Tsinghua University·Beijing Real-time dynamic hybrid testing coupled finite element and shaking table Jin-Ting Wang, Men-Xia Zhou & Feng Jin

Outlines Introduction to testing system 1 Finite element numerical substructure 2 Single-table testing for soil-structure interaction analysis 3 Dual-table testing for travelling wave effect analysis 4 Summaries 5

1. Introduction to testing system  System framework of Tsinghua real-time dynamic Hybrid testing System (THS) MTS Controller Host PC Ethernet Simulink Host PC Simulink Target PC Etherne t Fibe r Scramn et Control Room Data Acquisition Ethernet Table 1 Table 2 Ethernet

1.1. The shaking table loading system  Two identical uni-axial shaking tables  Working area: 1.5 X1.5 m 2 for each table  Bearing capacity: 2 tone.  The frequency range: 0–50 Hz.  The maximum acceleration: 3.6 g for bare table, 1.2 g for full loaded.

1.2. The distributed real-time calculation system  Real-time calculation system was constructed on a standard PC with the help of xPC TARGET software  Host PC: Develop procedure and debug code  Target PC: Execute real-time calculation

1.3. The shared common RAM network  SCRAMNet cards  The data transfer speed reaches up to 16.7 MB/s  The latency is not more than 250 ns.

1.4. The real-time data acquisition system  Hardware: PXI hardware system  Software: LabVIEW Real-Time Module  The sample rate of single channel can reach 4.4 kHz.

Outlines Introduction to testing system 1 Finite element numerical substructure 2 Single-table testing for soil-structure interaction analysis 3 Dual-table testing for travelling wave effect analysis 4 Conclusions 5

2.1. About FE substructure of RTDHT  Chen and Ricles (2012) developed an independently compiled program named “HybridFEM”.  The program was compiled in Matlab, and can perform FE analysis.  An RTDHT was carried out with the numerical substructure simulated as an FE model with 71 beam elements. Chen C, Ricles JM. Large scale real-time hybrid simulation involving multiple experimental substructures and adaptive actuator delay compensation. Earthquake Engineering and Structure Dynamics 2012; 41(3):

2.1. About FE substructure of RTDHT  Saouma et al. (2012) developed an independently compiled program named “Mercury”.  The program is a set of two identical programs: MATLAB version for instruction, prototyping, and pre-test evaluation; C++ version designed for embedding into real-time system.  Data was interacted by hybrid elements in the program.  An RTDHT was implemented with the numerical substructure simulated as an FE model with 140 flexibility-based elements. Saouma V, Kang DH, Haussmann G. A computational finite-element program for hybrid simulation. Earthquake Engineering and Structure Dynamics 2012; 41(3):

2.2. Our solution to FE substructure  An independently-developed FE analysis block was compiled in S-function.  The new developed block is fully compatible with built-in Simulink blocks.  Don’t need the hybrid elements for data interaction.  Solid elements are used in our FE model.

2.3. Generation of the user-compiled block  The FE analysis program is compiled in C++.  The C++ program is then transplanted into S-function following the special calling syntax.  Finally, the user-compiled block is incorporated into the Simulink procedure to develop the FE numerical substructure.

2.4. Execution of the user-compiled block

2.5. Task Execution Time  The dynamic response of a linear FE model with 66 nodes (132 DOFs) is solved to check the calculation speed of the numerical substructure with FE function.

2.5. Task Execution Time The task execution time  The frequency of the shaking table controller in THS is 1/2048 s.  The task execution time of most simulation steps is about 0.47 ms, but it may significantly increases at a certain step. This leads to the real-time calculation interrupt.

2.5 Task Execution Time  The system management interrupt occasionally occurs in the CPU chip.  A “disableSMI” block is added to the Simulink procedure.  The real-time calculation completed successfully. The task execution time

Outlines Introduction to testing system 1 Finite element numerical substructure 2 Single-table testing for soil-structure interaction analysis 3 Dual-table testing for travelling wave effect analysis 4 Conclusions 5

3.1. Finite soil foundation  A shear frame mounted on the finite soil foundation was tested.

(1) Physical substructure  The upper steel plate mass is 5.28 kg.  White noise excitation shows that the natural frequency of the frame is 4.57 Hz.  The stiffness and damping are calculated as 4350 N/m and N∙s/m, respectively.  It can be considered as a single DOF system in the in-plane movement. Physical substructure

(2) Numerical substructure  50 four-node solid elements, 66 nodes.  A total of 132 DOFs.  The material properties: mass density 2000 kg/m 3 ; elastic modulus 200 MPa; poisson’s ratio 0.2. FE numerical substructure

(3) Acceleration at frame top  The peak of the acceleration at frame top is 0.56 g by RTDHT while 0.49 g by pure FEM, the error is 10.9%.

(3) Acceleration at frame bottom  The peak of the acceleration, at frame bottom is 0.22 g by RTDHT while 0.19 g by pure FEM, the error is 12.1.

(4) Displacement at frame bottom  The peak of the displacement at frame bottom is 4.06 mm by RTDHT while 3.84 mm by pure FEM, the error is 5.4%

3.2. Infinite soil foundation  The foundation is regarded as infinite  The radiation damping is simulated by the viscous- spring artificial boundary.

(1) Effect of the radiation damping  The dynamic response remarkably decreases due to the radiation damping effect of the infinite foundation.  The peak of the acceleration decreases by 43% at frame top and 39% at frame bottom. Acceleration at frame top

(2) Effect of foundation stiffness  The dynamic response under soft soil is considerably smaller than that under hard soil.  The peak of acceleration decreases by 53% at frame top and 60% at frame bottom.  The SSI of different soil conditions differs remarkably. Acceleration at frame top

Outlines Introduction to testing system 1 Finite element numerical substructure 2 Single-table testing for soil-structure interaction analysis 3 Dual-table testing for travelling wave effect analysis 4 Conclusions 5

4.1. Design of the testing  Two shear frames are tested as the physical substructure by two shaking tables.  The foundation is simulated by the FE numerical substructure.

4.2. Physical substructure  The shear frame No.1 used in the experimental substructure is the same as before.  The shear frame No.2 is very similar with No.1. Mass / kgStiffness / N/mDamping / N∙s/m Natural frequency / Hz Damping ratio shear frame No shear frame No

4.3. Numerical substructure  There are 48 four-node solid elements and 65 nodes.  The viscous-spring artificial boundary is set at the truncated boundary.

4.4. Acceleration at the frame top  The dynamic responses of two shear frames have significant phase difference.  The phase difference is about s.  The travelling wave effect has been simulated.

Outlines Introduction to testing system 1 Finite element numerical substructure 2 Single-table testing for soil-structure interaction analysis 3 Dual-table testing for travelling wave effect analysis 4 Conclusions 5

Summaries  An FE analysis block is compiled in S-function. Thus an RTDHT system coupled finite element calculation and shaking table testing is achieved.  The dynamic soil-structure interaction and the travelling wave effect are simulated in RTDHT by using the FE numerical substructure.  The capacity of the real-time hybrid testing is improved due to the FE numerical substructure.

Acknowledgement This research was supported by the National Natural Science Foundation of China (Nos ). The support is gratefully acknowledged.

Thank you for your attention!