Generalized Craig-Bampton Method Using Robin Boundary Conditions

Abstract

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) (Craig and Bampton, AIAA J 6:1313–1319, 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 (MacNeal, Comput Struct 1:581–601, 1971) and Rubin’s method (Rubin, AIAA J 13:995–1006, 1975). The dual Craig-Bampton method (DCBM) (Rixen, Comput Appl Math 168:383–391, 2004) uses the same ingredients as the methods of MacNeal and Rubin, but assembles the substructures using interface forces (dual assembly). The mixed Craig-Bampton method can deal with a mix of CBMand DCBMreduced substructures but each substructure has to be reduced either with the CBMor with the DCBM (Voormeeren et al., AIAA J 49:1010–1020, 2011). The CBMand DCBMare using interface conditions which are extremal cases of the real connecting conditions. We want to generalize the CBMand the DCBMinterface conditions to substructures connected via Robin boundary conditions. The CBMand the DCBMare 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 (Chandler and Tinker, Proceedings of the AIAA Structures, Structural Dynamics and Materials Conference, Kissimmee, FL, pp 93–103, 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.