Shaking‐table substructure test using a MDOF boundary‐coordinating device

Abstract Boundary coordination is necessary for a shaking‐table substructure test (STST), which includes transferring forces and displacements between the tested and numerical substructures. Unlike other real‐time hybrid tests (RTHTs), the physical substructure is mounted on a shaking table and excited by the inertial force, which naturally requires a force control for boundary coordination. However, the natural velocity feedback in hydraulic actuators and high‐frequency noise in the force feedback signals makes it difficult to achieve force control. To solve these difficulties, in this study, a multi‐degree‐of‐freedom (MDOF) boundary‐coordinating device (BCD) is developed to simultaneously implement the boundary shear force and bending moment by the inertial force generated from shaking masses that are uniaxially driven by electromagnetic actuators. An STST framework was developed based on the BCD. The bottom two stories of a four‐story steel moment frame were selected as the physical substructure. A hydraulic shaking table was employed for ground excitation, and the BCD was used as the boundary coordinator for the numerical substructure, that is, the top two stories of the frame. To trace high‐frequency force signals, an enhanced three‐variable control (ETVC) method is proposed. Furthermore, an error‐response negative‐feedback compensation (ENC) method was developed to reduce the adverse effects of loading errors. Several rounds of STST tests demonstrated that the boundary commands were effectively traced by the BCD, so that the STST framework could consistently reproduce the seismic behavior of engineering structures.