research article performance of seismic restrainer with...

Research ArticlePerformance of Seismic Restrainer with SMA Springs forSliding Isolation of Single-Layer Spherical Lattice Shells

Peng Zhuang12 and Wenting Wang1

1School of Civil and Transportation Engineering Beijing University of Civil Engineering and Architecture Zhanlanguan Road 1Beijing 100044 China2Beijing Higher Institution Engineering Research Center of Structural Engineering and New MaterialsBeijing University of Civil Engineering and Architecture Zhanlanguan Road 1 Beijing 100044 China

Correspondence should be addressed to Peng Zhuang zhuang pengsinacom

Received 18 July 2016 Accepted 15 September 2016

Academic Editor Mario Terzo

Copyright copy 2016 P Zhuang and W Wang This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The seismic response of a single-layer spherical lattice shell controlled by restorable sliding isolator is studied under differentseismic excitations The isolation system consists of flat steel-Teflon sliding isolators and superelastic SMA spring restrainers TheNiTi-SMA is used to fabricate helical spring for recentering control of the isolation system In the first step of this investigationthe configuration scheme and functioning mechanism of a novel SMA spring restrainer are introduced briefly Then realisticmechanical behavior of large-scale superelastic NiTi helical spring is studied through a set of cyclic experimental tests According tothe obtained hysteresis loops a mechanical model combining multilinear model and hysteresis model is developed to simulate theoverall response of the SMA-based seismic restrainer Besides the sliding isolator is evaluated using a bilinear force-displacementhysteresis model Finally a 60m span single-layer spherical lattice shell with substructure is modeled with finite element programNonlinear timehistory analyses of the controlled anduncontrolled lattice shell are performed consideringmultidimensional seismicinputs The study shows that the seismic response of the controlled lattice shell can be effectively reduced by using isolation andcontrol devices Furthermore the seismic response of the isolation system such as peak displacement and residual displacementcan be effectively controlled by using the developed SMA spring restrainers

1 Introduction

Seismic isolation theory and technology have developedrapidly and become an effective way to improve seismicperformance of buildings and bridges In addition thepostdisaster cost for repair and rehabilitation of engineeringstructures can be substantially reduced by using seismicisolation devices As a result seismic isolation has beenconsidered as a reliable and cost-effective technology forprotecting civil engineering structures from seismic damageAn isolation system primarily is composed of isolators andenergy dissipation devices Nowadays two types of seismicisolators are widely used [1] (1) laminated rubber bearingsand (2) sliding isolation bearings Mostly four types ofauxiliary devices are currently employed [2] (1) viscousdevices (2) elastoplastic devices (3) viscoelastic devices and(4) friction devices

To develop high performance isolation control devicesseveral researchers have proposed the use of smart materialsfor structural control Recently there has been an increasinginterest in utilizing superelastic SMA devices for the devel-opment of new seismic isolation systems [3ndash6] Althoughthe analytical and experimental studies have proven that thestructures with superelastic SMA components usually in theform of wires and bars improve the seismic response [7ndash10] further research of large-scale SMA element is necessaryto fully explore the possibility of applying SMA in seismiccontrol of engineering structures Regarding themost currentSMA-based isolation system a main drawback is that verylong SMA wires and bars have to be adopted The solutionsof configurations of SMA wires or SMA bars in the isolationdevice proposed in previous work are perhaps applicableonly for small displacements To overcome limitations relatedto seismic application in realistic building scenarios some

Hindawi Publishing CorporationShock and VibrationVolume 2016 Article ID 9218317 11 pageshttpdxdoiorg10115520169218317

2 Shock and Vibration

researchers suggested the use of superelastic SMA helicalspring instead of SMA wires or SMA bars as energy dissipa-tion and recentering control system For example Speicheret al [11] developed a tensioncompression damper makinguse of SMA helical springs which provide stable recenteringanddamping characteristics Attanasi andAuricchio [12] pro-posed conceptual design of an innovative restorable isolationsystem in which a sliding bearing is coupled with superelasticSMA helical springs that function for recentering purposes

Most of the previous studies were focused on the develop-ment and application of SMA helical springs for isolation andcontrol of multistory buildings However very few attemptshave been given to the investigation of behavior of long spanand spatial structures that are isolated by seismic isolatorsand controlled by large-scale SMA helical spring devicesTheprimary objective of this study is to carry out an investigationon feasibility and efficiency of a new type of seismic restrainerwith SMA springs that is installed between substructure andspherical lattice shell roof to reduce structural responsesThe proposed isolation system for spatial lattice structuresconsists of a flat sliding isolator and superelastic SMArestrainers The use of flat sliding bearing can reduce thestructural response by limiting the force transfer from thesubstructure to the superstructure Beside such bearingsprovide dissipation of the seismic energy due to frictionmechanism However the flat sliding bearings alone do nothave any recentering capability and may generate significantresidual displacement A new type of SMA helical springrestrainers is proposed to provide recentering mechanismand additional energy dissipation ability The conceptualdesign and the functioning mechanism of the SMA springrestrainer are described A mechanical model is derived tocapture the hysteretic behavior of superelastic SMA helicalspring restrainer In order to investigate mechanical behav-iors of the developed device such seismic restrainers areintroduced in spherical lattice shell structures isolated by flatsliding isolators A set of nonlinear time history analysesusing SAP2000 software are performed to examine theeffectiveness of the developed SMA-based device in reducingand controlling the response of seismically excited single-layer spherical lattice shell with substructure

2 Conceptual Design ofSMA Spring Restrainer

The SMA spring restrainer device considered in this studyprimarily consists of several large diameter SMA helicalsprings Figure 1 shows a schematic diagram of the developedseismic restrainer In the design of the seismic restrainersuperelastic SMA helical springs work parallel to provide therecentering property and the additional energy dissipationcapability Such SMA helical springs are fixed to the connec-tion plate through clamping system and nuts A particularclamping system is used to connect ends of the SMA springsto the other elements as shown in Figure 2 The ends of theSMA helical springs are fastened by using the fixed pedestalsand the threaded rods According to the design the hook-like ends of the spring are mounted in the inner slots of

Nut

SMA helical spring

Fixed pedestal

External pipe

Internal pipe

Connection plate

Attachment bolt

Figure 1 Schematic diagram of SMA spring restrainer

Bolt

SMA helical spring

Fixed pedestal

Threaded rod

Fixed pedestal

Threaded rod

Figure 2 Configuration of the clamping system

the fixed pedestals and the superelastic springs are clampedby tightening the screws on the fixed pedestal Then thethreaded rods are fastened to the connection plate of thedamper It is observed that the installation and replacement ofthe SMA spring elements are convenient to be implementedBesides the attachment bolt in the control device is employedto prevent too large axial deformation of the device

When both ends of the seismic restrainer move mutuallythe SMA springs are stretched and shortened The mannersabove provide the new control device with necessary energydissipation ability and recentering capacity The proposedcontrol device can be used as link element in spatial latticestructures In engineering application the design parametersof the SMA spring restrainer such as the number the config-uration and the dimensions of the SMAhelical spring can bedetermined in accordance with the practical requirements

Shock and Vibration 3

Figure 3 Large-scale SMA helical spring

3 Modeling of the Seismic Restrainer

31 Superelastic Behavior of SMA Helical Spring A type oflarge-scale superelastic SMA helical spring is fabricated anda set of cyclic experimental tests for the developed SMAelement are executed to understand its realistic nonlinearbehavior The NiTi-SMA (Ni

508Ti498

atom ratio) is usedin this experimental study The martensite start temperature119872119904 the martensite finish temperature119872

119891 the austenite start

temperature 119860119904 and the austenite finish temperature 119860

119891of

the SMA are 119872119904= minus613

∘C 119872119891= minus400

∘C 119860119904= minus299

∘Cand 119860

119891= minus126

∘C The large-scale tensioncompressionSMA helical spring is made from the above-described NiTialloy The SMA helical spring with a free length of 350mmexternal diameter of 36mm and wire diameter of 12mmwas tested in a SANS testing machine as shown in Figure 3During the cyclic tension-compression tests the appliedforces and displacements were measured by the inherentsensor of the testing machine

