An experimental study on seismic behaviour of viscoelastically damped structures

An experimental study on seismic behaviour of viscoelastically damped structures R. C. Lin, Z. Liang, T. T. Soong a n d R. H. Z h a n g Department of Civil Engineering, State University of New York at Buffalo, Buffalo, New York 14260, USA

P. Malunoodi Corporation Research Laboratories, 3M Company, St. Paul, Minnesota 55144, USA (Received September 1989; revised November 1989)

The seismic behaviour of structures with added viscoelastic dampers is studied experimentally. Experiments were conducted using a model structure simulating firstly a single-degree-of-freedom structure and second a three-degree-of-freedom structure. The degree of reduction in relative displacements and absolute accelerations is used as a measure of effectiveness of added viscoelastic dampers. Temperature dependency of the damper is carefully examined together with the problem of damper placement. Experimental results show that significant improvement of structural performance under seismic conditions can be realized with addition of viscoelastic dampers, it is shown that damper effectiveness is strongly dependent upon environmental temperature. The importance of damper positioning within the structure is also stressed. Keywords: seismic behaviour, structural performance, viscoelastic damping

Viscoelastic materials have been used in the recent development of an energy dissipation device called the v i ~ (VE) damper. It is anticipated that incorporation of this device into a structure can improve the structure's dynamic performance by absorbing a amount of vibrational energy. Viscoelastic have been shown tO be effective in reducing wind-~ sway of high rise buildings ~-4, examples of ~ are the World Trade Center in New York City and the C o i ~ Center in Seattle. This study considers the possible use of viscoelastic dampers as energy absorbing devices, particularly whether or not they can effectively reduce structural to seismic excitations when installed in a building structure. This problem was studied recendy truing oomMmter simulatioFS. The results reported therein dtow that the respon~ of tall f r m ~ stmctures can be =kp~.cmey reduuxi. 1"heprinmy purpose of the present invmtigetion is to provide an experimental

verification by ~

out an experimental study using

a scaled-down model structure in the laboratory.

The model structure is a steel frame modelling a shear building by the method of artificial mass simulations . It is similar in geometry, material properties and boundary conditions to a structural model which has been extensively tested at other institutions7,s and it is approximately a 1:4 scaled model of a prototype structure (1:2 scaled model), which has also been extensively tested under seismic conditions 9'1°. Two series of tests were carried out on this model structure. In the first test series, the model was rigidly braced on the top two floors to simulate a single-degreeof-freedom (SDOF) system and then, in the sec~td, the braces were removed so that the dynamic behaviour of a multi-degree-of-freedom (MDOF) structure could be studied. As SDOF system, its structural ~ are as follows: mass = 16.69 l b - s c c 2 / i n , s t ~ s = 7,934 lb/ in, critical damping factor= 1.24%, and natural frequency = 3.47 Hz. The stmcuu-d properties of the 3DOF system are given in Table 1. The base motion of the model stn~ure is supplied by a shaking table. A total of 18 viscoelastic dampers were

0141-0296/91/010075~10 © 1991 Butterworth-Heinemann Ltd

Eng. Struct. 1991, Vol. 13, January 75

Seismic behaviour of viscoelastically damped structures: R. C. Lin et al. Table 1 Parameters of 3DOF model structure

Mass matrix M (Ib-sec 2/in) Stiffness matrix K (Ib/in) Damping matrix C (Ib-sec/in)

0 0

5.6 0

[ 1 649

-9370

- 9370 2107

2.185

-0.327 0.352

17250 - 9274

0327

2.608 -0.015

5.6

21077

- 9274 / 7612-1

FI2

F/2

I 0

I J O.

Steel flange

0.352]

-0.015 / 2.497_1

D.24] Modal frequency o~ (Hz)

1 6"83l [11.53J

I-1.627

Modal damping r (%) Modal matrix •

| 0.39| L0.36_1

0.262

0.743

~ 0.568 0.780

0.373 -0.555

V E material

Centreplate 0.583-0.728 0.360

F Figure I

selected for this study. The dynamic characteristics of these dampers were first determined in the laboratory. In the structural tests, special attention was paid to factors such as environmental temperature and damper positioning. Comments are made about their influence on the damper effectiveness. Experimental arrangement and procedure The experimental study was in three phases; damper property tests and two test phases using a model structure with viscoelastic dampers installed. Discussion on the structural tests will be the main concern of this paper. The results from the damper property tests are briefly summarized below to facilitate discussion of the structural test results. A detailed description of the damper property tests can be found in Ref. 11.

