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Improving the reduction process in flexible multibody dynamics by the use of 2nd order position Gramian matrices

Joerg Fehr, Peter Eberhard, Michael Lehner
An important issue within the field of flexible multibody dynamics is the reduction of the flexible body's degrees of freedom. By using frequency weighted Gramian matrix
based reduction techniques, the distribution of the loads is taken into account a priori. Furthermore, an energy interpretation of the reduction procedure and
error bounds in the frequency domain are available. This allows a fully automated reduction process. For numerical reasons, the dominant eigen vectors of the Gramian matrix have to be approximated. Within this paper, two different methods are shown. A numerical example demonstrates the approximation
capability in the frequency and time domain.
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