The mechanical tests were performed at room tempera-ture of about 20∘C First the test on the SMA specimen wasconducted for 50 cycles with 16mm displacement and 01Hzloading frequency to stabilize the hysteretic loops Then thecyclic loading with the amplitudes of cyclic displacementof 12 20 28 and 36mm and 02Hz loading frequency wasapplied to the spring specimen The shape of cyclic displace-ment during the tests was triangle type of waves Figure 4presents the force-displacement curves of the SMA helicalspring specimens under different cycles It can be observedthat the hysteresis loops of the SMA spring specimen slightlyshift with the increased loading cycle number The hysteresisloops tend to overlap and the superelastic behavior beginsto stabilize during the cyclic test case The experimentalforce-displacement curves of a single SMA helical springwith hook-like ends at different displacement amplitudesare shown in Figure 5 It can be seen that the superelasticSMA spring shows stable hysteretic behavior without any

minus20 minus15 minus10 minus5 0 5 10 15 20minus6

minus4

minus2

0

2

4

6

Forc

e (kN

)

Displacement (mm)

Cycle 1Cycle 30

Cycle 40Cycle 50

Figure 4 Hysteresis loops at different loading cycles

minus40 minus30 minus20 minus10 0 10 20 30 40minus10minus8minus6minus4minus2

02468

10

Forc

e (kN

)

Displacement (mm)

36mm28 mm

20 mm12 mm

Figure 5 Hysteresis loops at different displacement amplitudes

residual deformation After tests the specimen was checkedand measured and the spring was undamaged and the initialgeometry was perfectly recovered

32 Mechanical Model of SMA Spring Restrainer The behav-iors of the SMA helical spring can be modeled using solidfinite elements incorporating the stress-strain constitutiverelationship of SMA material [12 13] But it is generallyimpractical for nonlinear time history analysis of a com-plete engineering structure through such refined simulationmethod This paper develops an alternative modeling tech-nique of the SMA helical spring with a continuous hystereticsystem that is more physical and more efficient in describingnonlinear behavior of the SMA spring than the refinedmodels described above

In this study the SMA spring is modeled with a combi-nation of two nonlinear elements to simulate the superelasticbehavior The model consists of the following components

Element I Nonlinear Elastic Element This element is usedto capture the stiffness property of the SMA spring undercyclic loading-unloading process As shown in Figure 6(a)


F

X

Fb minus (1 minus 120578)Fa

120578Fa

Ks1

Ks2

minus120578Fa

minus (Fb minus (1 minus 120578)Fa)

minusxb minusxa xa xb

(a) Nonlinear elastic element

F

X

Fy

minusFy

minusxb xa xb

(b) Hysteretic model

Figure 6 Schematic diagram of theoretical model of SMA spring

the computational model of the nonlinear elastic element isgiven by

119865ml =

plusmn1198701199041 |119909| |119909| le 119909

119886

plusmn [1198701199041119909119886+ 1198701199042(|119909| minus 119909

119886)] 119909

119886lt |119909| le 119909

119887

(1)

where 119865ml is the restoring force provided by the nonlinearelastic element x is the displacement of the nonlinear elasticelement 119909

119886is the yield displacement 119909

119887is the design

displacement Ks1 is the initial stiffness of the nonlinearelastic element computed from the following equation

1198701199041=

(120578119865119886)

119909119886

(2)

Where 120578 is the ratio between 119865ml(119909119886) and 119865119886and can be

obtained by trial and adjustment Ks2 is the postyieldingstiffness of the nonlinear elastic element calculated by

1198701199042=

[119865119887minus (1 minus 120578) 119865

119886]

(119909119887minus 119909119886)

(3)

Element II Hysteretic Element This element describes anelastoplastic behavior with a smooth transition from theelastic to plastic range which is used to account for theenergy dissipation capacity of the SMA spring The elementas shown in Figure 6(b) is based on theBouc-Wenmodel [14]and its force-displacement relation can be given as follows

119865119908= 120572

119865119910

119909119886

119909 + (1 minus 120572) 119865119910119911 (4)

where 119865119908is the restoring force provided by the hysteretic

element 119865119910= (1 minus 120578)119865

119886is the yield force of the hysteretic

element 120572 is the ratio of the postyielding to elastic stiffnessz is the hysteretic dimensionless quantity expressed as

119909119886 + 120574 || 119911 |119911|

119899minus1+ 120573 |119911|

119899minus 119860 = 0 (5)

where 120574 120573 A and 119899 are dimensionless parameters thatcontrol the shape of the hysteresis loop

The nonlinear elastic element and the hysteretic elementwork in parallel under the same displacement to provide anoverall restoring force of the SMA helical spring which canbe computed as

119865SMA = 119865ml + 119865119908 (6)

where 119865SMA is the restoring force of the superelastic SMAspring

The overall restoring force of the superelastic seismicrestrainer is the sum of the nonlinear forces provided by theSMA helical springs which is given by

119865SR =

119899

sum

119895=1

119865119904119895 (7)

where 119865SR denotes the restoring force of the seismicrestrainer 119865

119904119895represents the restoring force of the jth SMA

helical springIn this study the parameters of the theoretical model

of the SMA spring specimens have been selected by fit-ting experimental hysteresis loops from the aforementionedcyclic tests obtained at various displacement amplitudesranging from 12 to 36mm A MATLAB-based program wasdeveloped and employed to describe response of the testedSMA specimens Figure 7 demonstrates the hysteretic loopstogether with the tests results at the displacement amplitudesof 12 20 28 and 36mm It is found that the nonlinearhysteretic behavior of the SMA spring can be effectively


minus15 minus10 minus5 0 5 10 15minus4minus3minus2minus1

01234

Forc

e (kN

)

Displacement (mm)

ExperimentSimulation

(a) Dmax = 12mm


minus25 minus20 minus15 minus10 minus5 0 5 10 15 20 25minus6

minus4

minus2

0

2

4

6

Forc

e (kN

)

Displacement (mm)

(b) Dmax = 20mm



02468

Forc

e (kN

)

Displacement (mm)

(c) Dmax = 28mm



minus8minus6minus4minus2

02468

10

Forc

e (kN

)

Displacement (mm)

(d) Dmax = 36mm

Figure 7 Experimental and numerical hysteretic curves of SMA spring

simulated As shown in the figure the simulated curves ofboth SMA spring specimens agree well with the experimentalresults

4 Seismic Analysis of a Controlled Single-Layer Lattice Shell Structure

41 Structural Model To investigate seismic performance ofthe superelastic restrainer in spatial lattice shell structures aKiewitt type of single-layer spherical lattice shell (K8-type)with 8 rings is selected The spherical lattice shell has aspan of 60m and a height of 10m The thickness betweenupper and lower chords is taken as 2m Several types of steeltubes 120601140 times 8 and 120601180 times 8 are selected as the internalsteel tube members of the lattice shell structure which aremodeled as beam elements Besides 120601377 times 10 beams areused as the bottom ring members of the spherical lattice shellroof Under the lattice shell roof the steel frame including500mmtimes300mmtimes20mmsteel box beams and120601480times12 steelcolumns are available for supporting the superstructure Allcomponents of the isolator are made of Q345 steel apart fromthe frictional material and SMAThe hinged supports for theuncontrolled shell and the SMA restrainers for the controlledshell are employed as link component between the lattice shellroof and the substructure

Figure 8 Finite element model of single-layer lattice shell

In this study SAP2000 software is applied to establishthe structural model and calculate its dynamic response Thefinite element model of the lattice shell structure is shownin Figure 8 The roof load is taken as 10 kNm2 All theloads and self-weight of the structure are treated as lumpedmasses concentrated at the nodes of the structure Nonlinearelements such as the nonlinear elastic element and Wenplastic element are combined to simulate the SMA spring inthe SAP2000 software in which the performance parametersof the tested SMA spring specimen are utilized to establish the


Table 1 Values of parameters for nonlinear element of SMA spring restrainer

Component Nonlinear element Performance parametersYield force (kN) Yield displacement (mm) Post yield stiffness ratio Yield exponent

