Stability and accuracy of central difference method for real-time dynamic substructure testing considering mass participation coefficient

For real-time dynamic substructure testing(RTDST),the influence of the inertia force of fluid specimens on the stability and accuracy of the integration algorithms has never been investigated.Therefore,this study proposes to investigate the stability and accuracy of the central difference method(CDM)for RTDST considering the specimen mass participation coefficient.First,the theory of the CDM for RTDST is presented.Next,the stability and accuracy of the CDM for RTDST considering the specimen mass participation coefficient are investigated.Finally,numerical simulations and experimental tests are conducted for verifying the effectiveness of the method.The study indicates that the stability of the algorithm is affected by the mass participation coefficient of the specimen,and the stability limit first increases and then decreases as the mass participation coefficient increases.In most cases,the mass participation coefficient will increase the stability limit of the algorithm,but in specific circumstances,the algorithm may lose its stability.The stability and accuracy of the CDM considering the mass participation coefficient are verified by numerical simulations and experimental tests on a three-story frame structure with a tuned liquid damper.

Velocity plus displacement equivalent force control for real-time substructure testing

This paper employs a velocity plus displacement（V＋D）-based equivalent force control（EFC） method to solve the velocity/displacement difference equation in a real-time substructure test. This method uses type 2 feedback control loops to replace mathematical iteration to solve the nonlinear dynamic equation. A spectral radius analysis of the amplification matrix shows that the type 2 EFC-explicit, Newmark-β method has beneficial numerical characteristics for this method. Its stability limit of Ω = 2 remains unchanged regardless of the system damping because the velocity is achieved with very high accuracy during simulation. In contrast, the stability limits of the central difference method using direct velocity prediction and the EFC-average acceleration method with linear interpolation are shown to decrease with an increase in system damping. In fact, the EFC-average acceleration method is shown to change from unconditionally stable to conditionally stable. We also show that if an over-damped system with a damping ratio of 1.05 is considered, the stability limit is reduced to Ω =1.45. Finally, the results from an experiment with a single-degree-of-freedom structure installed with a magneto-rheological（MR） damper are presented. The results demonstrate that the proposed method is able to follow both displacement and velocity commands with moderate accuracy, resulting in improved test performance and accuracy for structures that are sensitive to both velocity and displacement inputs. Although the findings of the study are promising, additional test data and several further improvements will be required to draw general conclusions.

Flexible substructure online hybrid test system using conventional testing devices

This paper presents a substructure online hybrid test system that is extensible for geographically distributed tests. This system consists of a set of devices conventionally used for cyclic tests to load the tested substructures onto the target displacement or the target force. Due to their robustness and portability, individual sets of conventional loading devices can be transported and reconfigured to realize physical loading in geographically remote laboratories. Another appealing feature is the flexible displacement-force mixed control that is particularly suitable for specimens having large disparities in stiffness during various performance stages. To conduct a substructure online hybrid test, an extensible framework is developed, which is equipped with a generalized interface to encapsulate each substructure. Multiple tested substructures and analyzed substructures using various structural program codes can be accommodated within the single framework, simply interfaced with the boundary displacements and forces. A coordinator program is developed to keep the boundaries among all substructures compatible and equilibrated. An Interuet-based data exchange scheme is also devised to transfer data among computers equipped with different software environments. A series of online hybrid tests are introduced, and the portability, flexibility, and extensibility of the online hybrid test system are demonstrated.