A strategy to stabilize the transient analysis and increase the approximation accuracy of dual Craig-Bampton reduced systems

We consider reduced systems obtained by a dual Craig-Bampton reduction, which are always unstable, and propose a modification of such systems allowing for stable transient analysis. Additionally, we use modal truncation augmentation to improve the approximation accuracy of such systems. The dual Craig-Bampton method for the reduction and successive coupling of dynamic systems employs free interface vibration modes, attachment modes, and rigid body modes to build the reduction bases of the substructures, but assembles the substructures using interface forces. Thereby, the interface kinematic conditions are transformed, enforcing only weak interface compatibility between the substructures and allowing for incompatibilities associated with the interface degrees of freedom. As a result, the dual Craig-Bampton reduced system has always as many negative eigenvalues as interface coupling conditions. The reduced system is unstable, rendering a straightforward time integration of the dual Craig-Bampton reduced system impossible. The feasibility of a reliable time integration of dual Craig-Bampton reduced systems is demonstrated and investigated in detail. The unstable behavior when time integrating such systems without further modifications is illustrated and an approach to overcome this instability is suggested: A modal analysis of the reduced system is performed as a subsequent step to the dual Craig-Bampton reduction. Only modes corresponding to positive eigenvalues are kept for transient analysis. This leads to a stable reduced systems and allows for stable time integration. The accuracy using this approach is demonstrated by two examples with either different initial conditions or varying external periodic excitations. Results are compared to the behavior of a classical Craig-Bampton reduction. Additionally, modal truncation augmentation is used to improve the approximation accuracy by capturing the spatial distribution of the external loading not captured by the retained modes of the dual Craig-Bampton reduction basis.