EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS Earthquake Engng Struct. Dyn. 2003; 32:483–494 (DOI: 10.1002/eqe.243)
Structural vibration control by shape memory alloy damper Yu-Lin Han1; 2; 3; ∗; † , Q. S. Li3 , Ai-Qun Li2; 4 , A. Y. T. Leung3 and Ping-Hua Lin5 1 Department
of Engineering Mechanics; College of Civil Engineering; Southeast University; Nanjing; Jiangsu Province 210096; People’s Republic of China 2 Key Laboratory of Concrete and Pre-Stressed Structures of The Ministry of Education of People’s Republic of China; Southeast University; Nanjing, Jiangsu Province 210096; People’s Republic of China 3 Department of Building and Construction; City University of Hong Kong; Kowloon; Hong Kong; People’s Republic of China 4 Department of Construction Engineering; College of Civil Engineering; Southeast University; Nanjing; Jiangsu Province 210096; People’s Republic of China 5 Department of Mechanical Engineering; Southeast University; Nanjing; Jiangsu Province 210096; People’s Republic of China
SUMMARY A damper device based on shape memory alloy (SMA) wires is developed for structural control implementation. The design procedures of the SMA damper are presented. As a case study, eight such SMA dampers are installed in a frame structure to verify the eectiveness of the damper devices. Experimental results show that vibration decay of the SMA damper controlled frame is much faster than that of the uncontrolled frame. The nite-element method is adopted to conduct the free and forced vibration analysis of the controlled and uncontrolled frame. The experimental and numerical results illustrate that the developed SMA dampers are very eective in reducing structural response and have great potential for use as ecient energy dissipation devices with the advantages of good control of force and no lifetime limits, etc. Copyright ? 2003 John Wiley & Sons, Ltd. KEY WORDS:
shape memory alloy (SMA); smart material; damper; structural control; vibration; earthquake; frame structure
INTRODUCTION The most famous characteristic of shape memory alloy (SMA) is shape memory eect (SME). Olander found SME when he investigated the property of AuCd alloy in 1932. Since then, SMA has been mainly applied in medical science, electrical, aerospace and mechanical engineering. Graesser and Cozzarelli explored the possibility of using SMA as a new material ∗ Correspondence
to: Yu-Lin Han, Department of Engineering Mechanics, College of Civil Engineering, Southeast University, Nanjing, Jiangsu Province 210096, People’s Republic of China. † E-mail: hanyl
[email protected] Contract=grant sponsor: National Science Foundation of People’s Republic of China; contract=grant numbers: 50038010, 59978009.
Copyright ? 2003 John Wiley & Sons, Ltd.
Received 20 December 2001 Accepted 2 August 2002
484
Y.-L. HAN ET AL.
for seismic isolation [1]. Rogers et al. proposed the use of SMA to control the vibration of composite structures. Some experimental and theoretical studies [2–6] have been conducted in recent years to exploit SMA-based devices for structural control implementation. Dolce et al. gave a state-of-the-art review of the development of passive control devices based on SMA up to 1999 [5]. Thus, only some recent works that are directly related to the present study are mentioned below. Duval et al. presented a study on the dynamic behaviour of a single-degree-of-freedom (SDOF) mechanical system, having an SMA spring as a restoring force element [6]. Van Humbeeck and Liu reported that the damping capacity of SMA increases with increasing amplitude of vibration or applied impact and is almost frequency independent [7]. Adachi et al. developed a damping device made of shape memory alloys, which can absorb seismic energy and reduce the seismic force by its pseudo yield eect [8]. Ip proposed an analytical formula to predict the energy dissipation in Ni–Ti shape memory alloy wires under cyclic bending [9]. Previous studies have shown that SMA can be used as passive and active vibration control devices. However, most of the previous studies considered the vibration control of exible beams or composite structures only. In this study, a damper device based on SMA wires is developed to control the vibration of a steel frame. In this paper, rst of all, the energy dissipation principle of SMA wire is presented and discussed. Second, damper devices made of SMA wires are developed for structural control implementation. Third, as a case study, eight such SMA dampers are installed in a steel frame 2m high to examine how the developed SMA dampers can reduce the vibration of the frame. Experimental results show that the vibration decay of the controlled frame is much faster than that of the uncontrolled structure. Then, the nite-element method (FEM) is used to analyse the vibration decay of the SMA damper controlled frame and the uncontrolled frame under the experimental condition. Finally, the dynamic response analysis of the SMA damper controlled frame and the uncontrolled frame subjected to earthquake action (El-Centro earthquake record) is conducted using FEM to verify the eectiveness of the proposed SMA damper for vibration control of building structures.
