experimental and theoretical study on two types of shape memory alloy devices

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICSEarthquake Engng Struct. Dyn. 2008; 37:407–426Published online 19 September 2007 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/eqe.761

Experimental and theoretical study on two types of shapememory alloy devices

Hui Li1,∗,†, Chen-Xi Mao1,2 and Jin-Ping Ou1,3

1School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China2School of Civil Engineering, Northeast Forestry University, Harbin 150040, China

3School of Civil & Hydraulic Engineering, Dalian University of Technology,Dalian 116024, China

SUMMARY

This study proposes two types of shape memory alloy (SMA)-based devices, the tension-SMA device(TSD) and the scissor-SMA device (SSD), for the increase of stiffness. Both devices employ superelasticNiTi wires with a diameter of 1.2mm. Performance tests to study pseudoelastic behavior of NiTi wiresfind that NiTi wire’s pseudoelastic property is insensitive to loading frequency within the meaningfulfrequency range of most structures in civil engineering. The detailed design of TSD and SSD using NiTiwire is then presented accordingly. Shaking table tests of a scaled 5-story steel frame incorporated withTSDs and SSDs, respectively, in the first story are carried out. The experimental results indicate that bothSMA devices can effectively reduce building seismic response. SSDs achieve greater response reductionthan TSDs due to their displacement magnification configuration. The seismic response of the buildingmodel with and without SMA devices is numerically simulated and the simulation results demonstratethat they are in good agreement with the experimental results. Finally, it is identified that by using thewavelet transform method the structures incorporated with SMA devices exhibit nonlinear behavior andthe time-dependent characteristics of natural frequency during earthquake excitation. Copyright q 2007John Wiley & Sons, Ltd.

Received 1 June 2006; Revised 11 August 2007; Accepted 14 August 2007

KEY WORDS: SMA; pseudoelasticity; seismic; stiffness; experiment and simulation; time–frequencyanalysis; damage; nonlinearity

∗Correspondence to: Hui Li, School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China.†E-mail: [email protected]

Contract/grant sponsor: 973 Program; contract/grant number: 2007CB714204Contract/grant sponsor: NSFC; contract/grant numbers: 50178025, 50278029

Copyright q 2007 John Wiley & Sons, Ltd.

408 H. LI, C.-X. MAO AND J.-P. OU

1. INTRODUCTION

Shape memory alloy (SMA) materials are receiving increasing attention in the field of civilengineering due to their excellent quality in shape memory, pseudoelasticity, high damping capacityand corrosion resistance. Many researchers have attempted to develop SMA-based actuators anddampers to mitigate earthquake-induced vibration in civil structures. The SMA-based passivedamper is more applicable than the SMA-based actuator. It can dissipate energy and add stiffness,thus protecting buildings from incurring earthquake damage. Furthermore, the superior propertiesof SMA materials give SMA-based dampers many advantages, such as close to unlimited lifetimeand a self-centering capability.

Generally, an SMA-based passive damper is designed using the energy dissipation capability ofaustenitic SMA wires subjected to tension or martensitic SMA bars/plates subjected to bending ortorsion. From the application point of view, SMA-based passive dampers can be used as braces forframed structures or as isolators for bridges and buildings [1–8]. For example, Aiken [1] developeda cross-bracing damping mechanism, which increased structural damping ratio from 0.5 to 3.0%and reduced the overall structural seismic response. Clark et al. [2] performed extensive tests on awire-based SMA device to evaluate the effects of temperature and loading frequency on the cyclicbehavior of the device. The results showed that SMA dampers using NiTi wires exhibited stablehysteresis with minor variations due to loading frequency and device configuration (single wireversusmultiple layers of wires). In the research on SMA passive dampers, it is worthwhile to reviewthe work of the MANSIDEs (memory alloys for new seismic isolation devices) project, which isaimed at exploring the great potential of applying SMA in the field of passive seismic protection ofstructures. In this project, Dolce et al. [3] developed two families of energy dissipating/recenteringdevices, which can be used as either seismic isolators of buildings and bridges or passive dampersof framed structures. A comprehensive review of SMA application in civil engineering structurescan be found in Reference [9].