SMA springs Multi-linear elastic 745 2 0594 mdashPlastic (Wen) 5 2 0 2

numerical modelThe sliding isolator is simulated by frictionisolator element in SAP2000

42 Seismic Response Analysis The performance parametersof the tested SMA helical spring specimen are utilizedto establish the damper model The SMA system in eachhybrid device consists of four NiTi-SMA helical springs Thedesign displacement of the SMA spring restrainer is taken asplusmn50mm Values of the parameters of the nonlinear elementsfor simulating the SMA restrainer in SAP2000 are listed inTable 1

The friction isolator element is used to simulate seis-mic isolation device applied to the single-layer lattice shellstructure The frictional force model for the aforementionedfriction isolator is given by [15]

119865119891119909

= 120583119875119911119891119909 (8)

119865119891119910

= 120583119875119911119891119910 (9)

where 120583 is the coefficient of friction 119875 is the normal loadcarried by the bearing interface 119911

119891119909and 119911

119891119910are hysteretic

dimensionless quantities computed from the following dif-ferential equations

119884119891119909

= Ω119887+ 120579

10038161003816100381610038161198871003816100381610038161003816 119911119891119909

10038161003816100381610038161003816119911119891119909

10038161003816100381610038161003816

119902minus1

minus 120582119887

10038161003816100381610038161003816119911119891119909

10038161003816100381610038161003816

119902

= 0 (10)

119884119891119910

= Ω119887+ 120579

10038161003816100381610038161198871003816100381610038161003816 119911119891119910

10038161003816100381610038161003816119911119891119910

10038161003816100381610038161003816

119902minus1

minus 120582119887

10038161003816100381610038161003816119911119891119910

10038161003816100381610038161003816

119902

= 0 (11)

where 119884 is the yield displacement 119887is the slip velocity of

the isolator 120579 120582Ω and 119902 are dimensionless parameters thatcontrol the shape of the hysteretic curve The recommendedvalues of these parameters to provide typical Coulombfriction force are Y = 05mm 120579 = 05 120582 = 05 Ω = 1and 119902 = 2 The Coulomb friction coefficient for the frictionisolator in structural analysis is taken as 010

Three ground motion records including the three com-ponents (ie the NS EW and UD components) of El-Centrowave Taft wave and Sylmar wave were selected as seismicinputs in the 119883 119884 and 119885 directions respectively The peakground acceleration was scaled to 020 g 030 g and 040 gin the simulation respectively The ratio of the accelerationsin three directions 119886

119909 119886119910 119886119911=1 085 065 Seismic response

analyses are performed for the single-layer spherical latticeshell under the conditions with and without seismic controldevices corresponding to the controlled shell and the uncon-trolled shell fromwhich seismic responses of both structuresand the isolation system have been obtained To display thecontrolling effects reduction ratio for earthquake responses

76

54

32

11 2345

(a) Selected nodes and beams

IsolatorRestrainer

(b) Selected isolator and restrainer

Figure 9 Selected nodes and elements in the lattice shell

under different seismic resistance conditions is definedby

Reduction ratio 120573 =(1198771minus 1198772)

1198771

(12)

where 1198771represents the response of the uncontrolled struc-

ture 1198772represents the response of the controlled structure

The selected nodes and elements for analyzing seismicresponse characteristics of the lattice shell structure areshown in Figure 9 The responses of the selected nodes alongwith the height of the roof are used to investigate the seismiccontrol effects for nodal acceleration of the single-layer latticeshell The selected beams are close to the boundary of thelattice shell and the responses of such element are employedto study the seismic control effect for internal force Fur-thermore an isolator element and a SMA spring restrainerare selected to investigate their seismic response Figure 10illustrate the peak value of acceleration in 119883 direction underSylmar wave for controlled and uncontrolled shell It isobserved that the peak values of acceleration response of theselected nodes are effectively reduced by using the isolation


11

2 3 4 5 6 7

152

253

354

455

556

Node number

Uncontrolled shellControlled shell

Acce

lera

tion

(ms

2)

(a) PGA = 02 g


1 2 3 4 5 6 7123456789

Node number

Acce

lera

tion

(ms

2)

(b) PGA = 03 g


1 2 3 4 5 6 7123456789

101112

Node number

Acce

lera

tion

(ms

2)

(c) PGA = 04 g

Figure 10 Peak value of acceleration in119883 direction for selected nodes under Sylmar wave

Table 2 Control effect of peak base shear in119883 direction (Units in kN)

Earthquake wave PGA = 02 g PGA = 03 g PGA = 04 gControlled Uncontrolled 120573 Controlled Uncontrolled 120573 Controlled Uncontrolled 120573

El-Centro 968 1177 0178 1445 1766 0182 1906 2353 0190Taft 1259 1522 0173 1478 2120 0303 1567 2831 0446Sylmar 1297 2103 0383 1530 3158 0516 1658 4205 0606

and control devices and the maximum is decreased fromabout 9 to 3ms2The slight variation of acceleration responsefor the controlled shell with the increasing PGA can alsobe observed The range of the nodal acceleration of theuncontrolled shell during this numerical case was from 45to 9ms2 When the hinged supports are replaced by theisolation and control devices all peak values of accelerationof the selected nodes are reduced to 35ms2 and belowFigure 11 shows reduction ratios for acceleration response ofthe selected nodes in the controlled and uncontrolled latticeshell under various seismic excitationsNote that the isolationand control effect is gradually improved with the increasingseismic input intensities Tables 2 and 3 give comparisonsfor peak values and reduction ratios of base shear responseof the lattice shell in 119883 and 119884 directions under differentseismic excitations and intensities The reduction ratio for

base shear is gradually enhanced while increasing the groundmotion intensities which is similar to the variation trendfor acceleration response As for other seismic responses ofthe lattice shell the peak axial force of beam elements canbe effectively reduced by using the isolation and controltechnology Tables 4ndash6 show comparisons for peak valuesand reduction ratios of axial force of the selected beamelements for the controlled and uncontrolled shell underdifferent earthquake waves It can be seen that the controleffect for axial force of the beam element in the latticeshell roof is still gradually improved with an increase ofPGAs The progressively increased reduction ratio for theabovementioned response quantities is due to the transitionfrom a relatively high initial stiffness to a postyield stiffness ofthe seismic restrainer and full energy dissipation provided bythe isolation and control device when the combined isolation


1 2 3 4 5 6 701

02

03

04

05

06

07

08

Node number

Redu

ctio

n ra

tio

PGA = 04 gPGA = 03 gPGA = 02 g

(a) Reduction ratio in X direction under El-Centro wave

1 2 3 4 5 6 701

01502

02503

03504

04505

Node number

Redu

ctio

n ra

tio


(b) Reduction ratio in Y direction under El-Centro wave

1 2 3 4 5 6 701

02

03

04

05

06

07

Node number

Redu

ctio

n ra

tio


(c) Reduction ratio in X direction under Taft wave

1 2 3 4 5 6 703

035

04

045

05

055

06

065

Node number

Redu

ctio

n ra

tio


(d) Reduction ratio in Y direction under Taft wave

1 2 3 4 5 6 702

03

04

05

06

07

08

Node number

Redu

ctio

n ra

tio


(e) Reduction ratio in X direction under Sylmar wave

1 2 3 4 5 6 70

00501

01502

02503

03504

04505

Node number

Redu

ctio

n ra

tio


(f) Reduction ratio in Y direction under Sylmar wave

Figure 11 Reduction ratio for peak value of nodal acceleration under various earthquake waves

system generates large deformation under strong groundmotions

Time histories of the displacement of the flat frictionisolator coupled with the SMA spring restrainers of thecontrolled shell structure subjected to various earthquakewaves are shown in Figure 12 Most displacement amplitudes

in 119883 direction and in 119884 direction of the steel-Teflon slidingisolator range from 30 to 50mm under the 3 ground motionrecords As shown in Figure 12 the residual displacementsof the isolator are very small and they can be neglectedFigure 13 illustrates the force-displacement hysteresis loops ofthe installed superelastic NiTi-SMA restrainer under various


