Simulation process of flexible multibody systems with non-modal model order reduction techniques

One important issue for the simulation of flexible multibody systems is the reduction of the flexible body’s degrees of freedom. In this work, nonmodal model reduction techniques for flexible multibody systems within the floating frame of reference framework are considered. While traditionally in the multibody community modal techniques in many different forms are used, here other methods from system dynamics and mathematics are in the focus. For the reduction process, finite element data and user inputs are necessary. Prior to the reduction process, the user first needs to choose boundary conditions fitting the chosen reference frame before defining the appropriate in- and outputs. In this work, four different possibilities of modeling appropriate interface points to reduce the number of inputs and outputs are presented. The main model reduction techniques to be considered in this context are moment-matching by projection on Krylov-subspaces, singular vaule decomposition (SVD)-based reduction techniques and combinations of those which are also compared to traditional modal approaches. All these reduction techniques are implemented in the model order reduction code Morembs. In addition, an error estimator for Krylov-subspace methods exists and an a-priori error bound can be calculated if frequency weighted Gramian matrices are used for the reduction process. This allows a fully automated reduction process. We evaluate and compare these methods in the frequency as well as in the time domain by reducing the flexible degrees of freedom of a rack used for active vibration damping of a scanning tunneling microscope.