Damper properties Typical viscoelastic dampers consist of viscoelastic material layers confined by steel plates. They can be classified into several categories based on the way in which the VE material layer deforms. For example, extension-type dampers consist of VE layers that undergo extension and compression, while VE layers in shear-type dampers experience nearly pure shear. The shear-type dampers were used in this study because they have higher energy dissipating capacity. Figure I shows a shear,type damper consisting of two VE layers bounded by three steel plates. The properties of the viscoelastic damper are characterized by two moduli, namely, shear storage modulus G' and shear loss modulus G", and its dimensions, i.e., thickness t and area A. G'>.'o.n the above information, both the stiffness k of the damper and the amount of energy E dissi~ted in one cycle by the damper can be determined by k = (G '2 + G"2)]/2A/t

76

Eng. S t r u c t . 1 9 9 1 , Vol 13, J a n u a r y

(1)

A shear-type damper

E = 7r72G"At

(2)

where 70 is the strain amplitude. The main purpose of the damper property test was to find the moduli G' and G" and to determine their variations with changes in the environmental temperature and loading frequency. Each damper was tested under up to five different temperatures to see the extent to which the damper's properties are dependent on temperature. One of the dampers was also loaded under four different frequencies to see the frequency effect on the damper's characteristics. During the test, the damper displacement was kept constant while the sinusoidal force applied to the damper was continuously measured in order that the moduli G' and G" can be determined as well as the hysteretic loop, indicating the amount of energy dissipated in the damper during each deformation cycle. One set of time history and hysteresis ~ for a damper at ambient temperature is given in Figure 2. Figure 3 shows its shear loss modulus G" as a function of temperature and frequency. The variation o f its she~r storage modulus G' follows a similar pattern. It is observed that G' and G" o f the damPer were sensitive to

the environmental temperature but not strongly dependent on the loading frequency in the frequency range considered. This general behaviour was observed for all dampers tested and used in the structural tests.

Structural tests As mentioned earlier, the smw..tural tests were carried out using a scaled-down three-storey steel ftaa~e model strucoare which simulates d y m c s of a prototype structure by means of artificial mass simuljttion. In the experiment, the model structure was bolted to a concrete block which in turn was connected to a shaking table that supplied the desired base excitation. In the first test

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system. ' r ~ vismelas~ dampers were installed along each side o f the smctore with various orientations. • F~m'e 4 s h e ~ the structural configuration and one of

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In this e ~ m t ~ s e a ~ study; sine waves, white noise ami seimsk metion were consklered for horizontal base excitation. Under seismic excitation, different fractions

of the El Centro earthquake acceleration ( N - S ) were used as inputs, and the full-scale time history is shown in Figure 6. Floor accelerations and displacements were. directly measured by accelerometers and displacement transducers installed on each floor. In the case of base excited structural response, relative d i s p l ~ t s to the base were of practical interest. For the SDOF test, a reference frame was mounted on the shaking table so that relative displacements could be directly monitored. For the MDOF test, since it was difficult to mount the

reference frame on the table, absolute displacements were measured and relative ~ t s were obtained by subtracting from them the base d ' u q ~ - m e n t .

Eng. Struct. 1991, Vol. 13, January

77

Seismic behaviour of viscoelastically damped structures: R. C. Lin et al. 2.0

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Since mechanical properties of the viscoelastic materials are sensitive to temperature, thermocouples were glued to the dampers to monitor the damper temperature so that temperature dependency of their damping effect could be investigated.

Single-Degree-of-Freedom System Structural tests were first carried out on the model structure with its top floors rigidly braced. The use of a simple SDOF system permitted a better exposition of the relationship between system seismic behaviour and several factors which may influence the damper energy absorbing capacity. These factors include the environmental temperature, damper positioning on the structure, and damper dimensions. The temperature factor was considered extensively. Since it was difficult to vary the room temperature, temperature increase in the dampers was realized by heating each individual damper. Table 2 summarizes the results from seismic tests at different temperatures. The system natural frequencies were taken from the acceleration transfer function, so were the damping factors using the half-power rule. The re~oonse time histories are shown in Figures 7 and 8 where the no-damper case is compared with the damper-added case at T = 26.6°C. It is worth mentioning that adding viscoelastic dampers to the structure will increase not only its damping but also its stiffness as given in equation (1). In

78

Eng. Struct. 1991, Vol 13, January

Ftgure 4

Structure

and damper

configurations

for SDOF

system

order to see the net damping effect of added dampers, a reference system was used for comparison purposes and ~t is referred to as the 'no-damper' system. This system is the same as the original structural system except that

Figure 5

MDOF

system

configuration

Seismic behaviour of viscoelastic'ally damped structures: R. C. Lin et el.