CONSTITUTIVE RELATIONS OF SMA The energy dissipation device is made of SMA wires. In the course of vibration, SMA wires can be simplied to one-dimensional straight stretch pole with equal area. So only onedimensional constitutive relations are introduced in this article. On the base of the analysis of thermo-mechanics and continuum mechanics, researchers have presented some constitutive relations. According to the simple relations presented by Tanaka, the constitutive relations which describe the deformation behaviour of M (martensite) and R phase transformation can be expressed as follows [10]: ˙ =D˙ + T˙ + ˙ + ˙
(1)
; and T represent, respectively, stress, strain and temperature. The point above the symbols shows the derivation to time. D and represent, respectively, modulus of elasticity and modulus of thermo-elasticity. =D and =D represent, respectively, the range of strain resulting from M and R phase transformation. and (0661; 0661 and 06 + 61) represent, Copyright ? 2003 John Wiley & Sons, Ltd.
Earthquake Engng Struct. Dyn. 2003; 32:483–494
SHAPE MEMORY ALLOY
485
respectively, the volume percentage of M and R phases. And the volume percentage of A (austenite) phase is 1 − ( + ). The volume percentage of M phase, , can be written as = 1 − exp[bM cM (MS − T ) + bM ]
(2)
= exp[bA cA (AS − T ) + bA ]
(3)
where bM ; cM ; bA ; cA are material coecients. MS and AS represent, respectively, the initial temperature of M phase transformation and M phase anti-transformation under conditions of without stress. Equations (2) and (3) represent, respectively, M phase transformation and M phase anti-transformation. The volume percentage of R phase, , can be written as cM (T − MS ) − bM = bM
(4)
= 1 + bA cA (AS − T ) + bA
(5)
; cM ; bA ; cA are material coecients. MS and AS represent, respectively, the initial where bM temperature of R phase transformation and R phase anti-transformation under conditions of without stress. Equations (4) and (5) represent, respectively, R phase transformation and R phase anti-transformation.
ENERGY DISSIPATION PRINCIPLE OF SMA WIRE Ti-55.2 at% Ni (Ni atom ratio is 55.2%) shape memory alloy wire is selected to make the energy dissipation damper in this study, because nickel–titanium alloy has better energy dissipation property and higher resistance to corrosion and fatigue. Such an SMA wire is made with 0:75 mm diameter in this study. The stress–strain relationship of Ti-55.2 at% Ni SMA at 333K is shown in Figure 1 [10]. It can be seen from this gure that when the Ti55.2 at% Ni wire is tensed, under 333K, the stress–strain relationship of the SMA wire will move along the curve o–e–a–b–f–g. If unloading from point ‘g’ (Figure 1), the stress–strain relationship of the wire will change along the curve g–h–c–d–i–o. If unloading from point ‘b’, the stress–strain relationship of the wire will follow the curve b–c–d–i–o. If unloading from point ‘b’, then loading from point ‘d’, the stress–strain relationship of the wire will move along the curve b–c–d–a–b. While the SMA wire is installed in a structure and the SMA wire is deformed by the structural vibration, curve b–c–d–a–b indicates one cycle of the vibration of the wire along axial direction. The area under the curve b–c–d–a–b is the dissipated vibration energy by the SMA wire. The stress–strain relationship shown in Figure 1 demonstrates the property of superelasticity (or pseudoelasticity) of the SMA wire. In order to make the SMA wire as damper, we can assign the SMA wire to follow its stress–strain relationship along curves such as the curve b–c–d–a–b. So, the SMA wire can dissipate the vibration energy eectively. Copyright ? 2003 John Wiley & Sons, Ltd.
Earthquake Engng Struct. Dyn. 2003; 32:483–494
486
Y.-L. HAN ET AL.
Figure 1. Stress–strain relationship of Ti-55.2 at% Ni SMA.
Figure 2. Two-storey frame (unit:mm).
The above descriptions explain the energy dissipation principle of the SMA wire or the SMA damper used in this study.
