CONSTRUCTION AND PERFORMANCE TEST OF A
LOW-COST SHAKE TABLE
I
n recent years, a great number of earthquake disasters occurred in the world, and thousands of people were killed as a result of the collapse of the buildings. These events emphasize the importance of earthquake engineering research about how structures behave under seismic excitations. There are many analytical approaches for investigating the behavior of the structures under seismic loads. However, these analytical models involve the idealization and assumption of the structure’s behavior based on current theoretical knowledge. Experimental work provides an alternate means of analysis and extending the limits of the theoretical knowledge. In addition, the capabilities of these analytical models can only be validated by experimental work. To investigate the real behavior of the structures against earthquakes, several seismic test methods are used. Most popular methods are (1) real earthquake experiences, (2) in situ tests, (3) static tests (pushover analysis), (4) shake table tests, (5) pseudo-dynamic tests, and (6) centrifuge tests.1 It is obvious that the shake table tests give exact behavior of the structures under the seismic loads if the real dynamic boundary conditions are simulated correctly. Hence, during the last decades many shake tables in different scales have been constructed and developed mainly in Japan, USA, and Europe.1,2The shake tables are classified as small (smaller than 3 m × 3 m), medium (from 3 m× 3 m to 9 m × 9 m) and large (greater than 9 m× 9 m) tables.3 Large shake tables are valuable tools for understanding the behavior of full-scale structures under seismic loads, whereas they involve high construction and operating expenses. On the other hand, in order to simulate a real earthquake completely, a shake table should have to be capable of moving in three reference directions. But, multicomponent shake tables are too expensive and require special knowledge and experience for construction and operation. Hence, smaller-sized, unidirectional tables are more suitable for the small-scale model analysis and for the educational aims due to their low constructing and operating cost, especially in the developing countries. From the preceding reasons, in recent years, research about the design process of shake tables have been focused on cost-effective, state-of-the-art small-sized unidirectional shake table facilities. For instance, Moncarz4 and Muhlenkamp5 studied on analysis, design and construction of shake table facilities. Trombetti6,7 developed an analytical model for construction and controlling of a hydraulic shake table as a prework for construction. Latendresse,8 made a study of development of a shake table founded at University of British Columbia, and he tested some various scaled structures on it. Results from the tests were used to demonstrate performance characteristics and limitations of shake table testing. Delgado9studied about development of an earthquake simulator at University of Porto Rico.T. Baran, Dr. Civil Engineer, Adana, Turkey; A.K. Tanrikulu (akt@cu.edu.tr), Prof. Dr., and C. Dundar, Prof. Dr., Civil Engineering Department, Cukurova University, Adana, Turkey; A.H. Tanrikulu, assistant professor, Civil Engineering Department, Cukurova University, Adana, Turkey.
In order to achieve meaningful and reliable results in performing dynamic tests with a shake table, the accurate reproduction of commanded dynamic signals (i.e., earthquake ground motions) through the shake table is important. The undesired signal distortion depends on the dynamic characteristics of the subsystems (mechanical, hydraulic, and electronic) of the shake table-payload system and their interaction. In literature, there is significant research about developing advanced control algorithms to improve the accuracy in the time history reproduction. Trombetti and Conte10studied on table dynamics for different pay load and operation conditions. They compared the analytical and the experimental dynamic behaviors of the shake table. Twitchell and Symans11developed an off-line pre- and postcorrection method for historical earthquake data to improve shake table performance. Chase et al.12 developed new control parameters and functions for shake table founded at University of Canterbury. Despite these valuable studies, the subject still remains incomplete and further research is needed through the theoretical and technological advances. There are mainly two types of shake tables according to their actuators: (1) electrodynamic shaker and (2) hydraulic actuator. Both have their advantages and disadvantages. The most important advantages of electrodynamic shakers are the low-price and low operation costs as educational equipments compared with hydraulic systems.
On the basis of the aforementioned considerations, the authors constructed a uniaxial electrodynamic shake table called CUSHAKE at the Civil Engineering Department of Cukurova University Adana, Turkey. CUSHAKE was constructed with make use of advances in electric, electronic, and computer technology on automation sector. The first part of the paper gives a brief description and construction principles of the table system. The second part of the paper is devoted to finding out the actual performance of the constructed system through the several experimental works.
