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The operator-splitting (OS) method for real-time substructure testing (RTST) provides explicit and unconditionally stable solutions for structures with softening type stiffness and damping has been widely used for precisely disclosing the seismic performance of structures with velocity-dependent specimens. However, the OS method for RTST provides only explicit target displacement and velocity but not an explicit target acceleration, so that it is essentially an implicit method for Dynamic real-time substructure testing (DRTST) with dynamic system specimens. For precisely disclosing the seismic performance of multiple-degree-of-freedom structures with dynamic system specimens, one improved OS method is proposed for DRTST in this paper. The methodology and stability of the proposed OS method are investigated, and the effectiveness of the proposed OS method is validated by numerical simulations and experimental tests. By using the predictor displacement, velocity, and acceleration approximations, the OS method is an explicit algorithm for DRTST. The stability analysis shows that the proposed OS method is conditionally stable for DRTST, and its stability limit decreases with the increase of the mass ratio and the stiffness ratio, while it increases first and then decreases with the increase of the damping ratio. The numerical and experimental results confirm the stability and accuracy of the OS method. The OS method for DRTST provides a practical and precise investigation strategy for structures with dynamic system specimens and may have broad application prospects in civil engineering.

For precisely disclosing the seismic performance of tuned liquid damper (TLD) vibration control structures, the shaking table substructure test (STST) method is presented and experimentally validated, and the parametric effects on the reduction efficiency of TLD are further investigated by using the STST method in this paper. Firstly, one optimal design method of TLD for high-rise structures is presented. Secondly, the STST based on three variable control method (TVCM) for the TLD vibration control structures is presented. Thirdly, the effectiveness and robustness of the STST for TLD vibration control structures are validated by a series of tests on one three-story-frame structure with a rectangular TLD. Finally, the parametric effects on the reduction efficiency of TLD, in terms of mass ratio and liquid depth, are investigated using the STST