Shaking Table – Specimen Interface Design in Substructure Testing

*Trung Vien Phan1)

, Van Thuan Nguyen2)

, Nasser Mohammad Khanlou3)

and Uwe E. Dorka4)

1), 2), 3), 4)

Steel and Composite Section, University of Kassel, Germany 1)

phanvien@uni-kassel.de,2)

thuan@uni-kassel.de,3)

khanlou@uni-kassel.de 4)

uwe.dorka@uni-kassel.de

ABSTRACT

Substructure testing using shaking tables requires careful considerations regarding the

interaction between the substructure specimen and the table. The design of the interface between

them is of particular importance since it has to recreate accurately the interface between the

numerical structure and the specimen, and also allow high-resolution measurements of the

emerging coupling forces. These play a major role in the substructure algorithm, which needs

them as a feed-back to calculate the motion of the table using a step-wise time integration

scheme.

This paper summarizes the experience gained in designing such tests for three projects,

namely: CEA-UNIKA5)

, SUBSHAKE6)

and E-FAST7)

project. Various arrangements of the

interface between the specimen and the table were made, especially with respect to the

measurements of the coupling forces between specimen and numerical model. The experience

gained with these arrangements is reported. Conclusions are drawn regarding the requirement

for stiffness and the measurements of forces in such interfaces.

1), 3) Doctoral student 2) Dr. -Ing. 4) Prof. Dr. -Ing. 5) CEA-UNIKA Project: “Common action between University of Kassel and the Commissariat à lÈnergie Atomique”, agreement No. SAV 33 156, 2006-2009. 6) SUBSHAKE Project: “Development of substructure test in real time for hydraulic shaking tables”, under contract

Do 360/22-1,2, German Research Foundation (DFG), 2006 – 2010. 7) E-FAST Project: “Design study of a European Facility for Advanced Seismic Testing”, EC Grant number. 212109, 2008 – 2011.

The 2011 World Congress on

Advances in Structural Engineering and Mechanics (ASEM'11+)

Seoul, Korea, 18-22 September, 2011

1. INTRODUCTION

Substructure testing is an advanced testing method in which most structures can be tested in a

dynamic manner without testing the entire structural system. To achieve this, the system is

divided into a numerical part, the one that can be modeled correctly on a computer, and an

experimental part, where the dynamic properties are unknown or are difficult to model. Thus it

needs to be tested as a real physical model. The substructure algorithm is based on a time

integration scheme. A number of such schemes have been developed (Thewalt 1987, Nakashima

1990, Shing 1991, Combescure 1997, Pegon 2000), but in the studies reported here, the

algorithm developed by Dorka (Dorka 1990) is used because of its superior performance and

versatility in Real Time Substructure Tests (RTST), even for aerospace applications (Bayer

2005).

Based on the general time discrete integration (Zienkiewicz 1977), Dorka developed a

substructure algorithm using implicit integration with digital feedback (Dorka 1990). The digital

feedback mechanism is described in Fig. 1a while the flow chart of the algorithm is shown in

Fig. 1b (Dorka 1990, 1998, 2002, 2011). The displacement vector, 1+iu , of the numerical model

at the next step is described as a linear control equation Eq. (1).

( )111

0

1 ++++

++=i

c

i

r

ii ffGuu (1)

where: 1+i

ou is a vector of explicit displacements that are known at the beginning each step, G is

the gain matrix, 1+i

rf is the vector of nonlinear numerical forces and,

1+i

cf is the vector of

coupling forces that are measured on the specimen.