Table 3 Control effect of peak base shear in 119884 direction (units in kN)



0 5 10 15 20 25 30 35 40minus40minus30minus20minus10

010203040

Disp

lace

men

t (m

m)

Time (s)


(a) Displacement in X direction under El-Centro wave

0 5 10 15 20 25 30 35 40minus50minus40minus30minus20minus10

010203040

Disp

lace

men

t (m

m)

Time (s)


(b) Displacement in Y direction under El-Centro wave


01020304050

Disp

lace

men

t (m

m)

Time (s)


(c) Displacement in X direction under Taft wave

0 5 10 15 20 25 30 35 40minus30

minus20

minus10

0

10

20

30

Disp

lace

men

t (m

m)

Time (s)


(d) Displacement in Y direction under Taft wave


010203040

Disp

lace

men

t (m

m)

Time (s)


(e) Displacement in X direction under Sylmar wave

0 5 10 15 20 25 30 35 40minus30

minus20

minus10

0

10

20

30

Disp

lace

men

t (m

m)

Time (s)


(f) Displacement in Y direction under Sylmar wave

Figure 12 Time histories of isolation system displacement subjected to various seismic excitations


minus50 minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40minus30minus20minus10

010203040

Displacement (mm)

Forc

e (kN

)

(a) Hysteresis loops under El-Centro wave

minus40 minus30 minus20 minus10 0 10 20 30 40minus40minus30minus20minus10

010203040

Displacement (mm)

Forc

e (kN

)

(b) Hysteresis loops under Taft wave

minus40 minus30 minus20 minus10 0 10 20 30minus40minus30minus20minus10

010203040

Displacement (mm)

Forc

e (kN

)

(c) Hysteresis loops under Sylmar wave

Figure 13 Force-displacement curves of the SMA spring restrainer under various earthquake wave (PGA = 04 g)

Table 4 Control effect of peak axial force under seismic excitations scaled to 02 g amplitude (units in kN)

Beam number El-Centro Taft SylmarControlled Uncontrolled 120573 Controlled Uncontrolled 120573 Controlled Uncontrolled 120573

1 511 668 0235 664 756 0122 976 1141 01452 503 657 0234 665 790 0158 965 1143 01563 362 422 0142 343 458 0251 284 323 01214 359 428 0161 350 452 0226 269 328 01805 992 1338 0259 836 1045 0200 934 1082 0137

Table 5 Control effect of peak axial force under seismic excitations scaled to 03 g amplitude (Units in kN)


1 756 1003 0246 807 1129 0285 1382 1713 01932 733 983 0254 809 1178 0313 1380 1718 01973 518 632 0180 465 684 0320 310 485 03614 519 630 0176 467 635 0293 311 529 04025 1397 2007 0304 1258 1665 0244 1366 1625 0159



1 802 1336 0400 938 1507 0378 1578 2289 03112 839 1309 0359 965 1573 0387 1564 2287 03163 686 846 0189 531 913 0418 455 730 03774 690 855 0193 532 828 0358 420 724 04205 1656 2675 0381 1346 2088 0355 1534 2161 0290


seismic excitation cases It can be observed that the seismicrestrainer exhibits perfect superelastic behavior which isgreatly important for recentering control of the friction isola-tion systemMoreover note that the displacement amplitudesof the superelastic restrainer are still kept in the designdeformation range during strong earthquakes

5 Conclusions

This study presents seismic performance analysis of a single-layer spherical lattice shell controlled by flat sliding isolationbearings and SMA spring restrainers This investigationdiscusses a simplified analytical approach for modeling thesuperelastic seismic restrainer that can be used in the seismicanalysis of the controlled lattice shell The controlled anduncontrolled lattice shell structures are analyzed for moder-ate and strong earthquake ground motions The numericalresults show that the installed isolation and control devicesare capable of mitigating peak nodal acceleration responsedynamic internal force of beam element of the lattice shellroof and base shear response of the structure while effec-tively restraining peak displacement response of the frictionisolators for all analytical cases Also it can be found thatthe residual displacements of the isolation device are almostzero in all cases considered in this study demonstrating thatthe recentering capability and large deformation property ofthe proposed superelastic seismic restrainer can be effectivelyused to eliminate the permanent deformation in sliding iso-lators and protect the lattice shell structure from earthquakedamage

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The authors gratefully acknowledge the support from BeijingNatural Science Foundation under Grant no 8132024 andthe Science and Technology Development Project of Bei-jing Municipal Commission of Education under Grant noKM201510016004

References

[1] American Association of State Highway and TransportationOfficials Guide Specifications for Seismic Isolation DesignAmerican Association of State Highway and TransportationOfficials Washington DC USA 1999

[2] T T Soong and G F Dargush Passive Energy DissipationSystems in Structural Engineering John Wiley amp Sons NewYork NY USA 1997

[3] E Graesser and F Cozzarelli ldquoShape memory alloys as newmaterials for aseismic isolationrdquo Journal of EngineeringMechan-ics vol 117 no 11 pp 2590ndash2608 1991

[4] M Dolce D Cardone and R Marnetto ldquoImplementation andtesting of passive control devices based on shape memoryalloysrdquo Earthquake Engineering and Structural Dynamics vol29 no 7 pp 945ndash968 2000

[5] RDesRoches JMcCormick andMDelemont ldquoCyclic proper-ties of superelastic shape memory alloy wires and barsrdquo Journalof Structural Engineering vol 130 no 1 pp 38ndash46 2004

[6] S Xue and X Li ldquoControl devices incorporated with shapememory alloyrdquo Earthquake Engineering and Engineering Vibra-tion vol 6 no 2 pp 159ndash169 2007

[7] F Casciati L Faravelli and K Hamdaoui ldquoPerformance ofa base isolator with shape memory alloy barsrdquo EarthquakeEngineering and Engineering Vibration vol 6 no 4 pp 401ndash408 2007

[8] Y Ding X Chen A Li and X Zuo ldquoA new isolation deviceusing shape memory alloy and its application for long-spanstructuresrdquo Earthquake Engineering and Engineering Vibrationvol 10 no 2 pp 239ndash252 2011

[9] O E Ozbulut and S Hurlebaus ldquoOptimal design of supere-lastic-friction base isolators for seismic protection of highwaybridges against near-field earthquakesrdquo Earthquake Engineeringand Structural Dynamics vol 40 no 3 pp 273ndash291 2011

[10] A Bhuiyan and M Alam ldquoSeismic vulnerability assessmentof a multi-span continuous highway bridge fitted with shapememory alloy bars and laminated rubber bearingrdquo EarthquakeSpectra vol 28 no 4 pp 1379ndash1404 2012

[11] M Speicher D E Hodgson R Desroches and R T LeonldquoShape memory alloy tensioncompression device for seismicretrofit of buildingsrdquo Journal of Materials Engineering andPerformance vol 18 no 5-6 pp 746ndash753 2009

[12] G Attanasi and F Auricchio ldquoInnovative superelastic isolationdevicerdquo Journal of Earthquake Engineering vol 15 supplement1 pp 72ndash89 2011

[13] RMirzaeifar RDesRoches andA Yavari ldquoA combined analyt-ical numerical and experimental study of shape-memory-alloyhelical springsrdquo International Journal of Solids and Structuresvol 48 no 3-4 pp 611ndash624 2011

[14] Y-KWen ldquoMethod for random vibration of hysteretic systemrdquoJournal of the EngineeringMechanics Division vol 102 no 2 pp249ndash263 1976

[15] M Constantinou AMokha andA Reinhorn ldquoTeflon bearingsin base isolation IImodelingrdquo Journal of Structural Engineeringvol 116 no 2 pp 455ndash474 1990

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



researchers suggested the use of superelastic SMA helicalspring instead of SMA wires or SMA bars as energy dissipa-tion and recentering control system For example Speicheret al [11] developed a tensioncompression damper makinguse of SMA helical springs which provide stable recenteringanddamping characteristics Attanasi andAuricchio [12] pro-posed conceptual design of an innovative restorable isolationsystem in which a sliding bearing is coupled with superelasticSMA helical springs that function for recentering purposes

