On the use of moment-matching to build reduced order models in flexible multibody dynamics

An important issue in the field of flexible multibody dynamics is the reduction of the flexible body's degrees of freedom. For this purpose, often modal reduction through projection onto a subspace spanned by some dominant eigenvectors is used. However, as in this method the dynamical boundary conditions are not taken into account, a large number of eigenmodes is required to obtain a good approximation and also the selection of the dominant modes can be quite difficult. Therefore, the authors propose an approach based on accounting for the flexible body as an input-output system in the frequency domain. The reduced order model is generated by imposing a set of interpolation conditions concerning the values and derivatives of the system's transfer function in a predefined frequency range. This procedure is known as moment-matching and can be realised through projection onto so-called Krylov-subspaces. As this technique allows the incorporation of the frequency content and the spatial distribution of the loads, in the chosen frequency range more accurate reduced order models can be obtained compared to other model reduction techniques available in structural mechanics. The calculation of the Krylov-subspaces can be implemented very efficiently, using the Arnoldi or Lanczos procedure in connection with sparse matrix techniques. The capability of the proposed technique is demonstrated by means of a numerical example.