In this digital feed back algorithm (see Fig. 1), the non-linear numerical forces,rf , and the

currently measured coupling forces, cf , are fed back at the sub steps, which are equally

distributed over the time step (Fig. 1a). At the end of each step, the equilibrium error is

calculated and the error force is identified. The error force is compensated at the beginning of

the next time step (Fig. 1b). Dorka proposed the PID error force compensation (Dorka 1990,

1991, 1998) and it was successfully applied in many substructure tests (Dorka 1991, 1998, 2002,

2006, 2007, Bayer 2005, Nguyen 2011). To allow the compensation adapting automatically to

changing testing environments, Nguyen and Dorka (Nguyen 2007, 2009) introduced an adaptive

force compensation based on data model and online system identification. The adaptive force

compensation is currently tested using a non-linear Tuned Mass Damper (TMD) with the

friction device UHYDE-fbr (Dorka 1995, US Patent number 5456047) and the hydraulic

shaking table at University of Kassel (UNIKA).

(b) Flow chart of substructure algorithm (a) Linear control mechanism

Fig. 1. Substructure algorithm with digital feedback and error force compensation

(Dorka 2002, 2011)

In order to perform RTST, actuators are used to impose the computed movement on the

experimental substructure and load cells are used to measure the coupling forces. Therefore, an

important issue in substructure testing is to design a proper interface between the two

substructures. It requires not only reliable measurements of the coupling forces but also a

faithful representation of the actual interface between substructure (specimen) and numerical

structure.

In the flow chart (Fig. 1), it can be seen that the role of the interface between table and

specimen is to transmit the calculated displacement and to measure the coupling forces as

exactly as possible. To transmit the calculated displacement exactly, the displacement control

system should be able to provide accurate response. The stiffness and damping properties of the

coupling should be well represented between specimen and table. In order to measure correctly

the coupling force, load cells with high resolution and low noise are required.

Due to inaccuracies in the transformations, the controllers and mechanical limitations of the

actuators, positioning errors will occur especially in continuous RTSTs. Although they can be

minimized by adaptive controllers (Stoten 2001, Wallace 2005, Nguyen 2008), but they cannot

be completely avoided. They appear as an overshoot or undershoot with a certain noise level

that depends on the quality of the testing equipment. In addition, measurement errors in the

coupling force and also regular errors (incorrect amplification or insufficient resolution) may

enter the algorithm. Except for the positioning errors of the actuators, they can be avoided

completely by a proper test setup.

In real applications, TMDs are mounted directly on the structure (Fig. 2). In a substructure

test, the structure is modeled numerically and the TMD is placed on a shaking table. Load cells

G(fr + fc)

u0

i-1

u0

i

u0

i+1

i-1 i i+1 step

Dis

pla

cem

ent

j=1 k-1 k 2

ui-1

ui

ui+1

j =

Calculate explicit displacement 1i

ou

+

at beginning of step j = 0

- Calculate velocity and acceleration at the end of step

- Calculate error force of the equilibrium equation

Apply displacement at each substep

( )cr

ii

ffGk

ju

k

juu +++−=

+

)()1(1

00

Calculate restoring force on nonlinear numerical

substructure fr

j = j+1Error force

compensation

Measure coupling force on experimental

substructure fc

No

Yes

Time integration algorithm:

( )111

0

1 ++++

++=i

c

i

r

ii ffGuu

is a linear control equation with constant gain G

must be installed between the shaking table and the specimen to measure the coupling forces

and this will introduce some inaccuracies into the interface. In order to minimize this

interference and make the behavior as close to the real structure as possible, the stiffness of the

connection should be high in this case and the measurement of the coupling forces must have

high accuracy.

(a) Bridge Britzer Damm, Berlin

(b) TMD fixed below the bridge

Fig. 2. A typical TMD application for a bridge (GERB Engineering GmbH)

2. INTERFACE DESIGNS

2.1. Interface design in the test setup of the CEA-UNIKA project

CEA-UNIKA was a project supported by UNIKA and CEA. The complete structure consists

of a two-storey steel frame and two TMDs located at the second floor (Fig. 3). Each TMD can

vibrate only in one direction. The steel frame was designed for tests with excitations in the two

horizontal directions (Dorka 2006).