Most of the previous studies were focused on the develop-ment and application of SMA helical springs for isolation andcontrol of multistory buildings However very few attemptshave been given to the investigation of behavior of long spanand spatial structures that are isolated by seismic isolatorsand controlled by large-scale SMA helical spring devicesTheprimary objective of this study is to carry out an investigationon feasibility and efficiency of a new type of seismic restrainerwith SMA springs that is installed between substructure andspherical lattice shell roof to reduce structural responsesThe proposed isolation system for spatial lattice structuresconsists of a flat sliding isolator and superelastic SMArestrainers The use of flat sliding bearing can reduce thestructural response by limiting the force transfer from thesubstructure to the superstructure Beside such bearingsprovide dissipation of the seismic energy due to frictionmechanism However the flat sliding bearings alone do nothave any recentering capability and may generate significantresidual displacement A new type of SMA helical springrestrainers is proposed to provide recentering mechanismand additional energy dissipation ability The conceptualdesign and the functioning mechanism of the SMA springrestrainer are described A mechanical model is derived tocapture the hysteretic behavior of superelastic SMA helicalspring restrainer In order to investigate mechanical behav-iors of the developed device such seismic restrainers areintroduced in spherical lattice shell structures isolated by flatsliding isolators A set of nonlinear time history analysesusing SAP2000 software are performed to examine theeffectiveness of the developed SMA-based device in reducingand controlling the response of seismically excited single-layer spherical lattice shell with substructure

2 Conceptual Design ofSMA Spring Restrainer

The SMA spring restrainer device considered in this studyprimarily consists of several large diameter SMA helicalsprings Figure 1 shows a schematic diagram of the developedseismic restrainer In the design of the seismic restrainersuperelastic SMA helical springs work parallel to provide therecentering property and the additional energy dissipationcapability Such SMA helical springs are fixed to the connec-tion plate through clamping system and nuts A particularclamping system is used to connect ends of the SMA springsto the other elements as shown in Figure 2 The ends of theSMA helical springs are fastened by using the fixed pedestalsand the threaded rods According to the design the hook-like ends of the spring are mounted in the inner slots of

Nut

SMA helical spring

Fixed pedestal

External pipe

Internal pipe

Connection plate

Attachment bolt

Figure 1 Schematic diagram of SMA spring restrainer

Bolt

SMA helical spring

Fixed pedestal

Threaded rod

Fixed pedestal

Threaded rod

Figure 2 Configuration of the clamping system

the fixed pedestals and the superelastic springs are clampedby tightening the screws on the fixed pedestal Then thethreaded rods are fastened to the connection plate of thedamper It is observed that the installation and replacement ofthe SMA spring elements are convenient to be implementedBesides the attachment bolt in the control device is employedto prevent too large axial deformation of the device

When both ends of the seismic restrainer move mutuallythe SMA springs are stretched and shortened The mannersabove provide the new control device with necessary energydissipation ability and recentering capacity The proposedcontrol device can be used as link element in spatial latticestructures In engineering application the design parametersof the SMA spring restrainer such as the number the config-uration and the dimensions of the SMAhelical spring can bedetermined in accordance with the practical requirements





508Ti498




119891of


∘C 119872119891= minus400

∘C 119860119904= minus299

∘Cand 119860

119891= minus126




minus4

minus2

0

2

4

6

Forc

e (kN

)

Displacement (mm)

Cycle 1Cycle 30

Cycle 40Cycle 50



02468

10

Forc

e (kN

)

Displacement (mm)

36mm28 mm

20 mm12 mm







F

X


120578Fa

Ks1

Ks2

minus120578Fa




F

X

Fy

minusFy

minusxb xa xb




119865ml =

plusmn1198701199041 |119909| |119909| le 119909

119886

plusmn [1198701199041119909119886+ 1198701199042(|119909| minus 119909

119886)] 119909

119886lt |119909| le 119909

119887

(1)



119887is the design


1198701199041=

(120578119865119886)

119909119886

(2)



1198701199042=

[119865119887minus (1 minus 120578) 119865

119886]

(119909119887minus 119909119886)

(3)


119865119908= 120572

119865119910

119909119886

119909 + (1 minus 120572) 119865119910119911 (4)


element 119865119910= (1 minus 120578)119865



119909119886 + 120574 || 119911 |119911|

119899minus1+ 120573 |119911|

119899minus 119860 = 0 (5)



119865SMA = 119865ml + 119865119908 (6)



119865SR =

119899

sum

119895=1

119865119904119895 (7)







01234

Forc

e (kN

)

Displacement (mm)


(a) Dmax = 12mm



minus4

minus2

0

2

4

6

Forc

e (kN

)

Displacement (mm)

(b) Dmax = 20mm



02468

Forc

e (kN

)

Displacement (mm)

(c) Dmax = 28mm




02468

10

Forc

e (kN

)

Displacement (mm)

(d) Dmax = 36mm














119865119891119909

= 120583119875119911119891119909 (8)

119865119891119910

= 120583119875119911119891119910 (9)


119891119909and 119911



119884119891119909

= Ω119887+ 120579

10038161003816100381610038161198871003816100381610038161003816 119911119891119909

10038161003816100381610038161003816119911119891119909

10038161003816100381610038161003816

119902minus1

minus 120582119887

10038161003816100381610038161003816119911119891119909

10038161003816100381610038161003816

119902

= 0 (10)

119884119891119910

= Ω119887+ 120579

10038161003816100381610038161198871003816100381610038161003816 119911119891119910

10038161003816100381610038161003816119911119891119910

10038161003816100381610038161003816

119902minus1

minus 120582119887

10038161003816100381610038161003816119911119891119910

10038161003816100381610038161003816

119902

= 0 (11)






76

54

32

11 2345


IsolatorRestrainer





1198771

(12)





11

2 3 4 5 6 7

152

253

354

455

556

Node number


Acce

lera

tion

(ms

2)

(a) PGA = 02 g


1 2 3 4 5 6 7123456789

Node number

Acce

lera

tion

(ms

2)

(b) PGA = 03 g


1 2 3 4 5 6 7123456789

101112

Node number

Acce

lera

tion

(ms

2)

(c) PGA = 04 g








1 2 3 4 5 6 701

02

03

04

05

06

07

08

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 701

01502

02503

03504

04505

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 701

02

03

04

05

06

07

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 703

035

04

045

05

055

06

065

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 702

03

04

05

06

07

08

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 70

00501

01502

02503

03504

04505

Node number

Redu

ctio

n ra

tio












010203040

Disp

lace

men

t (m

m)

Time (s)




010203040

Disp

lace

men

t (m

m)

Time (s)




01020304050

Disp

lace

men

t (m

m)

Time (s)



0 5 10 15 20 25 30 35 40minus30

minus20

minus10

0

10

20

30

Disp

lace

men

t (m

m)

Time (s)




010203040

Disp

lace

men

t (m

m)

Time (s)



0 5 10 15 20 25 30 35 40minus30

minus20

minus10

0

10

20

30

Disp

lace

men

t (m

m)

Time (s)






010203040

Displacement (mm)

Forc

e (kN

)



010203040

Displacement (mm)

Forc

e (kN

)



010203040

Displacement (mm)

Forc

e (kN

)





1 511 668 0235 664 756 0122 976 1141 01452 503 657 0234 665 790 0158 965 1143 01563 362 422 0142 343 458 0251 284 323 01214 359 428 0161 350 452 0226 269 328 01805 992 1338 0259 836 1045 0200 934 1082 0137



1 756 1003 0246 807 1129 0285 1382 1713 01932 733 983 0254 809 1178 0313 1380 1718 01973 518 632 0180 465 684 0320 310 485 03614 519 630 0176 467 635 0293 311 529 04025 1397 2007 0304 1258 1665 0244 1366 1625 0159



1 802 1336 0400 938 1507 0378 1578 2289 03112 839 1309 0359 965 1573 0387 1564 2287 03163 686 846 0189 531 913 0418 455 730 03774 690 855 0193 532 828 0358 420 724 04205 1656 2675 0381 1346 2088 0355 1534 2161 0290