To improve the performance of SMA dampers, which is currently an important issue in applyingSMA dampers to civil engineering structures, special configurations are frequently used in thedesign of dampers to increase their energy dissipation capability, such as the recentering SMAdamper developed by Dolce et al. [3]. A common feature of these dampers is the use of two groupsof austenitic pseudoelastic SMA wires acting as a double counter-reacting system of springs.Such an arrangement, however, provides only a small force for buildings and a large number ofSMA wires are needed in the dampers to achieve a meaningful result. Furthermore, an extensivelong-term experiment has not been performed to investigate if the relaxation of pre-stress onSMA wires is negligible. To improve the performance of SMA passive dampers, magnifyingthe displacement of dampers may be a good choice. This method has been demonstrated to beeffective for most energy dissipation devices, including yielding steel devices, viscoelastic fluidor solid devices and fluid viscous dampers. The representative case of such a configuration isthe toggle–brace–damper seismic energy dissipation system proposed by Constantinou et al. [7].Shaking table tests of a large-scale steel model structure installed with this toggle–brace–dampersystem have been conducted. The experimental results demonstrated substantial increases in thedamping ratio despite the use of small-sized damping devices. Therefore, it can be predicted thatthe magnification configuration will be a potential way to improve the performance of SMA passivedampers.

This paper proposes two novel SMA-based devices, which can provide both additional dampingand stiffness for a structure. However, the proposed SMA-based devices play a critical role in

Copyright q 2007 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 2008; 37:407–426DOI: 10.1002/eqe

EXPERIMENTAL AND THEORETICAL STUDY ON TWO TYPES OF SMA DEVICES 409

the increase of stiffness rather than the damping due to the poor energy dissipation capability ofSMA materials at the present stage. Therefore, they are mostly for the increase of stiffness inthis study. The response reduction achieved by the two types of SMA devices is experimentallyand analytically investigated through a series of shaking table tests on a small-scale 5-story steelframe. Finally, by using the wavelet transform (WT) method it is identified that the structuresincorporated with SMA devices exhibit nonlinear behavior and the time-dependent characteristicsof natural frequency during earthquake excitation.

2. PSEUDOELASTIC BEHAVIOR OF NiTi WIRES AND CONFIGURATION DESIGNOF TWO TYPES OF SMA DEVICES

Before designing SMA devices and conducting shaking table tests of structures incorporated withthese devices, tension loading–unloading tests on NiTi wires are carried out to investigate theirpseudoelastic behavior at room temperature. These tests are designed to reproduce the typical workconditions that the SMA wires are subjected to when they are incorporated into structures. On thebasis of above consideration, an appropriate range of loading frequency and the number of cyclesare selected as test parameters.

2.1. Pseudoelastic behavior of NiTi SMA wires

The test specimens are nitinol SMA wire (Ti–50.8at%Ni, atom ratio) with a diameter of 1.2mm.The martensite start and finish temperatures and austenite start and finish temperatures under nostress, provided by the manufacturer (Shenzhen NTN Co. Ltd., China), are −75,−56,−38 and−16◦C, respectively. Therefore, the nitinol wires are designed to show pseudoelastic effect at roomtemperature.

All loading tests are conducted in an Instron 8501 testing machine at the Harbin Institute ofTechnology (HIT). The full length of each specimen is 200mm and its effective length betweenjoints is 94mm. The strain (�) and stress (�) of specimens are, respectively, calculated by theirelongation and axial force recorded by the Instron 8501 testing machine. During the tests, all theNiTi wires are subjected to a sinusoidal cyclic loading at room temperature (≈20◦C). The loadingfrequencies are selected as 3, 4 and 5Hz, which are compatible with the natural frequency of thestructure model used in subsequent shaking table tests. For each case, 20 cycles are repeated andthe strain amplitude of each cycle is selected to be 3%.