Eigen-

frequencies

Hz

1st 3.75

2nd

4.5

3rd

12

1: AZALEE shaking table; 2: Frame of two stories; 3: Added mass at first floor; 4: Rigid columns;

5: TMD 2; 6: TMD 1

Fig. 3. Reference tests of the full structure including the steel frame and the TMDs using the

AZALEE shaking table in CEA (Dorka 2006)

Fig. 4 shows the interface in the reference tests, in which the TMDs are placed on the steel

frame. Fig. 5 shows instead the interface in the substructure test, in which the TMDs are placed

on two distributed shaking tables. Each interface includes seven single load cells. They are

installed in order to connect the steel frame and the TMD so that they can measure the coupling

forces. Three load cells are installed in the horizontal directions X and Y to transmit the

horizontal movement and to measure the horizontal coupling forces (labels 2 and 5 in Fig. 4),

and four are installed in the vertical direction (label 4 in Fig. 4).

The substructure tests were performed with a series of changing parameters such as time step,

∆t, in 10 ms or 20 ms, number of sub-steps, k, from 2 to 5 and with or without PID error force

compensation, P ranges from 0.85 to 1.0.

1: Second floor of the frame; 2: Load cell for measuring coupling force of TMD 1; 3: TMD 1; 4: Load

cell for checking other coupling forces; 5: Load cell for measuring coupling force of TMD 2; 6: TMD 2

Fig. 4. Interface between the steel frame and the two TMDs in the test setup in CEA

(Dorka 2006)

Fig. 5. Interface between the shaking table and the TMDs in the test setup in CEA

(Dorka 2006)

Fig. 6 shows the comparison between the substructure test and the reference test under an

earthquake load. In Fig. 6a, it can be seen that there are large pulses in the coupling force during

the substructure test. These are also present in the reference test, but they are smaller. The pulses

were generated by play in the ball bearings that connect that load cells to the table and specimen.

The ball bearings are needed to avoid forces perpendicular to the load cells. The reason behind

the smaller pulses in the reference test is a smaller stiffness of the interface there due to the

elasticity of the frame. Since these are high-frequency pulses, they hardly excite the structural

modes and thus have a negligible influence on the structural response. Also, they do not de-

stabilize

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,

Fig. 11. A comparison of the coupling forces (a, b, c) and the displacements (d, e, g) between

substructure test Sub02 (time step ∆t = 10ms, number of sub steps k = 3, PID compensation with P

= 0.9) and reference test No7 under earthquake Petrovec 1979 excitation, with air pressure p = 0.

In the SUBSHAKE project, the pulses due to play in the bearings was reduced (compare Fig.

11a and Fig.6) but not entirely avoided although the swivel supports were pre-stressed. The

coupling force shows a better match than in the CEA-UNIKA tests (Fig.6), but the accuracy is

still not satisfactory. The displacement response (Fig. 11d) does not match so well, which in this

case is due to the higher complexity of the steel frame: The numerical model used in these

RTSTs did not match as well as the model in the CEA-UNIKA tests.

2.3. Interface design in the test setup of the E-FAST project

The E-FAST project is a design study for a new European testing facility, and is performed in

collaboration between five leading European institutions in the field of earthquake engineering.

Some major goals of the new European facility include high performance, large capacity, great

flexibility, strong integration with other facilities and advanced networking capabilities not only

in Europe but also worldwide. In this context, the test setup at UNIKA has been used to study

real time substructure testing with shaking tables, to combine shaking tables with other on-site

facilities and to perform distributed testing.

The concept of the test setup for reference and substructure tests is given in Fig. 12. In the

reference tests, the leaf spring between actuator and table (Fig. 12a) is unlocked. Table and leaf

spring serve as the first DOF and the TMD on top of the table is the second DOF. The 2nd

DOF

system has two eigenfrequencies 1.875 Hz and 3.025 Hz. When the leaf spring is locked (Fig.

12b) a substructure test can be performed with just TMD modeling numerically the table and the

leaf spring.