SHAKE TABLE PROPERTIES
CUSHAKE is a uniaxial shake table controlled by a personal computer. The specifications and an illustrative picture of CUSHAKE are given in Table 1 and in Fig. 1, respectively. As seen from the figure, the table is based on a main frame constructed by using steel beams. This frame carries a servo driven AC motor, a rigid table, two rails, and four bearings. The upper part of the table is also made of steel and is actuated by the AC motor. A detailed section-cut of the table is seen in Fig. 2. The rotational movement of the AC motor is transferred as a uniaxial linear movement to the table by a continuous threaded steel bar. The table is protected by two limit switches from sudden and high forced crushes that can appear due to the high velocity values in the data or sudden high voltage values. These switches cut motor current off when a sudden movement over the stroke limits occurs. The upper part of the table can be rotated about vertical axis by doi: 10.1111/j.1747-1567.2010.00631.x
PERFORMANCE TEST OF A LOW-COST SHAKE TABLE
Table 1—Specifications of CUSHAKE
SPECIFICATION VALUE UNIT
Table dimensions (B× L) 150× 200 cm Displacement ±7.5 cm Velocity (bounded by software) ±40 cm/s Maximum acceleration 1 g (g= 9.81 m/s2)
Table frequency 0–25 Hz Maximum motor force 50 kN Motor current 45 kW Mass of the table 1500 kg Max. payload (theoretical) 3500 kg
25◦ angles up to 75◦ allowing the inclined movement of the structure fixed on it.
APPLICATION OF HISTORICAL DATA
AND DATA ACQUISITION
A personal computer software applies historical data by a control board to servo driver. The control board and the software (DEPSIM) were dedicated to shake table system, which was produced by a local firm in the city of Adana. The control board and DEPSIM communicate on personal
computer serial bus port. An algorithmic flowchart, given in Fig. 3, demonstrates the system work process.
During the test of a structure, a potentiometric displacement sensor acquires the table displacement with a low sampling rate at 100 S/s and the A/D converter control board stores the values. After the simulation, these values are requested by DEPSIM and are stored in a worksheet.
DEPSIM Software
DEPSIM is Win32 application software. Basically it takes historical tabular data from compatible software and sends the data to the A/D converter control board for the simulation. After the simulation, it acquires the displacement values of the table, which measured by potentiometric sensor from the control board (Fig. 3). DEPSIM applies the earthquake historical data as velocity. If the input data is acceleration, DEPSIM converts it to velocity according to Eq. 1 without any zero correction.
vi =
ai+ ai−1
2 t+ vi−1 (1) In Eq. 1, vi and vi−1 are ith and (i− 1)th step velocity
values respectively, t is time step value, aiand ai−1are the acceleration values of ith and (i− 1)th steps, respectively. It should be noted that the initial velocity value of the
Fig. 2: Section-cuts of CUSHAKE
vibration (v0) is considered as a correction value in order to obtain zero displacement at the end of the earthquake record. DEPSIM uses the historical data having uniform time steps of 5 or 10 ms. If the record has different time steps, the user has to calculate the new historical data values suitable with DEPSIM by using a basic interpolation algorithm.
Data Acquisition (DAQ) Instrumentation
CUSHAKE has a data acquisition (DAQ) system including (1) a four channel NI 9215A data logger; each channel has 100 kS/s sampling rate and is operated by NI VI Logger DAQ software, (2) three Schaevitz DC–SE series linear variable differential transformers (LVDTs) with stroke ranges 0–15 cm and (3) a±5.5 m/s2ranged MMF KB 12 VB seismic accelerometer.
Signal Processing
During the experimental work, there are noises in the acquired signal. For this reason, after the simulation, the acquired signal were filtered by using low pass filter for the displacements and band pass filter for the accelerations if needed. The cutoff frequency of the filter was obtained by means of the spectrum analysis of each signal set.
INVESTIGATION OF THE CUSHAKE
PERFORMANCE
Authors prepared three sets of tests to investigate the performance of CUSHAKE. The tests are described below.