VIBRATION CONTROL EXPERIMENT OF A FRAME STRUCTURE INSTALLED WITH THE SMA DAMPERS Frame structure and SMA dampers Vibration control experiment of a two-storey steel frame installed with the SMA wires-based damper is carried out in this study to examine the eectiveness of the SMA damper. The dimensions of the frame are 2 m high, 1 m long and 0:25 m wide, as shown in Figure 2, in which the blocks represent four mass blocks with 20 kg weight each, the cross lines means eight SMA dampers installed in the structure. Copyright ? 2003 John Wiley & Sons, Ltd.
Earthquake Engng Struct. Dyn. 2003; 32:483–494
487
SHAPE MEMORY ALLOY
steel wire
chuck SMA wire chuck
steel wire
Figure 3. SMA damper.
Action principle of SMA damper The energy dissipation principle of SMA wire, discussed in the second section of the present paper, is utilized to make SMA damper. The details of the SMA damper are shown in Figure 3. Each SMA damper consists of two steel wires ( 7 mm) and 1 SMA wire ( 0:75 mm). The steel wire is 582 mm long and the SMA wire is 250 mm long, as shown in Figure 3. Because the tension stiness of the steel wire is much larger than the SMA wire, making the SAM damper be in tension condition when the frame is vibrating, the SMA wire will thus take almost all the deformation of the SMA damper. As a result, the SMA damper can dissipate vibration energy eectively. Eight such SMA dampers are installed in steel frame structure. The SMA dampers are heated to 333 K. When frame vibrating, SMA damper dissipates vibration energy of the frame. The details of principle and process are listed as following. 1. Installed positions of SMA damper should be determined rst. The two xed points of each SMA damper should be determined mainly. In this paper, an SMA damper is xed between two points of one-storey frame diagonal of (Figure 1), because relative displacement of the two points are the largest one in one frame storey and it is easy to xed SMA damper in such position of frame. 2. The relative displacement of two xed points of each SMA damper should be calculated, according to vibration characteristics of structure. 3. The length and pre-deformation value of SMA wire of SMA damper could be determined according to the relative displacement, mentioned above. It should be considered to prevent breaking of SMA wire when the SMA wire length is designed. The size of SMA damper (Figure 3) is determined according to the above principle. 4 The SMA wire of SMA damper should be pre-deformed to the calculated value before it is xed into the structure. 5. After pre-deformed to calculated value, the SMA dampers can be installed in the structure. 6. The SMA wires of SMA damper are heated to working temperature (333K in this paper). When structure is vibrating, the SMA dampers will dissipate the vibration energy of the structure. 7. If the temperature of SMA wires is kept at 333 K, the SMA damper will dissipate vibration energy of the structure whenever the structure is vibrating. Vibration testing system The four poles of the frame are xed on the base. The procedure of conducting the vibration test of the frame is as follows: Firstly the top of the frame is stretched to a given position along the X-direction shown in Figure 2, then releasing the top of the frame suddenly. In Copyright ? 2003 John Wiley & Sons, Ltd.
Earthquake Engng Struct. Dyn. 2003; 32:483–494
488
Y.-L. HAN ET AL.
10
NonDimensional Disp
8 6 4 2 0 -2 -4 -6 -8 -10
0
10
20 30 Time, s
40
50
Figure 4. Vibration decay history of the uncontrolled frame.
such a condition, the frame will vibrate mainly in its rst mode. So the strain of variation at the bottom of each pole of the frame can display the variation displacement of the top part of the frame. By measuring the strain at the bottom of the frame pole, we get the vibration decay history of the frame. Dynamic strain measuring system is used to measure the strain. A strain gage is carefully attached to the frame to measure the vibration displacement of the frame along X-axial direction (Figure 2). The strain signal data is stored in hard disk of a computer by A=D converting card. In the following parts of this paper, the recorded strain data are called the displacement data representing the displacement of the top part of the frame along X -axial direction. Experimental results The vibration decay histories of the uncontrolled frame and the frame with the SMA dampers are shown in Figures 4 and 5, respectively. Figure 4 shows that it takes about 45 s for the frame to decay its vibration from the initial displacement to half of the initial displacement. Figure 5 illustrates that it only takes less than 1s for the controlled frame to decay its vibration from the initial displacement to half of it. In order to compare the speed of vibration decay for the controlled and uncontrolled frame, non-dimensional displacement co-ordinate is used in Figures 4 and 5 to display the vibration decay history.