5 Conclusions


Competing Interests


Acknowledgments


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













508Ti498




119891of


∘C 119872119891= minus400

∘C 119860119904= minus299

∘Cand 119860

119891= minus126




minus4

minus2

0

2

4

6

Forc

e (kN

)

Displacement (mm)

Cycle 1Cycle 30

Cycle 40Cycle 50



02468

10

Forc

e (kN

)

Displacement (mm)

36mm28 mm

20 mm12 mm







F

X


120578Fa

Ks1

Ks2

minus120578Fa




F

X

Fy

minusFy

minusxb xa xb




119865ml =

plusmn1198701199041 |119909| |119909| le 119909

119886

plusmn [1198701199041119909119886+ 1198701199042(|119909| minus 119909

119886)] 119909

119886lt |119909| le 119909

119887

(1)



119887is the design


1198701199041=

(120578119865119886)

119909119886

(2)



1198701199042=

[119865119887minus (1 minus 120578) 119865

119886]

(119909119887minus 119909119886)

(3)


119865119908= 120572

119865119910

119909119886

119909 + (1 minus 120572) 119865119910119911 (4)


element 119865119910= (1 minus 120578)119865



119909119886 + 120574 || 119911 |119911|

119899minus1+ 120573 |119911|

119899minus 119860 = 0 (5)



119865SMA = 119865ml + 119865119908 (6)



119865SR =

119899

sum

119895=1

119865119904119895 (7)







01234

Forc

e (kN

)

Displacement (mm)


(a) Dmax = 12mm



minus4

minus2

0

2

4

6

Forc

e (kN

)

Displacement (mm)

(b) Dmax = 20mm



02468

Forc

e (kN

)

Displacement (mm)

(c) Dmax = 28mm




02468

10

Forc

e (kN

)

Displacement (mm)

(d) Dmax = 36mm














119865119891119909

= 120583119875119911119891119909 (8)

119865119891119910

= 120583119875119911119891119910 (9)


119891119909and 119911



119884119891119909

= Ω119887+ 120579

10038161003816100381610038161198871003816100381610038161003816 119911119891119909

10038161003816100381610038161003816119911119891119909

10038161003816100381610038161003816

119902minus1

minus 120582119887

10038161003816100381610038161003816119911119891119909

10038161003816100381610038161003816

119902

= 0 (10)

119884119891119910

= Ω119887+ 120579

10038161003816100381610038161198871003816100381610038161003816 119911119891119910

10038161003816100381610038161003816119911119891119910

10038161003816100381610038161003816

119902minus1

minus 120582119887

10038161003816100381610038161003816119911119891119910

10038161003816100381610038161003816

119902

= 0 (11)






76

54

32

11 2345


IsolatorRestrainer





1198771

(12)





11

2 3 4 5 6 7

152

253

354

455

556

Node number


Acce

lera

tion

(ms

2)

(a) PGA = 02 g


1 2 3 4 5 6 7123456789

Node number

Acce

lera

tion

(ms

2)

(b) PGA = 03 g


1 2 3 4 5 6 7123456789

101112

Node number

Acce

lera

tion

(ms

2)

(c) PGA = 04 g








1 2 3 4 5 6 701

02

03

04

05

06

07

08

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 701

01502

02503

03504

04505

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 701

02

03

04

05

06

07

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 703

035

04

045

05

055

06

065

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 702

03

04

05

06

07

08

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 70

00501

01502

02503

03504

04505

Node number

Redu

ctio

n ra

tio












010203040

Disp

lace

men

t (m

m)

Time (s)




010203040

Disp

lace

men

t (m

m)

Time (s)




01020304050

Disp

lace

men

t (m

m)

Time (s)



0 5 10 15 20 25 30 35 40minus30

minus20

minus10

0

10

20

30

Disp

lace

men

t (m

m)

Time (s)




010203040

Disp

lace

men

t (m

m)

Time (s)



0 5 10 15 20 25 30 35 40minus30

minus20

minus10

0

10

20

30

Disp

lace

men

t (m

m)

Time (s)






010203040

Displacement (mm)

Forc

e (kN

)



010203040

Displacement (mm)

Forc

e (kN

)



010203040

Displacement (mm)

Forc

e (kN

)





1 511 668 0235 664 756 0122 976 1141 01452 503 657 0234 665 790 0158 965 1143 01563 362 422 0142 343 458 0251 284 323 01214 359 428 0161 350 452 0226 269 328 01805 992 1338 0259 836 1045 0200 934 1082 0137



1 756 1003 0246 807 1129 0285 1382 1713 01932 733 983 0254 809 1178 0313 1380 1718 01973 518 632 0180 465 684 0320 310 485 03614 519 630 0176 467 635 0293 311 529 04025 1397 2007 0304 1258 1665 0244 1366 1625 0159



1 802 1336 0400 938 1507 0378 1578 2289 03112 839 1309 0359 965 1573 0387 1564 2287 03163 686 846 0189 531 913 0418 455 730 03774 690 855 0193 532 828 0358 420 724 04205 1656 2675 0381 1346 2088 0355 1534 2161 0290



5 Conclusions


Competing Interests


Acknowledgments


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










F

X


120578Fa

Ks1

Ks2

minus120578Fa




F

X

Fy

minusFy

minusxb xa xb




119865ml =

plusmn1198701199041 |119909| |119909| le 119909

119886

plusmn [1198701199041119909119886+ 1198701199042(|119909| minus 119909

119886)] 119909

119886lt |119909| le 119909

119887

(1)



119887is the design


1198701199041=

(120578119865119886)

119909119886

(2)



1198701199042=

[119865119887minus (1 minus 120578) 119865

119886]

(119909119887minus 119909119886)

(3)


119865119908= 120572

119865119910

119909119886

119909 + (1 minus 120572) 119865119910119911 (4)


element 119865119910= (1 minus 120578)119865



119909119886 + 120574 || 119911 |119911|

119899minus1+ 120573 |119911|

119899minus 119860 = 0 (5)



119865SMA = 119865ml + 119865119908 (6)



119865SR =

119899

sum

119895=1

119865119904119895 (7)







01234

Forc

e (kN

)

Displacement (mm)


(a) Dmax = 12mm



minus4

minus2

0

2

4

6

Forc

e (kN

)

Displacement (mm)

(b) Dmax = 20mm



02468

Forc

e (kN

)

Displacement (mm)

(c) Dmax = 28mm




02468

10

Forc

e (kN

)

Displacement (mm)

(d) Dmax = 36mm














119865119891119909

= 120583119875119911119891119909 (8)

119865119891119910

= 120583119875119911119891119910 (9)


119891119909and 119911



119884119891119909

= Ω119887+ 120579

10038161003816100381610038161198871003816100381610038161003816 119911119891119909

10038161003816100381610038161003816119911119891119909

10038161003816100381610038161003816

119902minus1

minus 120582119887

10038161003816100381610038161003816119911119891119909

10038161003816100381610038161003816

119902

= 0 (10)

119884119891119910

= Ω119887+ 120579

10038161003816100381610038161198871003816100381610038161003816 119911119891119910

10038161003816100381610038161003816119911119891119910

10038161003816100381610038161003816

119902minus1

minus 120582119887

10038161003816100381610038161003816119911119891119910

10038161003816100381610038161003816

119902

= 0 (11)






76

54

32

11 2345


IsolatorRestrainer





1198771

(12)





11

2 3 4 5 6 7

152

253

354

455

556

Node number


Acce

lera

tion

(ms

2)

(a) PGA = 02 g


1 2 3 4 5 6 7123456789

Node number

Acce

lera

tion

(ms

2)

(b) PGA = 03 g


1 2 3 4 5 6 7123456789

101112

Node number

Acce

lera

tion

(ms

2)

(c) PGA = 04 g








1 2 3 4 5 6 701

02

03

04

05

06

07

08

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 701

01502

02503

03504

04505

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 701

02

03

04

05

06

07

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 703

035

04

045

05

055

06

065

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 702

03

04

05

06

07

08

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 70

00501

01502

02503

03504

04505

Node number

Redu

ctio

n ra

tio












010203040

Disp

lace

men

t (m

m)

