This study investigated the real-time substructure shaking table testing (RTSSTT) of an equipment-structure-soil (ESS) system and the effects of soil on the seismic energy responses of the equipment-structure (ES) subsystem. First, the branch modal substructure approach was employed to derive the formulas needed for the RTSSTT of the ESS system. Then, individual equations for calculating the energy responses of the equipment and the structure were provided. The ES subsystem was adopted as the experimental substructure, whereas the reduced soil model was treated as the numerical substructure when the RTSSTT was performed on the ESS system. The effectiveness of the proposed testing method was demonstrated by comparing the test results with those of the integrated finite element analysis. The energy responses of the ES subsystem in the case of rigid ground (i.e., the ES system) were compared with those considering the effects of soil (i.e., the ESS system). The input energy responses of the ES subsystem were found to decrease significantly after taking the effects of soil into account. Differences due to the soil effects should be considered in the seismic design for the ES system.
Dynamic equations are presented that have been deduced for a real-time dynamic substructuring shaking table test of an equipment-structure system, based on the branch mode substructure method. The equipment is adopted as the experimental substructure, which is loaded by the shaking table, while the structure is adopted as the numerical substructure. Real-time data communication occurs between the two substructures during the test. A real-time seismic energy calculation method was proposed for the calculation of energy responses, both in the experimental substructure and the numerical substructure. Taking a representative four-story steel frame/equipment model, real-time dynamic substructuring shaking table tests and overall model tests were executed. The proposed real-time dynamic substructuring shaking table testing method was verified by comparing the test results with shaking table test results for the overall model. The energy responses of each component in the equipment-structure system, using different connection types, also were studied. Changes in the connection types can lead to changes in the energy responses of the equipment-structure system, especially with respect to the equipment. The choice of the connection for the equipment-structure coupled system should take into account the operational performance objective of the equipment.
SummaryIn equipment–structure systems, the soil–structure interaction and connection types between the equipment and structure significantly affect the seismic response. To understand this effect, in this study, the motion equation of an equipment–structure–soil system was derived, and energy balance equations for each part of the coupled system were obtained. Further, the effects of the soil on the energy response were analyzed based on the results of shaking table tests of an equipment–structure system and real‐time substructure shaking table tests of equipment–structure–soil systems with different connection types. The energy response of the equipment–structure system with a rigid ground was compared with that of the equipment–structure–soil systems. The analysis results showed that the energy response of the equipment–structure–soil system with different connections was quite different from that of the system with a rigid ground. The soil decreased the total energy input to the equipment and structure and significantly changed the time distribution characteristics of the input energy. Additionally, the soil weakened the energy consumption of the connections. Therefore, the influence of the soil should be considered in the design of equipment–structure systems with connections.
Based on the principle of real-time substructure shaking table test, an interactive numerical computation method which built the calculation model of each substructure in different software programs was proposed for seismic analysis of equipment-high rise structure-soil systems in order to account the effect of nonlinear soil. Considering that the response of soil under strong earthquakes does not totally enter the nonlinear stage, a locally nonlinear soil model was introduced as the numerical substructure, and the equipment-high rise structure subsystem was treated as an experimental substructure in this method. The equation of motion for the equipment-high rise structure-soil system was derived through a combination of the branch modal substructure and linear-nonlinear hybrid constraint modal substructure approaches. A 13-layer steel framework system model is used as an analytical example that the equipment-high rise structure system and local nonlinear soil computing model are built by MATLAB and ANSYS, respectively. The time histories of the system dynamic responses were obtained by interactive numerical computation, to investigate the effects of equipment-high rise structure-soil interaction on the seismic performance of the equipment and structure.
The real-time hybrid test is an effective testing method for soil–structure interaction research. Due to the data interaction time requirement and formula derivation method, the traditional real-time hybrid test of soil–structure interaction mostly employs a simple numerical substructure model. This study investigated the model construction and numerical simulation of a finite element soil substructure with high simulation accuracy and calculation efficiency. The soil was subdivided into near-field and far-field zones. A constrained mode–damping solvent extraction combined method was applied to the latter zone, reducing the soil’s computational scale and simulating the far-field energy dissipation effect. Then, the basic formula of the near-field zone–structure system was derived using the branch mode method, and the motion equation of the soil–structure system applied to real-time hybrid test was obtained. The soil’s numerical model was realized by the joint application of ANSYS and MATLAB software packages and verified through the real-time hybrid test of the soil–structure system. The results show that the proposed constrained mode–damping solvent extraction combined method had high calculation efficiency and good accuracy. It satisfied the requirements of the soil numerical substructure in real-time hybrid tests.
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