DYNAMIC ANALYSIS OF THE FRAME BY FINITE-ELEMENT METHOD Vibration decay simulation and estimation of structural parameters Finite-element method is used to conduct the dynamic analysis of the uncontrolled and controlled frame. Several structural parameters of the frame, which are needed in the dynamic analysis, are selected according to our experience in the rst stage of the present paper. Although the rst simulated time history of vibration decay is not close to measured one based Copyright ? 2003 John Wiley & Sons, Ltd.
Earthquake Engng Struct. Dyn. 2003; 32:483–494
489
SHAPE MEMORY ALLOY
10
NonDimensional Disp
8 6 4 2 0 -2 -4 -6 -8 -10
0
4
2
6
Time, s
Figure 5. Vibration decay history of the frame with the SMA dampers.
Figure 6. Finite-element model of the uncontrolled frame.
on the rstly selected structural parameters by our experience, the simulated history is in good agreement to the experimental data after several times of adjustment of the parameters. In this way the structural parameters of the frame are determined, which will be used in the following dynamic analysis of the frame structure under earthquake action to study how eectiveness of the SMA damper in structural control implementation. A nite-element software-ANSYS is adopted to conduct the dynamic analysis of the controlled and uncontrolled frame. Finite-element models of the frame and the frame with the SMA dampers are shown in Figures 6 and 7, respectively. The forces, applied on the top nodes of the uncontrolled and controlled frame along X-axial direction, are shown in Figures 8 and 9, respectively. It is found that when the critical damping ratio is set to 0.7% for the Copyright ? 2003 John Wiley & Sons, Ltd.
Earthquake Engng Struct. Dyn. 2003; 32:483–494
490
Y.-L. HAN ET AL.
Figure 7. Finite-element model of the frame with the SMA dampers.
3.5 3.0 2.5
Force, N
2.0 1.5 1.0 0.5 0.0 -0.5
0
10
20 Time, s
30
40
50
Figure 8. Force applied on the uncontrolled frame.
frame structure, the calculated vibration decay history (Figure 10) of the frame is close to the measured results (Figure 4). In this study, an SMA damper is simplied as a linear spring. It is found, by several times of adjustments, that the calculated vibration decay history (Figure 11) of the frame installed with SMA dampers is in good agreement with the experimental data (Figure 5) when the spring constant and the critical damping ratio of the frame with the SMA dampers are selected as 16 000 N=m and 5%, respectively. Copyright ? 2003 John Wiley & Sons, Ltd.
Earthquake Engng Struct. Dyn. 2003; 32:483–494
491
SHAPE MEMORY ALLOY
3.5 3.0 2.5 Force, N
2.0 1.5 1.0 0.5 0.0 -0.5 1
0
3
2
4
5
6
Time, s
Figure 9. Force applied on the controlled frame.
0.010
Disp, m
0.005 0.000 -0.005 -0.010 0
10
20
30
40
50
Time, s
Figure 10. Simulation of vibration decay of the uncontrolled frame.
Vibration response simulation of the uncontrolled and controlled frame under earthquake action (El-Centro wave) The structural parameters of the frame and the SMA dampers are determined in the above section. In order to examine the eectiveness of the SMA damper in structural control application, in this section, the vibration responses of the uncontrolled frame and the SMA damper controlled frame subjected to earthquake action will be calculated using the nite-element method. El-Centro earthquake record is adopted as earthquake excitation and treated as node forces that are applied at nodes C and D (see Figures 8 and 9) along X-axial direction. The vibration Copyright ? 2003 John Wiley & Sons, Ltd.
Earthquake Engng Struct. Dyn. 2003; 32:483–494
492
Y.-L. HAN ET AL.
8 6
Disp, *E-5 m
4 2 0 -2 -4 -6 0
1
2
4
3
6
5
Time, s
Figure 11. Simulation of vibration decay of the frame with the SMA dampers.
