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This paper presents a new method, called the equivalent force control method, for solving the nonlinear equations of motion in a real-time substructure test using an implicit time integration algorithm. The method replaces the numerical iteration in implicit integration with a force-feedback control loop, while displacement control is retained to control the motion of an actuator. The method is formulated in such a way that it represents a unified approach that also encompasses the effective force test method. The accuracy and effectiveness of the method have been demonstrated with numerical simulations of real-time substructure tests with physical substructures represented by spring and damper elements, respectively. The method has also been validated with actual tests in which a Magnetorheological damper was used as the physical substructure. 1128 B. WU ET AL.technique, in which a structure is split into a physical test specimen and a numerical model. While the effective force method is conceptually simple and it does not require real-time numerical computation during a test, it is not as versatile and efficient as RST methods. On the other hand, RST methods face a number of challenges in terms of the robustness and efficiency of the numerical computation schemes and the interaction between the actual and numerically simulated dynamics of the structural specimen.While many different numerical algorithms are available for RSTs [3][4][5][6][7][8][9], for structures with many degrees of freedom, an integration method with unconditional stability is highly desirable. Wu et al. [10] have investigated the numerical properties of the operator-splitting method (OSM) [15] for RSTs (OSM-RST) and found that the method is unconditionally stable as long as the nonlinear stiffness and damping are of the softening type (i.e. the tangent stiffness and damping never exceed the initial values). The advantage of the OSM-RST method over other unconditionally stable methods is its explicit formulation. However, with the OSM or OSM-RST, the accuracy of the numerical solution may be significantly impaired when the predictor stiffness or damping is very different from the actual stiffness or damping of a structure [10, 16]. Shing and his coworkers have implemented the unconditionally stable -method of Hilber, Hughes, and Taylor [16, 17] for RSTs [11,12]. Their method adopts a special iterative solution procedure for real-time testing. This iterative procedure is based on the initial stiffness of the structure and may require very small time steps when severe strain softening occurs in the structure. This paper proposes a new method, called the equivalent force control (EFC) method, which is aimed to replace the numerical iteration in an implicit scheme by a force-feedback control loop. Furthermore, this method is formulated in such a way that it encompasses both the effective force test method and RST method. Figure 12. Photograph of MR damper in RST.capacity of the actuator was 2500 kN and the sampling frequency of the MTS digital co...

SUMMARYIt has been shown that the operator-splitting method (OSM) provides explicit and unconditionally stable solutions for quasi-static pseudo-dynamic substructure testing. However, the OSM provides only an explicit target displacement but not an explicit target velocity, so that it is essentially an implicit method for real-time substructure testing (RST) when the velocity-dependent restoring force is considered. This paper proposes a target velocity formulation based on the forward di erence of the predicted displacements so as to render the OSM explicit for RST. The stability and accuracy of the resulting OSM-RST algorithm are investigated. It is shown that the OSM-RST is unconditionally stable so long as the non-linear sti ness and damping are of the softening type (i.e. the tangent sti ness and damping never exceed the initial values). The stability of the OSM-RST for structures with inÿnite tangent damping coe cient or sti ness is also proved, and the stability of the method for MDOF structures with a non-classical damping matrix is demonstrated by an energy criterion. The e ects of actuator delay and compensation are analysed based on the bilinear approximation of the actuator step response. Experiments on damped SDOF and MDOF structures verify that the stability of the OSM-RST is preserved when the experimental substructure generates velocity-dependent reaction forces, whereas the stability of real-time substructure tests based on the central di erence method is worsened by the damping of the specimen.

SUMMARYThe central di erence method (CDM) that is explicit for pseudo-dynamic testing is also believed to be explicit for real-time substructure testing (RST). However, to obtain the correct velocity dependent restoring force of the physical substructure being tested, the target velocity is required to be calculated as well as the displacement. The standard CDM provides only explicit target displacement but not explicit target velocity. This paper investigates the required modiÿcation of the standard central di erence method when applied to RST and analyzes the stability and accuracy of the modiÿed CDM for RST.

In this paper, we propose a new actuator control algorithm that achieves the design flexibility, robustness, and tracking accuracy to give real-time hybrid-simulation users the power to achieve highly accurate and robust actuator control. The robust integrated actuator control (RIAC) strategy integrates three key control components: loop shaping feedback control based on H 1 optimization, a linear-quadratic-estimation block for minimizing noise effect, and a feed-forward block that reduces small residual delay/lag. The combination of these components provides flexible controller design to accommodate setup limits while preserving the stability of the H 1 algorithm. The efficacy of the proposed strategy is demonstrated through two illustrative case studies: one using large capacity but relatively slow actuator of 2500 kN and the second using a smallscale fast actuator. Actuator tracking results in both cases demonstrate that the RIAC algorithm is effective and applicable for different setups. Real-time hybrid-simulation validation is implemented using a three-DOF building frame equipped with a magneto-rheological damper on both setups. Results using the two very different physical setups illustrate that RIAC is efficient and accurate.In HS and RTHS, a structure system is divided into numerical and experimental (also known as physical substructure) components. The numerical substructure contains the well-understood components and leaves the hard-to-model components in the physical setup. An illustration of a hybrid simulation

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A novel type of angle steel buckling-restrained brace (ABRB) has been developed for easier control on initial geometric imperfection in the core, more design flexibility in the buckling restraining mechanism and easier assembly work. The steel core is composed of four angle steels to form a non-welded cruciform shape restrained by two external angle steels, which are welded longitudinally to form an external tube. Component test was conducted on seven ABRB specimens under uniaxial quasi-static cyclic loading. The test results reveal that the consistency between the actual and design behavior of ABRB can be well achieved without the effect of weld in the core. The ABRBs with proper details exhibited stable cyclic behavior and satisfactory cumulative plastic ductility capacity, so that they can serve as effective hysteretic dampers. However, compression-flexure failure at the steel core projection was found to be the primary failure mode for the ABRBs with hinge connections even though the cross-section of the core projection was reinforced two times that of the yielding segment. The failure mechanism is further discussed by investigating the N u -M u correlation curve. It is found that the bending moment response developed in the core projection induced by end rotation was the main cause for such a failure mode, and it is suggested that core projection should be kept within elastic stage under the possible maximum axial load and bending moment response.