effectivesemiactivebaseisolationsystemunder...

Research ArticleEffective Semiactive Base Isolation System underMultiple Earthquakes

Mohtasham Mohebbi and Hamed Dadkhah

Faculty of Engineering Department of Civil Engineering University of Mohaghegh Ardabili Ardabil Iran

Correspondence should be addressed to Mohtasham Mohebbi mohebbiumaacir

Received 22 August 2017 Revised 11 December 2017 Accepted 13 December 2017 Published 27 February 2018

Academic Editor Hossein Moayedi

Copyright copy 2018 Mohtasham Mohebbi and Hamed Dadkhah is is an open access article distributed under the CreativeCommons Attribution License which permits unrestricted use distribution and reproduction in any medium provided theoriginal work is properly cited

A method is proposed to design an effective semiactive control system composed of a linear low damping base isolation anda supplemental magnetorheological (MR) damper when the structure subjected to multiple earthquakes In the proposeddesign method the parameters of semiactive control system have been determined based on minimizing the average ofmaximum response of isolated structure under multiple design ground motions To select appropriate value for force relatedweighting parameter defined in performance index a range has been suggested for each design objective For numericalsimulations a scaled three-story base-isolated frame subjected to different scaled real earthquakes as well as filtered whitenoise excitations and the proposed method has been applied to design semiactive base isolation system under multipleearthquakes e results of numerical simulations have shown the capability of the proposed method in designing aneffective semiactive base isolation system the performance of which under multiple earthquakes has been almost close to thecase that it is designed optimally for each earthquake separately Also under multiple earthquakes using the passive-off andpassive-on forms of MR damper can be recommended respectively regarding to the objectives of minimizing the maximumacceleration and base drift

1 Introduction

Base isolation system is widely recognized as one of themost effective control strategies used for mitigating thestructural response which helps a structure survivea potentially devastating seismic impact through a properinitial design or subsequent modifications In many casesthe application of the base isolation system has beenconsiderably helpful in improving a structurersquos seismicperformance and its sustainability However beinga passive control system it suffers from some limitationssuch as large base drifts and the inability to adapt todifferent earthquakes and vibrations To reduce the basedrift of base isolation system different strategies havebeen previously considered including increasing thedamping of the natural rubber [1] and using supplementalpassive dampers in conjunction with the base isolation

system [2] More recently in order to both mitigate thebase drift and make the base isolation system adaptable todifferent earthquakes using active and semiactive controlschemes along with the base isolation system have beeninvestigated e active control systems directly apply thedesired force for controlling the seismic response ofstructures [3] while in the semiactive control schemes thecharacteristics of control system are adjusted to make theapplied force track the desired control force Hybrid activebase isolation systems have been studied by a number ofresearchers [4ndash6] and have shown effective performancein both mitigating the base drift and adapting to differentconditions Nagarajaiah et al [5] performed an experi-mental and analytical study to investigate the effectivenessof an active base isolation system in controlling a sliding-isolated bridge and found significant reduction in theresponse of the bridge Since active control systems

HindawiAdvances in Civil EngineeringVolume 2018 Article ID 7382481 12 pageshttpsdoiorg10115520187382481

require high external power supplies semiactive systemshave been proposed to replace them Several semiactivemechanisms have been examined in combination withthe base isolation system such as variable orifice damper[7 8] and variable stiffness system [9 10] Weber et al[11] studied the performance of structure equipped witha semiactive friction pendulum against the seismicloading and determined the optimal friction coefficientof isolation system for minimizing the structure accel-eration Magnetorheological (MR) damper is also an-other effective semiactive control system consideredseparately [12 13] or together with the base isolationsystem for controlling the structural response [14ndash18]Ramallo et al [19] demonstrated the effectiveness ofadding a MR damper to conventional isolated structuresby achieving notable decreases in base drifts comparedto passive systems Sahasrabudhe and Nagarajaiah [20]proved experimentally the effectiveness of the semiactivebase isolation system in reducing the base drift and otherresponse of the superstructure under near-fieldearthquakes