The experimental stress–strain curves of the specimens subjected to sinusoidal cyclic loadingwith frequencies of 3, 4 and 5Hz are shown in Figure 1. In order to clearly observe the influenceof cyclic number on pseudoelastic behavior of NiTi wire, the stress–strain curves for the 1st, 10thand last cycle of loading with a frequency of 3Hz are depicted in Figure 1(a). It can be observedthat for a given loading frequency, the post-yield modulus increases and the energy dissipationcapability decreases slightly with an increasing cyclic number. However, the 10th loop nearlyoverlaps with the 20th loop, which means that pseudoelastic behavior of NiTi wire becomes stableafter a number of loading cycles. The stress–strain curves under loading with frequencies of 4and 5Hz, respectively, demonstrate similar behavior; hence, they are not listed here in this paper.Therefore, the NiTi SMA wires should be acclimatized by uniaxial cyclic loading before theyare incorporated into SMA devices. Figure 1(b) shows the last cycle of stress–strain curves underloading with frequencies of 3, 4 and 5Hz, respectively. It can be seen that pseudoelastic behavior



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Figure 1. Experimental stress–strain curves and simplified model of NiTi wires: (a) the 1st, 10th and 20thcycle under excitation with a frequency of 3Hz; (b) last cycle under excitations with frequencies of 3, 4

and 5Hz, respectively; and (c) the simplified model.

of NiTi wires is insensitive to a loading frequency over the range of 3–5Hz in this study, which issimilar to the results presented in [10]. Thus, the strain rate dependence of pseudoelastic behaviorof NiTi wires used in this study can be ignored.

On the basis of the behavior observed in the above experiments, a simplified flag-like modelis employed to fit the pseudoelastic stress–strain curves of SMA wires as shown in Figure 1(c).In Figure 1(c), �y and �y represent, respectively, yield stress and strain, and �u and �u areelastic unloading stress and strain, respectively. Additionally, E0 and E ′ are the initial elasticmodulus and post-yield modulus. To determine the parameters of this simplified model, the exper-imental stress–strain curve is first divided into loading (OAB) and unloading (BCDO) phases.The loading phase is then linearized piecewise by the least-square method. The unloading phaseof the simplified model is determined by the principle that energy dissipated by the simplifiedmodel is equivalent to that dissipated by the experimental stress–strain curve. The characteristicparameters of NiTi wire subjected to sinusoidal excitation with a frequency of 3Hz are markedin Figure 1(c).



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Figure 2. Schematic diagram of TSD: (a) 3D pictures and (b) plan view.

2.2. Design of the two types of SMA devices for added stiffness

2.2.1. Tension-SMA device (TSD). A TSD can be installed within the frame bay of a buildingbetween an inversion chevron brace and an underlying beam. Basically, a TSD consists of sevensteel plates and an adequate number of SMA wires. Figure 2 shows the 3D rendering of TSD todescribe its operating principle. A T-shaped plate (referred to as plate 1) in the center of TSD isconnected to the inversion chevron brace of a building, and thus moves together with the overlyingbeam of the building. Rectangular steel plates 2 and 3 are placed perpendicular to plate 1 and atboth ends of it without a gap. They can be pushed by plate 1 and slide on the underlying beam.



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Figure 3. Schematic diagram of SSD: (a) 3D picture and (b) plan view.



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Figure 4. Computational model of SMA devices.

Additionally, baffle plates 4, 4′ and 5, 5′ are located symmetrically in front of and behind plate 1.These baffle plates are rigidly fixed to the underlying beam of a building to prevent plate 2 frommoving to the right and plate 3 to the left. SMA wires strung through plates 2 and 3 transverselyand are then clamped outside of plates 2 and 3.

During an earthquake, plates 2 and 3 are pushed alternately by plate 1 and deviate from thebalance position of device, which leads to elongation of the SMA wires. The elongation of theSMA wires is identical to the interstory drift of a building, if deformation of the brace is ignored.It can be readily concluded that the SMA wires in the device are always subjected to elongationduring the entire earthquake excitation process; thus, the buckling of SMA wires is avoided. As aresult, the SMA wires dissipate energy induced by an earthquake and add stiffness to a structure. Inaddition, the SMA device has a self-centering capability due to its configuration and pseudoelasticproperty of SMA wires.

