Refining characteristic constraint modes of component mode synthesis with residual modal flexibility

The Craig–Bampton component mode synthesis uses interface constraint modes and deformed substructural modes for model reduction. In some instances, it may be of interest to realize additional reductions after reducing the substructural degrees of freedom, and this is generally done by the reduction of the interface degrees of freedom. The characteristic constraint modes were developed to achieve the interface reduction of the Craig–Bampton method. However, the interface reduction process can compromise accuracy because using a small number of characteristic constraint modes, focusing on low-frequency range, may interrupt vibration energy transmission between substructures in relatively mid and/or high-frequency ranges. Based on this motivation, an improved reduction technique of the interface regions is introduced for refining characteristic constraint modes. Considering a residual modal effect is the main point of refinement of the characteristic constraint modes. The modified characteristic constraint modes and fixed-interface normal modes computed by a newly derived formulation with residual modal flexibility can represent the characteristics of interface motion better than the conventional constraint modes. Consequently, the improved transformation matrix may facilitate vibration energy transmission between substructures. Numerical experiments indicate that the proposed refinement method can complement the conventional method in terms of accuracy, and the refined constraint and fixed interface normal modes are better representations of the original mode shapes than conventional approaches are.