In previous researches mostly only one excitation hasbeen used in the design procedure of semiactive controlsystem while the characteristics of earthquakes maystrongly affect its performance As examples for de-signing a semiactive base isolation system Johnson et al[21] designed the control system under one excitationand Yoshioka et al [22] used the H2LQG algorithm tominimize the peak acceleration under only the El Centroearthquake Also Mohebbi et al [23] determined theoptimal weighting parameter of semiactive base isolationsystem under one excitation with design objective ofminimizing the peak base drift However althoughRamallo et al [19] designed the control system to reducethe base drift without increasing acceleration based onthe results of four historical earthquakes they de-termined the design variables of the control algorithmbased on try and error

Hence in previous researches which use only oneexcitation in designing semiactive base isolation systemsthe effect of earthquake characteristics on designing andperformance of semiactive base isolation has not beenstudied in detail On the other hand according to regu-lations of seismic design codes to take into account theeffect of different earthquake characteristics in designoutput and design a structure to be resistant under dif-ferent excitations it is recommended to consider multipledesign records in a design procedure where the designrecords are selected based on site seismic conditionerefore following this recommendation and extendingit in designing control system to be effective under dif-ferent earthquakes in this paper it has been decided todesign the semiactive base isolation system based onconsidering multiple earthquakes in the design procedurethat the earthquake records have been selected randomlyHowever in addition to considering the randomly se-lected earthquake records the filtered white noise

excitations are considered in this paper If the obtainedresults based on the selected earthquakes are satisfiedunder the filtered white noise excitations it can beconcluded that the results are valid for a wide range ofearthquakes as well as sits Also instead of trial-and-errormethod a systematic procedure is explained to design thesemiactive base isolation system According to the seismicdesign codes the acceleration and drift have been knownas the proper criteria of designing structure that re-spectively represent the criteria of the occupant comfortability and the structure safety In most previous researches ithas been seen that the maximum acceleration of isolatedstructure increases when adding the supplemental MRdamper to the base isolation system which can causeproblems regarding occupant comfort ability criterion[23 24] Hence in this research controlling the base driftand superstructure acceleration separately or simulta-neously under multiple records has been considered asdesign objectives For numerical simulations a three-story frame subjected to different earthquakes and fordifferent design objectives the parameters of controlsystem have been determined based on minimizing theaverage of responses obtained under several excitationsIn addition the performance of control system designedbased on using multiple records in the design procedurehas been evaluated under different test records

2 System Model

Assuming that the performance of the hybrid base isolationand MR damper system is adequate to keep the structure inthe linear region the equation of motion of the semiactivebase isolation system can be written as

Ms eurox + Cs _x + Ksx ΓfminusMsΛeuroxg (1)

where Γ [minus1 0itimes1]T which indicates the position of MRdampers Λ is the vector that all of its components areunity f is the force of the MR damper euroxg is the groundacceleration x is the vector of the displacements of thestructure relative to the ground andMs Ks and Cs are themass stiffness and damping matrices of controlledstructure respectively

e state-space form of the equation of motion is given by

_Z AZ + Bf + E euroxg(2)

y CZ + Df + ] (3)

where Z is the state vector (Z [x _x]T) ] is the mea-surement noise vector y is the vector of measured outputsand A B C D and E are the system matrices Defining y asthe vector that includes the acceleration of the base iso-lation floor accelerations of the isolated structure and thedisplacement of the base isolation (ie y [ eurox1 euroxn x1])the system matrices of (2) and (3) for a system with ndegrees of freedom can be written as

2 Advances in Civil Engineering

A 0ntimesn Intimesn

minusMminus1s Ks minusMminus1s Cs[ ]

B 0ntimes1Mminus1s Γ[ ]

E 0ntimes1Λntimes1[ ]

C minusMminus1s Ks minusMminus1s Cs1 01timesnminus1 01timesn

[ ]

D Mminus1s Γ

0[ ]

(4)

