Generalized Craig-Bampton Method Using Robin Boundary Conditions

Dynamic substructuring is an efficient way to reduce the size and to analyse the dynamical behaviour of large models. The most popular approach is a fixed-interface method, the Craig-Bampton method (CBM, 1968), which is based on fixed-interface vibration modes and interface constraint modes. On the other hand, free-interface methods employing free-interface vibration modes together with attachment modes are also used, e.g. MacNeal's method (1971) and Rubin's method (1975). The dual Craig-Bampton method (DCBM, 2004 proposed by Rixen) uses the same ingredients as the methods of MacNeal and Rubin, but assembles the substructures using interface forces (dual assembly). The mixed Craig-Bampton (2011, proposed by Voormeeren et al.) method can deal with a mix of CBM and DCBM reduced substructures but each substructure has to be reduced either with the CBM or with the DCBM. The CBM and DCBM are using interface conditions which are extremal cases of the real connecting conditions. We want to generalize the CBM and the DCBM interface conditions to substructures connected via Robin boundary conditions. The CBM and the DCBM are then the two extreme cases of this generalized formulation, either having infinite stiffness or zero stiffness on the interface. Although reduction bases using interface loading were proposed in the past by Chandler and Tinker (1997), we want to combine in a coherent manner the way the bases are computed at substructure level and the way the assembly is formulated, hoping to construct a quasi-diagonal form for the reduced system.