bracings were added at damper locations whose stiffnesses were the ~ as those of the VE dampers. All the comparisons are made with ~ to this reference system. The effectiveness of the added dampers in reducing ~ respomm of the ~ucmre can clearly be seen from Table 2 and Figures 7 and 8. Compared to the reference system, redactions in the relative displacement range from 75 % to 87 % with a corresponding decrease in absolute accelerations of approximately 60%. The increase in damping is also substantial as the original structure's damping factor was 1.24%. Significant temperature dependency of the damping effect was observed. When the temperature rises, the damping factor increases and natural frequency decreases, and response is a combined consequence of variations in these two parameters. Since the structural system with added dampers is no longer a lightly damped system in this experiment, the damping factors obtained using the half-power rule are not exactly

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Acceleration of El Centro Earthquake ( N - S)

Experimental results for SDOF system at different temperatures Structural parameters

Case and temperature

Natural

oC

frequency, (Hz)

No damper

Responses under seismic

Damping factor, (%)

5.124

4.27

Max. relative displacement, (in)

Max. absolute acceleration, (g's)

0.29

1.0

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0.445 0.424 0.414 0.412 0.395

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10.75 9.75 9.44 8.63 6.63

7.13 18.58 20.61 28.62 49.57

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Eng. Struct. 1991, Vol. 13, January

79

Seismic behaviour of viscoelastically damped structures: R. C. Lin et al. 1.0

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considered as qualitative, especially for high damping cases, showing trend of change with increasing lemperature. To support this idea, a computer simulation using system parameters of the model structure was conducted, with results closely matching those obtained from the experiments. Figure 10 shows the ccn,aparison of maximum relative displacements from test results and from computer simulation. The second factor examined was the effect of damper positioning within the structure. In this case, dampers were installed at different inclinations with respect to the horizontal direction and the temperature was kept at around 30°C. The results of these tests are listed in Table 3. The data indicate that, when the dampers are installed along the main diagonal with an inclination of 37 ° for this structure, the response reduction is at its

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Seismic behaviour of viscoelastically damped structures: R. C. Lin et aL Table

3

Results for different damper placements Responses under seismic

Structural parameters Angle from horizontal,

Natural

Damping

Max. relative

Max. absolute

frequency, (Hz)

factor, (%)

displacement, (in)

accelecation, (g's)

29,6 29, 5

3.19 3.62

10.78 9.83

0.10 0.097

0,094 O. 148

°37.0

26.6 29.8t 32.9

7.75 6.66 5.56

10.49 22.94 35.39

0.018 0.020 0.021

0.161 O. 126 0.09

52.0 71.0

30.1 30.2

5.19 3.56

16.87 12.72

0.035 0.085

O. 106 O. 111

(o)

'Temperature, (°c)

21.1 15.5

*Diagonal direction between first floor and base; t()sta obtained by interpolation

maximum. This is expected since the maximum deformat,on takes place in this direction with resulting maximum damper deformation.

Multi-Degree-of-Freedom system In this test phase, the same model structure was used except that braces were removed from the top floors to simulate a 3DOF system. It thus provided more flexibility in the placement of dampers in more realistic settings. The effect of ~ and damping positioning was again investigated. Emphasis, however, was placed on damper placement with three cases studied. In Case 1, dampers were installed on each of the three floors. In Case 2, dampers were installed on the.first and second floors, and in Case 3, dampers were only added to the

first floor. As for the temperature consideration, experiments were conducted at two different temperatures: one at the ambient temperature of 22.2°C and the other at the relatively high temperature of 27.5°C. Typical responses of the structure to seismic excitation are given in Figures 1 1 - 1 3 for Case 1. The response quantifies with dampers at T = 27,50C are not plotted as they are similar to those at T = 22.20C. As can be seen, response levels at all floors are reduced significantly. A comparison of maximum responses for all three cases is given in Table 4 which also shows the damper placement for each case. It is seen from Tabte 4 that, comparing each case to its corresponding reference system, viscoelastic dampen are effective even when only added to one floor. A reduction of about 50% in displacement and more than 60% in acceleration can be realized. By comparing the three cases, it is

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Eng. Struct. 1991, Vol. 13, January

81

Seismic behaviour of viscoelastically damped structures: R. C. L i n e t al. 0.4

observed from Table 5 that Case 1, with dampers: added to all floors, is the optimal one for reducing structural response. Although Case 2 may appear to be the best from the point of view of reduction percentage, the top floor response is not well controlled in this case, These experimental results suggest that the effectiveness of viscoelastic dampers is governed more by their placement within the structure than by their sheer number. For more complicated structures with a limited number of dampers available, the optimal plaecmr~nt of viscoelastic dampers is a problem of significance and n e ~ s to be further explored.