Time (s)




010203040

Disp

lace

men

t (m

m)

Time (s)




01020304050

Disp

lace

men

t (m

m)

Time (s)



0 5 10 15 20 25 30 35 40minus30

minus20

minus10

0

10

20

30

Disp

lace

men

t (m

m)

Time (s)




010203040

Disp

lace

men

t (m

m)

Time (s)



0 5 10 15 20 25 30 35 40minus30

minus20

minus10

0

10

20

30

Disp

lace

men

t (m

m)

Time (s)






010203040

Displacement (mm)

Forc

e (kN

)



010203040

Displacement (mm)

Forc

e (kN

)



010203040

Displacement (mm)

Forc

e (kN

)





1 511 668 0235 664 756 0122 976 1141 01452 503 657 0234 665 790 0158 965 1143 01563 362 422 0142 343 458 0251 284 323 01214 359 428 0161 350 452 0226 269 328 01805 992 1338 0259 836 1045 0200 934 1082 0137



1 756 1003 0246 807 1129 0285 1382 1713 01932 733 983 0254 809 1178 0313 1380 1718 01973 518 632 0180 465 684 0320 310 485 03614 519 630 0176 467 635 0293 311 529 04025 1397 2007 0304 1258 1665 0244 1366 1625 0159



1 802 1336 0400 938 1507 0378 1578 2289 03112 839 1309 0359 965 1573 0387 1564 2287 03163 686 846 0189 531 913 0418 455 730 03774 690 855 0193 532 828 0358 420 724 04205 1656 2675 0381 1346 2088 0355 1534 2161 0290



5 Conclusions


Competing Interests


Acknowledgments


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











01234

Forc

e (kN

)

Displacement (mm)


(a) Dmax = 12mm



minus4

minus2

0

2

4

6

Forc

e (kN

)

Displacement (mm)

(b) Dmax = 20mm



02468

Forc

e (kN

)

Displacement (mm)

(c) Dmax = 28mm




02468

10

Forc

e (kN

)

Displacement (mm)

(d) Dmax = 36mm














119865119891119909

= 120583119875119911119891119909 (8)

119865119891119910

= 120583119875119911119891119910 (9)


119891119909and 119911



119884119891119909

= Ω119887+ 120579

10038161003816100381610038161198871003816100381610038161003816 119911119891119909

10038161003816100381610038161003816119911119891119909

10038161003816100381610038161003816

119902minus1

minus 120582119887

10038161003816100381610038161003816119911119891119909

10038161003816100381610038161003816

119902

= 0 (10)

119884119891119910

= Ω119887+ 120579

10038161003816100381610038161198871003816100381610038161003816 119911119891119910

10038161003816100381610038161003816119911119891119910

10038161003816100381610038161003816

119902minus1

minus 120582119887

10038161003816100381610038161003816119911119891119910

10038161003816100381610038161003816

119902

= 0 (11)






76

54

32

11 2345


IsolatorRestrainer





1198771

(12)





11

2 3 4 5 6 7

152

253

354

455

556

Node number


Acce

lera

tion

(ms

2)

(a) PGA = 02 g


1 2 3 4 5 6 7123456789

Node number

Acce

lera

tion

(ms

2)

(b) PGA = 03 g


1 2 3 4 5 6 7123456789

101112

Node number

Acce

lera

tion

(ms

2)

(c) PGA = 04 g








1 2 3 4 5 6 701

02

03

04

05

06

07

08

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 701

01502

02503

03504

04505

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 701

02

03

04

05

06

07

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 703

035

04

045

05

055

06

065

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 702

03

04

05

06

07

08

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 70

00501

01502

02503

03504

04505

Node number

Redu

ctio

n ra

tio












010203040

Disp

lace

men

t (m

m)

Time (s)




010203040

Disp

lace

men

t (m

m)

Time (s)




01020304050

Disp

lace

men

t (m

m)

Time (s)



0 5 10 15 20 25 30 35 40minus30

minus20

minus10

0

10

20

30

Disp

lace

men

t (m

m)

Time (s)




010203040

Disp

lace

men

t (m

m)

Time (s)



0 5 10 15 20 25 30 35 40minus30

minus20

minus10

0

10

20

30

Disp

lace

men

t (m

m)

Time (s)






010203040

Displacement (mm)

Forc

e (kN

)



010203040

Displacement (mm)

Forc

e (kN

)



010203040

Displacement (mm)

Forc

e (kN

)





1 511 668 0235 664 756 0122 976 1141 01452 503 657 0234 665 790 0158 965 1143 01563 362 422 0142 343 458 0251 284 323 01214 359 428 0161 350 452 0226 269 328 01805 992 1338 0259 836 1045 0200 934 1082 0137



1 756 1003 0246 807 1129 0285 1382 1713 01932 733 983 0254 809 1178 0313 1380 1718 01973 518 632 0180 465 684 0320 310 485 03614 519 630 0176 467 635 0293 311 529 04025 1397 2007 0304 1258 1665 0244 1366 1625 0159



1 802 1336 0400 938 1507 0378 1578 2289 03112 839 1309 0359 965 1573 0387 1564 2287 03163 686 846 0189 531 913 0418 455 730 03774 690 855 0193 532 828 0358 420 724 04205 1656 2675 0381 1346 2088 0355 1534 2161 0290



5 Conclusions


Competing Interests


Acknowledgments


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















119865119891119909

= 120583119875119911119891119909 (8)

119865119891119910

= 120583119875119911119891119910 (9)


119891119909and 119911



119884119891119909

= Ω119887+ 120579

10038161003816100381610038161198871003816100381610038161003816 119911119891119909

10038161003816100381610038161003816119911119891119909

10038161003816100381610038161003816

119902minus1

minus 120582119887

10038161003816100381610038161003816119911119891119909

10038161003816100381610038161003816

119902

= 0 (10)

119884119891119910

= Ω119887+ 120579

10038161003816100381610038161198871003816100381610038161003816 119911119891119910

10038161003816100381610038161003816119911119891119910

10038161003816100381610038161003816

119902minus1

minus 120582119887

10038161003816100381610038161003816119911119891119910

10038161003816100381610038161003816

119902

= 0 (11)






76

54

32

11 2345


IsolatorRestrainer





1198771

(12)





11

2 3 4 5 6 7

152

253

354

455

556

Node number


Acce

lera

tion

(ms

2)

(a) PGA = 02 g


1 2 3 4 5 6 7123456789

Node number

Acce

lera

tion

(ms

2)

(b) PGA = 03 g


1 2 3 4 5 6 7123456789

101112

Node number

Acce

lera

tion

(ms

2)

(c) PGA = 04 g








1 2 3 4 5 6 701

02

03

04

05

06

07

08

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 701

01502

02503

03504

04505

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 701

02

03

04

05

06

07

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 703

035

04

045

05

055

06

065

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 702

03

04

05

06

07

08

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 70

00501

01502

02503

03504

04505

Node number

Redu

ctio

n ra

tio












010203040

Disp

lace

men

t (m

m)

Time (s)




010203040

Disp

lace

men

t (m

m)

Time (s)




01020304050

Disp

lace

men

t (m

m)

Time (s)



0 5 10 15 20 25 30 35 40minus30

minus20

minus10

0

10

20

30

Disp

lace

men

t (m

m)

Time (s)




010203040

Disp

lace

men

t (m

m)

Time (s)



0 5 10 15 20 25 30 35 40minus30

minus20

minus10

0

10

20

30

Disp

lace

men

t (m

m)

Time (s)






010203040

Displacement (mm)

Forc

e (kN

)



010203040

Displacement (mm)

Forc

e (kN

)



010203040

Displacement (mm)

Forc

e (kN

)





1 511 668 0235 664 756 0122 976 1141 01452 503 657 0234 665 790 0158 965 1143 01563 362 422 0142 343 458 0251 284 323 01214 359 428 0161 350 452 0226 269 328 01805 992 1338 0259 836 1045 0200 934 1082 0137



