Comparison of Craig-Bampton Approaches for Systems with Arbitrary Viscous Damping in Dynamic Substructuring

The classical Craig-Bampton method does not take any damping effects into account for the model order reduction of damped systems. There is generally no justification to neglect damping effects. If damping significantly influences the dynamic behavior of the system, the approximation accuracy can be very poor. One procedure to handle arbitrary damped systems is to transform the second-order differential equations into twice the number of first-order differential equations resulting in state-space representation of the system. Solving the corresponding eigenvalue problem allows the damped equations for the internal degrees of freedom of the substructures to be decoupled, but complex eigenmodes and eigenvalues occur.