According to the simplified model of a single SMA wire shown in Figure 1, the simplified modelof a TSD can be obtained as shown in Figure 4. In this figure, Fy1 and Xy1 denote the yield forceand displacement of TSD, Fu1 and Xu1 represent its elastic unloading force and displacement,K01 is the initial stiffness, �1 is the post-yield stiffness coefficient (ratio of post-yield stiffnessto initial stiffness), Xm1 denotes the displacement amplitude and Fm1 is the corresponding forceat the displacement amplitude Xm1. The displacement of a TSD is equal to the deformation ofthe SMA wires and the interstory drift of a building when the deformation of brace is ignored.Therefore, the force provided by a TSD to structure is just equal to the total force generated bythe SMA wires.

2.2.2. Scissor-SMA device (SSD). An SSD can be incorporated into a building as a TSD does. Itis made of five main components as shown in Figure 3. Similar to the TSD, a T-shaped steel plate(referred to as plate 1) in SSD is rigidly connected with an inversion chevron brace and is able tomove together with the overlying beam. Steel spindle 4 and baffle plate 5 are fixed to the underlyingbeam of a building. Knee levers 2 and 3 can rotate around spindle 4 by the pushing of plate 1 at oneend. The SMA wires drill through the other ends of levers 2 and 3 and are then clamped outside ofthem. Obstructed by baffle plate 5, knee levers 2 and 3 can rotate only by deviating from the central



position of the device. As a result, the SMA wires are always subjected to elongation during anearthquake event. If the distance between plate 1 and the center of spindle 4 is defined as L1, and thedistance between the center of spindle 4 and SMA wire is defined as L2, L2 can be designed to beseveral times L1. Such arrangement makes knee levers 2 and 3 work like a pair of scissor handles.The deformation of SMA wires can then be several times the displacement of plate 1, which isnearly identical to the interstory drift of a building. Therefore, the deformation of the SMA wires ismagnified compared with that of TSD. The yield displacement of an SSD is smaller than that of aTSD. Hence, an SSD can provide a larger force on a building than a TSD even using the same SMAwires. The simplified force–displacement model of an SSD is also shown in Figure 4, only replacingsubscript 1 by 2.

3. SHAKING TABLE TESTS AND RESULTS

Extensive shaking table tests of a scaled 5-story steel frame incorporated with SSDs or TSDs in thefirst story are carried out. These tests aim to investigate the effect of the two types of SMA-addedstiffness devices on structural seismic response reduction.

3.1. Test facilities and building model

The experimental program is carried out using the shaking table at HIT. The shaking table measures3m×4m in plane and can support test specimens up to 15 000 kg. Seismic motions can be appliedin one horizontal direction with a maximum acceleration of 1.0g. The frequency band of theshaking table is 0–15Hz.

The test structure is a 14 -scaled 5-story steel frame. Its overall dimensions are 1.8×1.8m

in plane and 4.15m in elevation. The height of each story is as labeled in Figure 5(a). Theframe is 2-bay along the direction of earthquake excitation (X -direction). The brace system isconstructed on the frames along the Y -direction to ensure that the building model oscillatesonly along the X -direction. The columns in the building are made of double angle iron whilethe beams are made of channel iron. All parts are welded together. The sections of columnsand beams are also labeled in Figure 5(a). The yield stress and Young’s modulus of the mate-rial are 215MPa and 206GPa, respectively. Responses measured during the shaking table testsinclude floor displacements and accelerations of structure and shaking table. The first modalnatural frequency and damping ratio of the test frame are 3.17Hz and 0.4%, respectively. Thedamping ratio of the test frame is smaller than an actual building because it does not have fillerwalls.

3.2. SMA-added stiffness devices

Two testing devices (either TSDs or SSDs) are symmetrically mounted on the first story of thebuilding through inversion chevron braces. There are a total of two NiTi wires with a diameter of1.2mm as the key components in each TSD or SSD. The total length of each NiTi wire is 260mm,while the effective length between two clamps is 80mm. The properties of NiTi wires are shown inFigure 1. The yield displacements of TSD and SSD are 0.093 and 0.072 cm, respectively; the initialstiffness of TSD and SSD are 15.46 and 26.13kN/cm, respectively; the ultimate displacements ofTSD and SSD are 0.62 and 0.48 cm; and the post-yield stiffness coefficients of TSD and SSD are0.226 and 0.174, respectively. The inversion chevron braces are made of double angle iron with



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section of 2L40×4. The lateral stiffness of these braces is 106 kN/cm, which is much larger thanthe additional stiffness of SMA devices. Consequently, the deformation of the inversion chevronbraces can be ignored. Figure 5(b) shows the photographs of the building model with SSDs andTSDs in the first story, respectively.

