TIME INTEGRATION OF DUAL CRAIG-BAMPTON REDUCED SYSTEMS

Abstract eng:
In this paper, time integration procedures are demonstrated and investigated for dual Craig-Bampton reduced 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, allowing for incompatibilities associated with the equilibrium residual in the substructure. Hence, the eigenvalues of the reduced-order model are not guaranteed to be upper bounds for the unreduced system’s eigenvalues. Furthermore, the dual Craig-Bampton reduced system will always have 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 two approaches to overcome this instability are suggested: on the one hand, 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 thereby kept for transient analysis. This allows for a stable time integration. On the other hand, a modal interface reduction during the dual Craig-Bampton reduction process is performed and only interface modes corresponding to positive eigenvalues are kept. This makes the final reduced system also positive definite. The accuracy using these two approaches is demonstrated in examples with either different initial conditions or varying external periodic excitations.

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