0.15
Displacement, m
0.10 0.05 0.00 -0.05 -0.10 -0.15
0
10
20
30
40
50
Time, s
Figure 12. Vibration response of the uncontrolled frame under El-Centro earthquake wave.
responses of the uncontrolled and controlled frame at node A along X-axial direction are shown in Figures 12 and 13, respectively. In Figures 12 and 13, it is the vibration response of frame under El-Centro earthquake excitation from 0 to 30 s. The residual part of Figures 12 and 13, from 30 to 50 s, is vibration decay history of frame without any excitation. By comparing these gures, we can see that the largest vibration response of the SMA dampers controlled frame is about 15% of that of the uncontrolled frame, and the vibration decay speed of the controlled frame is much faster than that of the uncontrolled frame, suggesting that the proposed SMA damper is very eective to reduce structural response. Copyright ? 2003 John Wiley & Sons, Ltd.
Earthquake Engng Struct. Dyn. 2003; 32:483–494
493
SHAPE MEMORY ALLOY
0.015
Displacement, m
0.010 0.005 0.000 -0.005 -0.010 -0.015 0
10
20
30
40
50
Time, s
Figure 13. Vibration response of the frame with SMA dampers under El-Centro earthquake wave.
CONCLUSION REMARKS Energy dissipation principle of SMA wire is presented and discussed in this paper rst. A damper device, made of SMA wire, is developed for structural control implementation and eight such SMA dampers are installed on a steel frame with 2 m height to examine the eectiveness of the SMA dampers in vibration reduction of the frame. Experimental data show that vibration decay speed of the SMA dampers controlled frame is much faster than that of the uncontrolled frame. Finite-element method is used in free vibration analysis of the SMA dampers controlled frame and the uncontrolled frame. By comparing with the measured vibration decay history and adjusting the structural parameters for several times, the structural parameters of the frame and the SAM dampers are determined. Finally, dynamic responses of the uncontrolled frame and the SMA dampers controlled frame subjected to earthquake action (E1-Centro record) are simulated based on the nite-element method to study how eectiveness of the SMA damper to reduce the dynamic response of the frame. From the experimental data, it is found that the proposed SMA dampers can signicantly increase the vibration decay speed of the frame. The numerical simulations of the controlled and uncontrolled frame under earthquake action also show that the proposed SMA dampers can reduce the structural response eectively. Considering the excellent property of energy dissipation and higher resistance to corrosion and fatigue, nickel–titanium SMA is quite suitable for making damper devices for vibration control.
ACKNOWLEDGEMENT
This project is sponsored by the National Science Foundation of People’s Republic of China (Grant No. 50038010, 59978009). Copyright ? 2003 John Wiley & Sons, Ltd.
Earthquake Engng Struct. Dyn. 2003; 32:483–494
494
Y.-L. HAN ET AL.
REFERENCES 1. Graesser EJ, Cozzarelli FA. Shape memory alloys as new material for aseismic isolation. Journal of Engineering Mechanics (ASCE) 1991; 117:2590 – 2608. 2. Aiken ID, Nims DK, Whittaker AS, Kelly JM. Testing of passive energy dissipation systems. Earthquake Spectra 1993; 9:335 –369. 3. Witting PR, Cozzarelli FA. Shape memory structural dampers: material properties, design and seismic testing. NCEER Report, No. 92=13, State University of New York, Bualo, USA, 1992. 4. Hodgson DE, Krumme RC. Damping in structural application. Proceedings of the 1st International Conference on Shape Memory and Superelastic Technologies, Pacic Grove, CA, USA, 1994. 5. Dolce M, Cardone D, Marnetto R. Implementation and testing of passive control devices based on shape memory alloys. Earthquake Engineering and Structural Dynamics 2000; 29:945 –968. 6. Duval L, Noori MN, Hou Z, Davoodi H, Seelecke S. Random vibration studies of an SDOF system with shape memory restoring force. Physica B 2000; 275(1–3):138–141. 7. Van Humbeeck J, Liu Y. Shape memory alloys as damping materials. Materials Science Forum (Shape Memory Materials) 2000; 327(3):331–338. 8. Adachi Y, Unjoh S, Kondoh M. Development of a shape memory alloy damper for intelligent bridge systems. Materials Science Forum (Shape Memory Materials) 2000; 327(3):31–34. 9. Ip KH. Energy dissipation in shape memory alloy wires under cyclic bending. Smart Materials and Structures 2000; 9(5):653 – 659. 10. Lin PH, Tobushi H, Tanaka K, Ikai A. Deformation properties of TiNi shape memory alloy. JSME International Journal 1996; 39(1):108–116.
Copyright ? 2003 John Wiley & Sons, Ltd.
Earthquake Engng Struct. Dyn. 2003; 32:483–494