3.3. Earthquake ground motions

The following four earthquake ground motions, including two far-field and two near-field historicalrecords, are inputs to the shaking table: (i) El Centro: The N–S component recorded at the ImperialValley Irrigation District substation in El Centro, California, during the Imperial Valley, Californiaearthquake of 18 May 1940. (ii) Hachinohe: The N–S component recorded at Hachinohe Cityduring the Tokachi-oki earthquake of 16 May 1968. (iii) Northridge: The N–S component recordedat Sylmar County Hospital parking lot in Sylmar, California, during the Northridge, Californiaearthquake of 17 January 1994. (iv) Kobe: The N–S component recorded at the Kobe Japanese



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Figure 6. Drift of first interstory of bare structure and structures with TSDs or SSDsunder various earthquake excitations.



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Figure 7. Overall response comparison between bare structure and structures protected by TSDs or SSDsunder various earthquake excitations.



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Figure 8. Frequency response of structure without and with TSDs or SSDsunder various earthquake excitations.

Meteorological Agency station during the Hyogo-ken Nanbu earthquake of 17 January 1995. Theresulting absolute peak acceleration is adjusted to be 0.15g for both El Centro and Hachinoheearthquakes, and 0.16g for the Northridge and Kobe earthquakes to maintain the structure in anelastic stage.

3.4. Shaking table test results

The time histories of the first interstory drift of the structure with and without the testing devices(either TSDs or SSDs) subjected to various earthquakes are shown in Figure 6. In this figure, thedotted line and solid line represent the interstory drifts of bare structure (BS) and structure withthe testing devices, respectively. Control effectiveness on the peak value is also marked in thisfigure. It is clear that both TSDs and SSDs effectively reduce the first interstory drift. Furthermore,SSDs achieve a greater reduction in the first interstory drift than TSDs for various earthquakeexcitations.

Figure 7 shows the envelope curves of interstory drift, lateral displacement and story shear ofBS and structures with TSDs and SSDs subjected to various earthquakes. Since TSDs and SSDsare mounted only in the first story of this building, the other interstory drifts, except the first one,are not reduced and even larger than that of BS, which may be attributed to the high additionalstiffness and low additional damping of SMA devices. Additionally, although the first interstory



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Figure 9. Force–displacement curves of TSD and SSD under Hachinohe earthquake.

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Figure 10. Equivalent damping ratios of building with TSDs or SSDs under various earthquakes.

drifts of structures with added SMA devices are reduced, the corresponding shear force is stilllarger than that of BS. This phenomenon also results from the high additional stiffness and lowadditional damping of SMA devices.

Figure 8 shows the frequency response of BS and structures with added TSDs and SSDs, respec-tively, under various earthquake excitations. It is clear that the natural frequencies of structures



with TSDs or SSDs shift to the right compared with that of BS, indicating that the SMA devicesprovide additional stiffness to the structure. Furthermore, SSDs shift the frequency farther rightthan TSDs since they add a greater stiffness to the structure.

Because no proper load cell is available to measure the force of SMA devices in the shaking tabletests, the force–displacement curves of TSD and SSD during earthquakes are obtained by usingthe deformation of SMA devices recorded by LVDTs mounted on the devices and the simplifiedpseudoelastic model as shown in Figure 4. The force–displacement curves of TSDs and SSDsunder the Hachinohe earthquake are shown in Figure 9. It can be seen that both TSD and SSDbehave as flag-like hysteresis loops. An SSD generates a larger force and adds a greater stiffnessthan TSD even with the same SMA wires. The equivalent damping ratio of structure with TSDsor SSDs is calculated and presented in Figure 10. It is clear that SSDs add larger damping ratiothan TSDs. However, the results presented in Figures 9 and 10 indicate that both TSD and SSDprovide little damping for the structure in the shaking table tests due to poor energy dissipationcapability of SMA materials at the present stage. Thus, the added stiffness of SMA devices playsa significant role in the reduction of structural seismic responses. The improvement of energydissipation capability of SMA materials in the future will be beneficial to achieve larger dampingratio by the proposed SMA devices. In spite of the fault in energy dissipation capability, the SMAdevices do have recentering behaviors.