1 756 1003 0246 807 1129 0285 1382 1713 01932 733 983 0254 809 1178 0313 1380 1718 01973 518 632 0180 465 684 0320 310 485 03614 519 630 0176 467 635 0293 311 529 04025 1397 2007 0304 1258 1665 0244 1366 1625 0159



1 802 1336 0400 938 1507 0378 1578 2289 03112 839 1309 0359 965 1573 0387 1564 2287 03163 686 846 0189 531 913 0418 455 730 03774 690 855 0193 532 828 0358 420 724 04205 1656 2675 0381 1346 2088 0355 1534 2161 0290



5 Conclusions


Competing Interests


Acknowledgments


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










11

2 3 4 5 6 7

152

253

354

455

556

Node number


Acce

lera

tion

(ms

2)

(a) PGA = 02 g


1 2 3 4 5 6 7123456789

Node number

Acce

lera

tion

(ms

2)

(b) PGA = 03 g


1 2 3 4 5 6 7123456789

101112

Node number

Acce

lera

tion

(ms

2)

(c) PGA = 04 g








1 2 3 4 5 6 701

02

03

04

05

06

07

08

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 701

01502

02503

03504

04505

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 701

02

03

04

05

06

07

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 703

035

04

045

05

055

06

065

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 702

03

04

05

06

07

08

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 70

00501

01502

02503

03504

04505

Node number

Redu

ctio

n ra

tio












010203040

Disp

lace

men

t (m

m)

Time (s)




010203040

Disp

lace

men

t (m

m)

Time (s)




01020304050

Disp

lace

men

t (m

m)

Time (s)



0 5 10 15 20 25 30 35 40minus30

minus20

minus10

0

10

20

30

Disp

lace

men

t (m

m)

Time (s)




010203040

Disp

lace

men

t (m

m)

Time (s)



0 5 10 15 20 25 30 35 40minus30

minus20

minus10

0

10

20

30

Disp

lace

men

t (m

m)

Time (s)






010203040

Displacement (mm)

Forc

e (kN

)



010203040

Displacement (mm)

Forc

e (kN

)



010203040

Displacement (mm)

Forc

e (kN

)





1 511 668 0235 664 756 0122 976 1141 01452 503 657 0234 665 790 0158 965 1143 01563 362 422 0142 343 458 0251 284 323 01214 359 428 0161 350 452 0226 269 328 01805 992 1338 0259 836 1045 0200 934 1082 0137



1 756 1003 0246 807 1129 0285 1382 1713 01932 733 983 0254 809 1178 0313 1380 1718 01973 518 632 0180 465 684 0320 310 485 03614 519 630 0176 467 635 0293 311 529 04025 1397 2007 0304 1258 1665 0244 1366 1625 0159



1 802 1336 0400 938 1507 0378 1578 2289 03112 839 1309 0359 965 1573 0387 1564 2287 03163 686 846 0189 531 913 0418 455 730 03774 690 855 0193 532 828 0358 420 724 04205 1656 2675 0381 1346 2088 0355 1534 2161 0290



5 Conclusions


Competing Interests


Acknowledgments


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1 2 3 4 5 6 701

02

03

04

05

06

07

08

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 701

01502

02503

03504

04505

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 701

02

03

04

05

06

07

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 703

035

04

045

05

055

06

065

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 702

03

04

05

06

07

08

Node number

Redu

ctio

n ra

tio



1 2 3 4 5 6 70

00501

01502

02503

03504

04505

Node number

Redu

ctio

n ra

tio












010203040

Disp

lace

men

t (m

m)

Time (s)




010203040

Disp

lace

men

t (m

m)

Time (s)




01020304050

Disp

lace

men

t (m

m)

Time (s)



0 5 10 15 20 25 30 35 40minus30

minus20

minus10

0

10

20

30

Disp

lace

men

t (m

m)

Time (s)




010203040

Disp

lace

men

t (m

m)

Time (s)



0 5 10 15 20 25 30 35 40minus30

minus20

minus10

0

10

20

30

Disp

lace

men

t (m

m)

Time (s)






010203040

Displacement (mm)

Forc

e (kN

)



010203040

Displacement (mm)

Forc

e (kN

)



010203040

Displacement (mm)

Forc

e (kN

)





1 511 668 0235 664 756 0122 976 1141 01452 503 657 0234 665 790 0158 965 1143 01563 362 422 0142 343 458 0251 284 323 01214 359 428 0161 350 452 0226 269 328 01805 992 1338 0259 836 1045 0200 934 1082 0137



1 756 1003 0246 807 1129 0285 1382 1713 01932 733 983 0254 809 1178 0313 1380 1718 01973 518 632 0180 465 684 0320 310 485 03614 519 630 0176 467 635 0293 311 529 04025 1397 2007 0304 1258 1665 0244 1366 1625 0159



1 802 1336 0400 938 1507 0378 1578 2289 03112 839 1309 0359 965 1573 0387 1564 2287 03163 686 846 0189 531 913 0418 455 730 03774 690 855 0193 532 828 0358 420 724 04205 1656 2675 0381 1346 2088 0355 1534 2161 0290



5 Conclusions


Competing Interests


Acknowledgments


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














010203040

Disp

lace

men

t (m

m)

Time (s)




010203040

Disp

lace

men

t (m

m)

Time (s)




01020304050

Disp

lace

men

t (m

m)

Time (s)



0 5 10 15 20 25 30 35 40minus30

minus20

minus10

0

10

20

30

Disp

lace

men

t (m

m)

Time (s)




010203040

Disp

lace

men

t (m

m)

Time (s)



0 5 10 15 20 25 30 35 40minus30

minus20

minus10

0

10

20

30

Disp

lace

men

t (m

m)

Time (s)






010203040

Displacement (mm)

Forc

e (kN

)



010203040

Displacement (mm)

Forc

e (kN

)



010203040

Displacement (mm)

Forc

e (kN

)





1 511 668 0235 664 756 0122 976 1141 01452 503 657 0234 665 790 0158 965 1143 01563 362 422 0142 343 458 0251 284 323 01214 359 428 0161 350 452 0226 269 328 01805 992 1338 0259 836 1045 0200 934 1082 0137



1 756 1003 0246 807 1129 0285 1382 1713 01932 733 983 0254 809 1178 0313 1380 1718 01973 518 632 0180 465 684 0320 310 485 03614 519 630 0176 467 635 0293 311 529 04025 1397 2007 0304 1258 1665 0244 1366 1625 0159



1 802 1336 0400 938 1507 0378 1578 2289 03112 839 1309 0359 965 1573 0387 1564 2287 03163 686 846 0189 531 913 0418 455 730 03774 690 855 0193 532 828 0358 420 724 04205 1656 2675 0381 1346 2088 0355 1534 2161 0290



5 Conclusions


Competing Interests


Acknowledgments


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











010203040

Displacement (mm)

Forc

e (kN

)



010203040

Displacement (mm)

Forc

e (kN

)



010203040

Displacement (mm)

Forc

e (kN

)





1 511 668 0235 664 756 0122 976 1141 01452 503 657 0234 665 790 0158 965 1143 01563 362 422 0142 343 458 0251 284 323 01214 359 428 0161 350 452 0226 269 328 01805 992 1338 0259 836 1045 0200 934 1082 0137



1 756 1003 0246 807 1129 0285 1382 1713 01932 733 983 0254 809 1178 0313 1380 1718 01973 518 632 0180 465 684 0320 310 485 03614 519 630 0176 467 635 0293 311 529 04025 1397 2007 0304 1258 1665 0244 1366 1625 0159



1 802 1336 0400 938 1507 0378 1578 2289 03112 839 1309 0359 965 1573 0387 1564 2287 03163 686 846 0189 531 913 0418 455 730 03774 690 855 0193 532 828 0358 420 724 04205 1656 2675 0381 1346 2088 0355 1534 2161 0290



5 Conclusions


Competing Interests


Acknowledgments


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











5 Conclusions


Competing Interests


Acknowledgments


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article performance of seismic restrainer with...

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