Determining the Limits of CUSHAKE
First set of the tests was prepared to determine the maximum performance of the table. In these tests, a series of sine sweep acceleration records is prepared. In the records, at the first step, the amplitude was constant but the frequency was variable, at the second step, the amplitude was variable but the frequency was constant and at the last step both were variable. The records were applied to CUSHAKE and responses were recorded. The maximum performance curve of the table is given in tripartite plot form in Fig. 4. As seen from the figure, the performance of the table is limited by displacement, velocity, and acceleration in small, medium, and high frequencies, respectively.
Validation of CUSHAKE
Validation of CUSHAKE Under Sine Sweep
In the second set of the tests, the authors investigated whether the driver applies the expected acceleration data
PERFORMANCE TEST OF A LOW-COST SHAKE TABLE
Fig. 3: Algorithm of CUSHAKE system
to the table or not. To see that, a simple structure (a single degree of freedom [SDOF] system) was mounted on the table and the fundamental natural frequency of the system was calculated as 1.5314 Hz from the data presented in Fig. 5, which was recorded during the free vibration of the struc-ture. Then, a set of sine sweep acceleration data with constant amplitude and variant frequencies were applied to the table. During the simulation, response of the table and the struc-ture were recorded in the displacement manner. It should be noted that, the acceleration data with the frequencies having the values close to the natural frequency of the structure were applied to the CUSHAKE. The properties of the struc-ture and the test setup are given in Figs. 5 and 6, respectively. It should be noted that excitation time of each test was 3 s. The time history of the input and of the measured signal of the table without filtering by means of displacement values are compared in Fig. 7. As shown from the figure, the table displacements obtained experimentally are in good agreement with the input signal. The maximum top point displacements of the structure obtained for each excitation frequency were also presented in Fig. 8. As expected, the experimental results show that the top point displacements increased when the excitation frequency was around the
fundamental natural frequency of the structure. As seen from Figs. 7 and 8, it may be concluded that the CUSHAKE is capable of applying the sine sweep acceleration values with expected frequency in sufficient sensitivity.
Validation of CUSHAKE Under Random
Acceleration
The last step of the tests includes a historical data which was acquired from well-known El Centro earthquake. This step was realized to obtain whether the CUSHAKE successfully simulates the random excitation or not. Owing to the limitation of the displacement stroke of the CUSHAKE, in the experiments, the El Centro acceleration data was scaled down by a scale factor according to the acceleration similarity law (ASL).1As is well known, in the ASL, the dynamic system quantities are scaled down by using the multipliers given in Table 2, where n is the multiplier for ASL of the model. In the experiments n was taken as 10.
The comparison of the spectrum graphs of command and measured acceleration signals of CUSHAKE are given in Figs. 9 and 10. From the figures, it can be clearly seen that, although there is a negligible delay in the measured table
Fig. 4: Maximum performance of CUSHAKE
PERFORMANCE TEST OF A LOW-COST SHAKE TABLE
Fig. 6: The test setup, control, and measurement scheme of CUSHAKE for the second set of tests
Fig. 8: Top point frequency response curve for SDOF structure near its fundamental natural frequency of vibration
Fig. 9: Command and feedback acceleration signal amplitude spectrum curves for a scaled-down El Centro earthquake
displacement because of the filtering process while acquiring the table displacement signal, the CUSHAKE’s performance on applying a random acceleration record is acceptable. In the El Centro earthquake simulation, SDOF structure top point lateral displacements were also recorded and a numerical solution was realized by means of SAP2000®13 finite element software for the structural analysis. Figure 11 shows time history of the numerical and the experimental displacements of the top point of the test structure under
a scaled-down El Centro earthquake. As seen from the figure, the displacement values between experimental and numerical are in good agreement. This figure also verifies the reasonably good performance of CUSHAKE and the numerical model of the structure.
