Dual Craig-Bampton Method With Reduction Of Interface Coordinates

Dynamic substructuring techniques divide large models into substructures whereby each substructure is reduced and then assembled into a reduced model of low order which approximates the behaviour of the original model. Thereby the boundary degrees of freedom (degrees of freedom shared with adjacent substructures) are kept and only the internal degrees of freedom of each substructure are reduced to a small number of generalized coordinates.If the interfaces between the substructures are large or if many substructures are used, the number of interface degrees of freedom is high. In that case the boundary degrees of freedom form a large subset of the generalized coordinates of the reduced substructures, which often is not necessary for the accurate description of the overall dynamics, but is present just for the interface assembly. To overcome this drawback and get a reduced model of low order, the interface degrees of freedom have to be reduced as well.In this contribution, the reduction of interface coordinates for the dual Craig-Bampton method is demonstrated. The dual Craig-Bampton method employs free-interface vibration modes together with attachment modes to build the reduction bases of the substructures and assembles the substructures using interface forces (dual assembly). Considering the interface problem, a static reduction (Guyan reduction) of the interface coordinates is derived to obtain interface modes for the approximation of the interface degrees of freedom. Further, a reduction of interface coordinates using interface normal modes is demonstrated. The approximation accuracy of the different interface reduction approaches is evaluated. Focus will be directed to the influence on the negative eigenvalues of the reduced system which are intrinsic to the dual Craig-Bampton method. The proposed approach will be illustrated on examples where interface modes can be visualized in order to analyze their influence on the approximation quality of the reduced system.