**Substructure Shake Table Testing of Frame Structure–Damper System Using Model-Based Integration Algorithms and Finite Element Method: Numerical Study**

**Bo Fu 1,2, Huanjun Jiang 3 and Jin Chen 1,4,\***


**Abstract:** Substructure shake table testing (SSTT) is an advanced experimental technique that is suitable for investigating the vibration control of secondary structure-type dampers such as tuned mass dampers (TMDs). The primary structure and damper are considered as analytical and experimental substructures, respectively. The analytical substructures of existing SSTTs have mostly been simplified as SDOF structures or shear-type structures, which is not realistic. A common trend is to simulate the analytical substructure via the finite element (FE) method. In this study, the control effects of four dampers, i.e., TMD, tuned liquid damper (TLD), particle damper (PD) and particletuned mass damper (PTMD), on a frame were examined by conducting virtual SSTTs. The frame was modeled through stiffness-based beam-column elements with fiber sections and was solved by a family of model-based integration algorithms. The influences of the auxiliary mass ratio, integration parameters, time step, and time delay on SSTT were investigated. The results indicate that the TLD had the best performance. In addition, SSTT using model-based integration algorithms can provide satisfactory results, even when the time step is relatively large. The effects of integration parameters and time delay are not significant.

**Keywords:** substructure shake table testing; integration algorithm; finite element method; damper