3 MR Damper Model

MR dampers are semiactive control systems whose dy-namic behaviors can easily be adjusted by changing voltagelevels is enables the device to produce high variabledamping forces with less energy requirements than otherdevices of its class So hybrid isolation systems consisting ofthe base isolation system and MR dampers can reasonablyadapt to dierent excitations even to near-eld earthquakeswhere the isolated structure is more susceptible to damage[25] A simple mechanical idealization of the MR damper isdepicted in Figure 1

e applied force f predicted by this model is given as[26]

f az + c0( _x minus _y) + k0(xminusy) + k1 xminusx0( ) (5)

or equivalently

f c1 _y + k1 xminusx0( )

_z minusc| _xminus _y|z|z|nminus1 minus β( _xminus _y)|z|n + A( _xminus _y)

_y 1

c1 + c0az + c0 _x + k0(xminusy)

(6)

where k1 c0 and c1 represent the accumulator stiness theviscous damping and the dashpot respectively x0 is theinitial displacement of spring k1 k0 is present to controlthe stiness at the large velocities and the parameters c βand A are the parameters used to dene the shape ofhysteresis loops

e force of the MR damper depends on its volt-age Spencer et al [27] have suggested the followingequations to obtain the dynamic parameters of the MRdamper

a a(u) aa + abuc1 c1(u) c1a + c1buc0 c0(u) c0a + c0bu

(7)

where u is given as the output of a rst-order lter given by

_u minusη(uminusV) (8)

where V is the MR damper voltage and η is a constantmodulus with dimension of secminus1

4 Control Algorithm

In this paper the H2LQG control algorithm has beenused to determine the optimum control force required formitigating the response [28] To design the controller euroxgis taken to be the stationary white noise and the responseof the structure is minimized using the following costfunction

J limτrarrinfin1τE int

τ

0yT(t)Qy(t) + rf2

c( )dt[ ] (9)

where Q and r are the response weighting matrix and forceweighting parameter that aect the performance of the activeand semiactive control systems [29] and should be selectedproperly Similar to the previous researches in designingsemiactive control systems in this paper too the responserelated weighting matrix Q has been considered such thatdierent weights are assigned to accelerations and drifts asfollows [19 21]

Q qaccelsI 0

0 qdriftsI[ ] (10)

where qaccels and qdrifts are respectively the weights assignedto the accelerations and drifts of the structure In this paperthe output vector y includes accelerations of the stories andthe base drifts y [euroxb eurox1 euroxn xb] hence the costfunction dened in (9) for a structure with N degrees offreedom can be written as

J limτrarrinfin1τEint

τ

0qaccels sum

N

i1eurox2i + eurox2b

+ qdriftx2b + rf

2cdt

(11)

e optimal control force is given as follows

fc minuskcz

_z Az + Bf + L(yminusCzminusDf)(12)

c1

c0

k1

k0

y x

f

BoucminusWen

Figure 1 Simple mechanical model of MR damper

Advances in Civil Engineering 3

where kc is the gain matrix for the linear quadratic regulator(LQR) and L is the gain matrix for the state estimator whichis determined as

kc BprimePr

L (CS)prime

(13)

where P and S are the solution of the algebraic Riccatiequation given by

PA + AprimePminusPBprimeBPr

+ CprimeQC 0

SAprime + ASminus SCprimeCS + cEEprime 0

(14)

Because MR damper force cannot be changed to theoptimal control force directly the second algorithm isemployed to apply MR damper voltage by comparing theMR damper force and the optimal control force eclipped-optimal control has been used to apply MR dampervoltage that is determined as [26]

V VmaxH fc minusf( )f (15)

where Vmax is the maximum voltage that can be applied tothe MR damper and H is the Heaviside step functionWhen the force produced by the MR damper is smallerthan the optimal control force and two forces have thesame sign the voltage applied to the MR damper is in-creased to the maximum level Otherwise the voltageapplied is set to zero