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An experimental investigation has been conducted to determine whether viscoelastic dampers, when installed in a building structure, can he effective in reducing structural response to seismic excitations. The experiments were performed using a 1:4 scale model structure simulating a multi-degree-of-freedom frame structure. By proper bracing, a single-degree-of-freedom as well as a multi-degree-of-freedom system was simulated. Experimental results show that significant improvement of structural performance under seismic conditions can be realized with the addition of viscoelastic dampers at appropriate locations. In the SDOF case, it is shown that response reductions can he as high as 87 % for the relative displacement and 60% for the absolute acceleration. Results from the MDOF sysmm tests show that,

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Table 4

Experimental results o f M D O F seismic tests, f r e q u e n c y and damping characteristics

With dampers

Case

Configuration of s t r u c t u r e

Parameters

Mode

7--

Natural frequency (Hz)

I 2 3

Damping factor (%)

I 2 3

Natural frequency (Hz)

I 2 3

Damping factor (%)

I 2 3

Natural frequency (Hz) Damping factor (~)

\

\ J

82

Eng. Struct. 1991, Vol 13, January

No dampers (reference)

2.54 7.71 12.99 I .684 0.621 0.155 2.05 5.96 12.04

Ambient temperature

Higher temperature

5.76 14.84 19.04

5,18 I 4.36 18,85

2. 052 2. 679 4.996

12,935 5,956 4,026

4.30 11.04 19.24

3.91 10.55 18.85

2. 523 0.28 0.075

3.10 3.52 6.45

11.0 5,81 5.47

I 2 3

I .855 6.25 11.23

2.734 9. 765 18.85

2. 734 9. 668 17.875

I 2 3

2.566 I .025 0.164

I .482 0.892 2.566

2.78 2,51 7,54

Seismic behaviour of viscoelasticMly damped structures: R. C. Lin et al. Table 5

Experimental results of MDOF seismic test, response With dampers

No dampers

(reference} Case

Configuration of structure

Max. y a h

Floor

Max. val.

Max. y a h

Relative displacement

1 2 3

0.1675 0.26/42 0.3560

0.0326 0.0525 0.0830

80.5 80.1 76.7

0. 0329 0.0/482 0.0691

80. q 81.8 80.6

Storeydrift displacement (in)

0-1 1-2

0.1675 0.1367

0.0326 0.0/416

80.5 69.6

0.0329 0.0495

2-3

O. 1172

O. 0427

63.6

0.0/49/4

80.4 63.8 57.8

Absolute acceleration

1 2 3

O. 23/45 0. 2588 0.3/48/4

O. 1170 0.178/4 0. 2373

50.3 31.1 31.9

O. 0961 0. 1213 0.1862

61.1 53.1 /46.6

1 2 3

0.3159 0.4180 0.5181

0.0378 0.0775 0.2102

88.0 81.5 59./4

0.0325 0.0723 0.1/419

89.7 82.7 72.6

0-1 1-2 2-3

0.3159 0.15/47 0.1910

0.0378 0.0615 0.1377

88.0 60.2 27.9

0.0325 0.0623 0.0979

89.7 59.7 /48.7

1 2 3

0.3623 0. 3233 O./48/40

0.1073 0.1923 O./4134

70./4 /40.5 1/4.6

0.1081 0.1/483 O. 2766

70.2 5/4.1 /42.8

1 2 3

0. 3234 0. 4963 0,5935

0. 0511 0.2865 0.4521

84.2 /42.3 23.8

0.0467 0.1745 0.286/4

85.6 6/4.8 52.0

0-1 1-2 2-3

0. 323/4 0.1924 0.1821

0.0511 0.2/4/48 0.205/4

8/4.2 -19.2 -12.8

0.0/467 0J365 0.1277

85.6 29.1 29.9

Absolute acceleration

1

(g~s)

3

0. 2889 0. 2242 0. 3769

0.1058 0.2916 0.3711

63. q -30.1 1.5

0.0945 0.1968 0.2688

67.3 12.2 28.7

(g's)

Relative displacement (in)

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Responses

(in)

\

Ambient temperature

Storeydrift displacement (in)

Absolute acceleration (g~s)

Relative displacement (in)