Eigen-

frequencies

Hz

1st 1.875

2nd

3.025

(a) Test setup for reference test

(b) Test setup for substructure test (locking device at leaf spring)

Fig. 12. The test setups for reference test (a) in which the leaf spring is unlocked and for

substructure test (b) in which the leaf spring is locked by a locking device.

In using this concept, there is no difference in the structure of substructure tests and reference

tests. This allows focusing mainly on the accuracy of the substructure algorithm and on the

control of the hydraulic shaking table.

An advanced force measurement concept using multi-directional load cells was developed

and applied. Four multi-directional load cells are placed between the TMD and the shaking table

(Fig. 13). Each load cell measures two horizontal forces and a vertical load. The two horizontal

forces can be used as coupling forces in substructure tests while the vertical force is mainly used

for adjusting the distribution of static vertical loads when placing the TMD on the table. The

coupling force Fc in substructure test is the sum of the measured forces by the four load cells in

the horizontal y-direction.

The measurement of the coupling forces using multi-directional load cells avoids the pulses

in the coupling forces observed in the previous tests. It provides high stiffness within compact

dimensions.

Fig. 13. Multi-directional load cells for substructure tests with non-linear TMD on the shaking

table at UNIKA

The load cells have been calibrated using a dynamic testing machine with a calibration load

cell (Fig. 14).

(a) Test setup for calibration

(b) Comparison between new and calibration load cell

Fig. 14. Calibration of the multi-directional load cells

Calibration of multi-load cells

-12

0

12

-12 0 12

Reference Force (kN)

Multi-lo

ad c

ell forc

e (kN)

More than twenty reference tests with different types of excitation (sine, sine sweep and

earthquake) and air pressure in the UHYDE-fbr as well as several substructure tests with and

without compensation (PID, phase lag or adaptive force compensation) have been performed

(Nguyen 2011).

In Fig. 15, the comparison between the results of the tests Ref016 and Sub066 under

earthquake excitation is shown.

Fig.15. Comparison between reference test Ref016 (Kobe earthquake 1995 excitation, amplitude

is 10% of the real record TAZ090; air control pressure p = 0) and substructure test Sub066 (time

step ∆t = 10ms, number of sub step k= 4, adaptive force compensation with nu = 7, λ = 0.99;

phase lag compensation with nu = 5, λ = 0.99)

3.025 Hz1.875 Hz

3.025 Hz, 2nd

eigenfrequency

1.875 Hz, 1st

eigenfrequency

Because of the solid connection of the load cells in this interface, no pulses are observed and

an acceptable match is reached for the coupling force of the RTST in comparison to its reference

test (Fig. 15a). Since the interface in the RTST and reference test are exactly the same the small

deviations in the response around the first eigenfrequency are related to other sources. These can

now be studied in detail without serious inference by the interface.

3. CONCLUSIONS

Besides using an advanced substructure algorithm, the design of a good interface between

specimen and shaking table has proven to be very important in order to achieve meaningful and

accurate results in substructure testing.

The tests where spherical bearings have been used between specimen and shaking table exhibit

large pulses in the coupling force due to play in the bearings. However, these pulses have

negligible influence on the substructure test when the substructure algorithm developed by Dorka

is used. It remains stable and overall results, like displacements may be reproduced with good

accuracy. The design of adjustable swivel supports with spherical bearings allows adjusting the

gap of the bearings but it is not a solution to reduce large pulses in the coupling forces. Therefore,

any interface solution based on ball bearings is not recommended, since an acceptable accuracy

cannot be achieved for the coupling force, which reduces the confidence in the test results.

Within the E-FAST project, a new interface using multi-directional load cells between the

specimen and the shaking table at UNIKA has been developed. This new kind of interface can

provide up to six force components with high accuracy, has compact size and high stiffness in the

couplers. No pulses were observed and the accuracy of the coupling force was greatly enhanced.

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