Stability Analysis of Central Difference Method for Dynamic Real-time Substructure Testing

This paper studies the stability of the central difference method (CDM) for real-time substructure test considering the mass of specimen (i.e., experimental substructure). To obtain correct reaction inertia force, an explicit acceleration formulation is assumed for the CDM. The analytical work shows that the stability of the algorithm decreases with increasing specimen mass if the experimental substructure is a pure inertia specimen. The algorithm becomes unstable whatever the time integration interval, i.e., unconditionally unstable, when the mass of specimen equal or greater than that of its numerical counterpart. For the case of dynamic specimen, the algorithm is unconditionally unstable when there is no damping in the whole test structure; a damping will make the algorithm stable conditionally. The behavior of the CDM for vanishing time integration interval is verified with the zero-stability analysis method for coupled integration. Part of the analytical results is validated by an actual test.