CONCLUSION
In this paper the authors buildup a shake table and investigated its performance. It is shown that the table
PERFORMANCE TEST OF A LOW-COST SHAKE TABLE
Fig. 10: Time history of the command and feedback displacement of the shaking table for the scaled-down El Centro earthquake
Fig. 11: Top point lateral displacement of the test structure under a scaled-down El Centro earthquake
performance is reasonably acceptable. The cost of the table is about US$45,000, which is approximately half of the global marketing price of a single-axis shake table that can handle a test payload of about 1000 kg.14,15Hence, the shake tables having the design characteristics presented in this paper may be preferred because of their low-cost, low operation budget, and acceptable performance. They may be more useful by using scaling/similarity laws and every kind of structural replicas may be shaken on them.
For the future studies, table performance could be upgraded using miscellaneous pre- and postprocessing procedures. In addition, various types of structure and boundary conditions related to structural dynamics would be tested on it, for the investigation of earthquake related phenomena such as rate of loading effects, effects of mass and stiffness irregularities, torsional and overturning effects, dynamic instability, failure mechanisms, idealized soil-structure interaction effects, etc. The demonstration of the integrity and safety of designed
Table 2—Multipliers for acceleration
similarity law
QUANTITY ACCELERATION SIMILARITY (λ= 1/n) Displacement λ Velocity √λ Acceleration 1 Mass λ2 Density 1λ Weight λ2 Force λ2 Time √λ Frequency √1 λstructures under various levels of earthquake inputs would also be possible.
ACKNOWLEDGMENT
This study was funded by Cukurova University Academic Research Projects Unit. Project No: 2004K120360-17.
References
1. Sollogoub, P., Seismic Testing, Advanced Course on Advanced
Earthquake Engineering Analysis, CISM, Udine, Italy (2006).
2. Harris, H.G., and Sabnis, G.M., Structural Modeling and
Experimental Techniques, 2nd Edition, CRC Press, LLC, USA
(1999).
3. Mills, R.S., Model Tests on Earthquake
Simulators-Develop-ment and ImpleSimulators-Develop-mentation of ExperiSimulators-Develop-mental Procedures, Ph.D. Thesis,
Stanford University, California, June (1979).
4. Moncarz, P.D., Theory and Application of Experimental
Model Analysis in Earthquake Engineering, Ph.D. Thesis, Stanford
University, California (1981).
5. Muhlenkamp, M.J., Analysis, Design and Construction of
Shake Table Facility, M.S. Thesis, Rice University, Houston, Texas
(1997).
6. Trombetti, T., Analytical Modeling of a Shaking Table
Sys-tem, M.S. Thesis, Rice University, Houston, Texas (1996).
7. Trombetti, T., Experimental/Analytical Approaches to
Mod-eling, Calibrating and Optimizing Shaking Table Dynamics for Structural Applications, Ph.D. Thesis, Rice University, Houston,
Texas (1998).
8. Latendresse, V., Operation and Control of a Seismic
Simula-tor, Ph.D. Thesis, The University of British Columbia, Vancouver
(1999).
9. Delgado, M.D.C., Development of the UPRM Earthquake
Simulator Facility for Dynamic Model Analysis, M.S. Thesis,
University of Puerto Rico, Mayag ¨uez (2005).
10. Trombetti, T., and Conte, J.P., ‘‘Shaking Table Dynamics: Results from a Test-analysis Comparison Study,’’ Journal of
Earthquake Engineering 6(4):513–551 (2002).
11. Twitchell, B.S., and Symans, M.D., ‘‘Analytical Modeling, System Identification, and Tracking Performance of Uniaxial Seismic Simulators,’’ Journal of Engineering Mechanics 129(12): 1485–1488 (2003).
12. Chase, J.G., Hudson, N.H., Lin, J., Elliot, R., and Sim, A., ‘‘Nonlinear Shake Table Identification and Control For Near-field Earthquake Testing,’’ Journal of Earthquake Engineering 9(4): 461–482 (2005).
13. Computers and Structures Inc., SAP2000-Integrated Structural Analysis & Design Software, Berkeley, California
(1997).
14. Ammanagi, S., Poornima, V., Sera, A., and Sunder, R., ‘‘Development of a Digitally-controlled Three-axis Earthquake Shake Table,’’ Current Science 91(2):190–203 (2006).
15. Leatham, C., Hofman, M., and Wong, A.J.-K., Dual
Applica-tion VibraApplica-tion Simulator, BSc Thesis, Santa Clara University, Santa