4. ANALYSIS OF STRUCTURAL SEISMIC RESPONSE

Next, the analysis of structural seismic response is conducted. The frame building used in theshaking table tests is employed in this numerical study. A shear model is used for modeling theBS. Quantities of mass and shear stiffness are obtained by updating the initial model (obtainedaccording to geometrical dimensions of the structure) using the shaking table test results. Theresulting mass from the bottom to the top story are 651.17, 666.42, 653.29, 646.07 and 813.76 kg,while the quantities of stiffness from the 1st to the 5th story are 26.2, 43.5, 30.6, 39.5 and36.5kN/cm, respectively. The model updating is performed by using the eigenvalue sensitivityanalysis method based on the first three modal frequencies, obtained from the frequency responsefunction of the recorded displacement in the shaking table tests. To verify the accuracy ofthe updated model, the seismic response of BS is simulated. The time histories of interstorydrift and story shear of each story under the Hachinohe earthquake are shown in Figures 11(a)and 12(a), respectively. For comparison, the corresponding experimental results are also shownin these figures. It is clear that the numerical results agree with the experimental results. Forthe controlled structures, the resulting hysteresis model of frame with TSDs or SSDs in the firststory can be obtained by incorporating the simplified model of the SMA devices into the force–displacement relationship of BS. The effect of mass of SMA devices on mass matrix of thecontrolled structures is ignored because it is small compared with floor mass. The time-historyresponse analysis of structures incorporated with TSDs and SSDs is performed by using theNewmark method. The nonlinear analysis program used herein is compiled by the authors usingMATLAB. Figure 11(b) and (c) shows the time histories of interstory drifts of structure withTSDs and SSDs, respectively, obtained by simulation and experiments under the Hachinohe earth-quake. Comparison of story shear at each story between experiments and simulation is shown inFigure 12(b) and (c). It can be observed that the simulation responses agree with the experimentalresults.



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Figure 11. Experimental and simulated interstory drifts under the Hachinohe earthquake: (a) bare structure;(b) structure with TSDs; and (c) structure with SSDs.



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Figure 12. Experimental and simulated story shear under the Hachinohe earthquake: (a) bare structure;(b) structure with TSDs; and (c) structure with SSDs.



5. WAVELET TRANSFORM-BASED IDENTIFICATION METHOD OF BUILDINGSWITH SMA DEVICES

It is generally recognized that the strength and stiffness of a civil structure will decrease underan intensive earthquake and that the force–displacement relationship of structural members willexhibit hysteretic nonlinear characteristics. In such cases, the frequencies of structures are timevariant and the variation of frequency is associated with the level of nonlinearity in the system.Therefore, the nonlinearity or even damage of a system can be characterized by its time varyingfrequency. As a powerful time–frequency analysis tool, the WT has been extensively employedby many researchers to capture frequency variation with time of nonlinear systems [11–14].However, the study of time–frequency responses of hysteretic nonlinear systems is insufficientand its accurate physical meaning is not yet clear. In this section, the time–frequency responseof structure incorporated with SMA devices is addressed using the WT method and the physicalmeaning of the time-varying frequency of hysteretic nonlinear system is also discussed.

The WT of a signal x(t) is presented as an example of time-scale decomposition obtained bydilating and translating a chosen analytical function (mother wavelet) along the time axis. Thecontinuous WT is defined as follows:

W�(a,b)= 1√a

∫ +∞

−∞x(t)�∗

(t−b

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)dt (1)

where b is the parameter localizing the wavelet function in the time domain, a is the dilationparameter defining the analytical window stretching and �∗ is the complex conjugate of the basicwavelet function. Therefore, b represents a time parameter and a is related to frequency. The Gaborwavelet function is used in this paper to obtain the structural time–frequency response. The Gaborwavelet function is defined as

�= 1

(�2�)1/4e−t2/(2�2) ·ei�t (2)

where parameter � and the initial scale define the time and frequency spread of the Gabor waveletfunction, and � is the parameter of frequency modulation. As often indicated in literature, theridge extracted from the scalogram of WT describes the frequency variation of structures. Detailedexplanations of the various methods for ridge extraction can be found in [13, 15] and will not beincluded here because of space limitations.

