Operator-splitting Method And Equivalent Force Control Method For Dynamic Substructure Testing

Real-time substructure testing can accurately reflect the performance of velocitydependent type specimens, and plays more and more important role on investigating theseismic performance of civil engineering structures in nowadays. One of the keyelement for real-time substructure testing is the performance of numerical integrationalgorithms. Operator-splitting (OS) method and Equivalent force control method(EFCM) for real-time substructure testing behavior good performance for validatingdisplacement and/or velocity dependent type specimens. However, many kinds of newlydeveloped vibration control devices (such as TLD, TMD, etc.) are applied to structuresfor improving seismic performance. Some of these devices are acceleration dependentdynamic substructure systems, which presents new challenges on the OS method andEFCM for real-time substructure testing. This paper investigates the OS method andEFCM for dynamic substructure testing. Main contents and conclusions are as follows:(1) The OS method for dynamic substructure testing is proposed by introducingadditional acceleration assumption, and the corresponding stability and accuracy areanalyzed. It is shown from the results that for linear systems the algorithm isunconditionally stable for the case of the mass ratio of experimental substructure tonumerical substructure no more than1, otherwise, the algorithm is unstable.(2) The inertia force correction for OS method of dynamic substructure testing isproposed, and the stability and accuracy of the corrected algorithm are analyzed. Theresults show that the corrected algorithm is unconditionally stable for linear andsoftening type systems, and is conditionally stable for hardening systems.(3) The dynamic substructure testing OS method for systems that numerical andexperimental substructures do not share the same degrees of freedom is analyzed. It isshown from the results that the stable range of the proposed algorithm decreases withincrease of the mass ratio and/or stiffness ratio of the experimental substructure tonumerical substructure.(4) The dynamic substructure testing EFCM for systems that numerical andexperimental substructures do not share the same degrees of freedom is analyzed andvalidated with shaking table substructure tests of three stores structure with TLDvibration control device. It is shown from the comparison results between the wholestructure tests and substructure tests that the proposed EFCM for dynamic substructuretesting behaviors good performance in terms of stability and accuracy.