Generalization of the Craig-Bampton CMS procedure for general damping

The dynamic analysis of structural systems should be based very often on systems with a very limited number of degrees of freedom. This is for example the case when there are llull llueallble~ 1 I I V W L V b U LJL W l bl1 C l l b I I I 2 b l I ~ L I I S C L " S I ILl"U"1 11 " t . " yluJ u ""IIIIUI %VI" 1 strategy. To reduce the order of the system (the number of degrees of freedom) methodologies have been developed based on fysical understanding, the so-called Component Mode Synthesis (CMS) techniques. An important step in the development of these procedures is the assumption that the (sub)systems should be weakly damped or at least be based o11 so-called proportional or Rayleigh damping. In many systems this will not be so such as in the case of rotorbearing systems or with models for mechatronic systems. In that case a formalism based on real vibration modes will give very bad results. In this report a well-known CMS procedure (the Craig-Bampton CMS technique) will be generalized for the case of general damping leading to a transformation based on leftand right staticand dynamic modes (complex Ritz-vectors). The fysical meaning of these modes will be illustrated and some examples will be presented and discussed showing the potential of this extension of the CMS procedure. -,--i:,Ac: : n = r n k a A Alx x r \ n n thn m tham tip 1 mnA-1 h 2 ~ tn n l c a ~ r 9 rentrnl rnlp iD a ce~trgl