the set of retained degrees of freedom is developped to avoid singularities and to
improve the conditioning of the reduced set of equations. Furthermore, the effect of the approximation
error on the configuration space and the dynamical properties of the system is investigated.