In order to discuss the physical meaning of the time-varying frequency of structures identifiedby WT, the free vibration of the structure incorporated with two TSDs in the first story is analyzed.The model structure and TSDs are the same as those used in previous shaking table tests. Thesinusoidal impulse with peak acceleration of 100cm/s2 and 0.3 s duration is used as input tothe structure. The interstory drift and force–displacement relationship in the first story are shownin Figure 13(a). The figure also presents two time-varying frequency histories, one calculatedbased on the time-variant secant stiffness and structural mass and the other identified by WTof the first interstory drift. Comparison of these two curves indicates that the instant frequencyidentified by WT is approximately the same as that calculated by using the structural time-variantsecant stiffness on the whole. Thus, the time-varying frequency may be an indicator of the levelof nonlinearity and damage of a structure.

Generally, the frequencies of the building and input earthquake are both involved in the time–frequency history. Therefore, the influence of input earthquake frequency cannot be separated from



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Figure 13. Time–frequency curves of tested model mounted with TSDs under various excitations: (a) sinu-soidal impulse; (b) the Chi-Chi earthquake; and (c) the Hachinohe earthquake.



the time–frequency response of the structure. However, WT can be used to identify the time–frequency response of a structure subjected to a wideband frequency stochastic process (such aswind [11] and a near-field earthquake). Figure 13(b) presents both the structural drift and time-varying frequencies of the test model (calculated by using the secant stiffness and identified by theWT, respectively) subjected to the Chi-Chi earthquake (the N–S component recorded at TCU052station during the Chi-Chi earthquake of 21 September 1999), which is a near-field earthquake. Itcan be seen that the frequency variation of the hysteretic nonlinear system identified by the WTmethod and calculated by structural secant stiffness is approximately the same over the time rangeof 6.75–8.5 s, when the model behaves nonlinearly. Therefore, the time-varying frequency can alsobe an indicator of the level of nonlinearity and damage of the structure in this case. Figure 13(c)presents respectively the frequency time histories of the test structure calculated by using the secantstiffness and identified by the WT, subjected to the Hachinohe earthquake. It can be seen that thetime-varying frequency calculated from the structural secant stiffness and identified by the WTmethod is still related to the level of nonlinearity (over the range of 2–6 s and 8–12.5 s) in thiscase. However, identification of the nonlinearity level of a system from the variation of frequencyobtained by the WT method is not always available because the frequency of an earthquake isusually involved with the time–frequency curve of the structural response. Further work should becarried out on this topic.

6. CONCLUSIONS

This study performed an extensive experimental and numerical study on two types of SMA-addedstiffness devices. The main conclusions of this study are summarized as follows:

(i) Two novel SMA-added stiffness devices, TSD and SSD, are proposed in this study usingpseudoelastic SMA wires. Both devices have recentering capability and provide stiffnessfor a structure. The SMA wires in the devices are always subjected to elongation duringearthquakes.

(ii) Shaking table tests and numerical studies are then performed for a 5-story steel frameincorporated with the two types of SMA devices in the first story. The experimentaland simulated results indicate that both TSD and SSD can mitigate the first-story driftresponse. However, the shear forces and other story drifts may increase. In addition, SSDcan provide greater stiffness and force than TSD due to its displacement magnificationfunction. Therefore, it can achieve a greater seismic response reduction than TSD.

(iii) WT method is used to identify the frequency variation of nonlinear hysteresis systems,which provides a potential method of identifying level of nonlinearity in systems anddetecting earthquake-induced damage of structures.

ACKNOWLEDGEMENTS

This study is financially supported by the 973 Program with grant no. 2007CB714204 and the NSFC withgrant nos. 50178025 and 50278029.

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11. Kareem A, Kijewski T. Time–frequency analysis of wind effects on structures. Journal of Wind Engineering andIndustrial Aerodynamics 2002; 90:1435–1452.

12. Kijewski T, Kareem A. Wavelet transform for system identification in civil engineering. Computer-Aided Civiland Infrastructure Engineering 2003; 18:339–355.

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experimental and theoretical study on two types of shape memory alloy devices

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