Storeydrift displacement (in}

2

with the most favourable damper configuration, the average reductions in structural response were 80% for relative displacements, 70% for storey-drifts and about 50% for absolute accelerations. The t ~ ~ effect on the effectiveness of viscoelastic dampers when installed in a structure was carefully investigated. The experiments were carried out at temperatures hinging from about 22°C to 35°C ~ d the results show that both damper properties H and their effectiveness i n reducing stngtural response are strongly ~ dependent. Hence, environmental temperature must be taken into account when designing viscoelastic dampers for structural applications. Attention was also paid to damper positioning. While the diagonal plaoement is apparently the best choice in the s i n g ~ - f r e e d o m case, multi-degree-offreedom systems do pose the problem of optimally placing a limited number of viscoelastic dampers in a complicated smtcture. The advantage of choosing such optimal placement was demonstrated in the test. O n e limitation associated with this experimental investigetion is that, since the...,r~lel structure used is light in comparison with the weil~t of the dampers and their fixtures, the ~ of dampers not only results in an increase in its damping ratio, bat also its stiffness. A significant stiffness increase is generally not expected in real structural applications and hence the results

Red. t

Red.

presented in this study must be interpreted with care. However, simulation studies have been made under the assumption of no increase in stiffness, which support the general conclusions stated above. Finally, while damper additions are accompanied by damping increase, their effectiveness in structural response reduction diminishes as damping is increased 0.3

E

0.2 "0

_.m

~ o.~E E X

o o

I

10

I I 20 30 Damping factor ~; (~)

I

qo

50

Figure 14 Maximum relative dtsplacemmnt as function of damping factor

Eng. Struct. 1991, Vol. 13, January

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Seismic behaviour of viscoelastically damped structures: R. C. L i n e t al.

beyond a certain range. In this connection, results in relative displacement for the SDOF system were generated through computer simulation as a function of the damping factor with the structural stiffness kept constant. The results are shown graphically in Figure 14 which demonstrates this diminishing effect when the damping factor is increased beyond 20%.

Acknowledgements The authors are grateful to the 3M Company for supplying the viscoelastic dampers used in these experiments. Student support provided by the 3M Company is also gratefully acknowledged. Thanks are also due Mark Pitman and Dan Walsh, who were responsible for operating the Earthquake Simulator Facility at the State University of New York at Buffalo. This research was supported in part by the National Center for Earthquake Engineering Research, State University of New York at Buffalo, under Grant No. NCEER-86-3025.

References Mahmoodi, P. 'Design and analysis of viscoelastic vibration dampers for structures', Proc. INOVA-73 World Innovative Week Conf., E.D Eyrolles, Paris, 1974, 25-39

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2 Mahmoodi. P. 'Structural dampers'. J. Struct. Div.. ASCE 1972. 95 (ST8). 1661 - 1672 3 Keel. C. J. and Mahmoodi, P 'Desigmng of viscoelastic dampers for Colombia Center Building', in Building motion in wind, (Eds. N. Isyumov and T. Tschanz), ASCE, New York, 1986.66-82 4 Mahmoodi. P. and Keel. C. J. 'Performance of structural dampers for the Columbia Center Building', in Building motion in wind reds. N. Isyumov and T. Tschanz) ASCE. New York. 1986,[83-106 5 Zhang, R H.. Soong, T. T. and Mahmoodi, P. 'Seismic response of steel frame structures with added Viscoelastic dampers'. Earthquake Eng. Struct. Dyn. 1989, 18 (3), 389-396 6 Soong, T. T.. Reinhorn. A. M. and Yang, J. N "A standardized model for structural control experiment and some experimental results', in Active control, fed. H.H.E. Leipholz), Martinus Nijhoff Publ., 1987. 669-693 7 Miller. R. S.. Krswinlder. H. and Gere, J. M. Model tests on earthquake simulators development and implementation of experimental procedures. Rep. No. 39. Dept. of Civil Engineering, Standford Univrsity, Stanford. CA 1979 8 Moncarz, P. D. and Krawinkler, H. Theory and application of experimental model analysts in earthquake engineering, Rep. No. 50, Dept. of Civit Engineering, Standford University, Stanford, CA 1981 9 Clough, R. W. and Tang, D. T. Earthquake simulator study of a steel frame structure, Vol. 1: experimental results, EERC Rep. No. 7 5 - 6 . University of Calirfornia, Berkeley, CA 1975 10 Tang, D. T Earthquake simulator study of a steel frame structure, Vol. 2: analytical results. EERC Rep. No. 75-36. University of California, Berkeley, CA 1975 11 Lin. R. C.. Liang, Z. Soong. T. T. and Zhang, R. H. An experimental study of seismic structural response with added viscoelastic dampers. Technical Report NCEER 88-0018. State University of New York at Buffalo, Buffalo. NY. 1988