5 Numerical Example

For numerical analysis a scaled model of a three-story shearbuilding frame has been considered in xed-base and base-isolated forms In the isolated system an MR damper hasbeen installed between the ground and the base isolationsystem e conguration of the considered dynamic modelhas been shown in Figure 2

e structural properties of both the xed-base andthe isolated structures are the same taken as m1m2m3 983 kg k1516 and k2 k3 684 kNm and c1125and c2 c3 50Nmiddotsm [26] For the isolated system one de-gree of freedom is added to the dynamic model of thestructure e properties of this degree of freedom depend onthe characteristics of the base isolation system e base massm0 is chosen equal to the poundoor mass and the base damping c0is chosen such that the damping ratio of the isolated modeequals to 2 of the critical damping [1] Since the base iso-lation system is in combination with the MR damper utili-zation of high damping base isolation is not needed e basestiness k0 is also selected such that the natural period of theisolated structure is equal to triple the natural period ofthe xed-base structure [30] So the properties of the baseisolation system are m0 983 kg c0180Nmiddotsm andk0 56 kNm For numerical simulations a program has beendeveloped using theMATLAB software For the isolated shearbuilding considered in the numerical example the matrices ofsystem in (1) can be written as

Ms

m0 0 0 0

0 m1 0 0

0 0 m2 0

0 0 0 m3

Cs

c0 + c1 minusc1 0 0

minusc1 c1 + c2 minusc2 0

0 minusc2 c2 + c3 minusc30 0 minusc3 c3

Ks

k0 + k1 minusk1 0 0

minusk1 k1 + k2 minusk2 0

0 minusk2 k2 + k3 minusk30 0 minusk3 k3

(16)

e dynamical parameters of the MR damper used inthis research are given in Table 1 [26]emaximum voltageand the capacity of the MR damper have been 225V and3000N respectively e design earthquake records are se-lected randomly while according to regulations of seismicdesign codes the earthquake records should be selected basedon the seismic conditions of a specic site Hence the ob-tained results from the randomly selected earthquake recordsare validated under the ltered white noise excitations By thisvalidation it can be concluded that the results will be valid fora wide range of earthquakes as well as sits Also the designearthquake records should be scaled based on the regulationsof seismic design codes while because the considered struc-ture in this paper is a scaled model the earthquake recordscannot be scaled based on the scaling method described inseismic design codes erefore the design earthquake re-cords are employed in the unscaled form

c1

m1

k1

c0

m0

k0

c2

m2

k2

c3

m3

Semi-active base isolated Fixed base

k3

c1

m1

k1

c2

m2

k2

c3

m3k3

MR damper

Figure 2 Model of the structure and control system

Table 1 Dynamical parameters of the MR damper [26]

Parameter Value Parameter Valuec0a 21Nmiddotseccm aa 140NcmC0b 35NmiddotseccmmiddotV ab 695NcmmiddotVK0 469Ncm c 363 cmminus2

C1a 283Nmiddotseccm β 363 cmminus2

C1b 295NmiddotseccmmiddotV A 301K1 5Ncm n 2X0 143 cm η 190 secminus1


Numerical analysis conducted in this research can beclassified into four cases as follows

Case (a) base isolation system and supplementalpassive MR damperCase (b) designing semiactive hybrid base isolationsystem under multiple earthquakesCase (c) validating the proposed design procedureunder filtered white noise excitationsCase (d) assessing the performance of the designedcontrol system under testing earthquakes

51 Case (a) Hybrid Base Isolation System and Passive MRDamper In this case the performance of hybrid control systemis evaluatedwhen theMRdamper voltage has been constant andcontrol system acts in the passive form e maximum re-sponses of structure under different scaled earthquakes havebeen reported in Table 2 for constant voltages of 0 (P-Off) and225V (P-On) Since the considered structure is a scaled modelthe earthquake records have been reproduced at five times therecorded rate e maximum response of the fixed-base (F-B)structure and the controlled structure by using the single baseisolation (S-B-I) system has been presented in Table 2

As shown in Table 2 adding the single base isolationsystem to the structure decreases the maximum response offixed-base structure which under multiple excitations themaximum interstory drift and acceleration have been aver-agely reduced by 77 and 80 respectively while the basedrift has been high For mitigating the peak base drift thesupplemental passive MR damper is employed in combina-tion with base isolation control system From the results it isclear that using the passive MR damper has mitigated themaximum base drift of base-isolated structure significantlyAbout 62 and 78 reduction in the average of the maxi-mum base drifts under different excitations has been achievedfor the passive-off and passive-on forms respectively whilethe average of the maximum accelerations of isolatedstructure has been increased about 48 and 141 for thepassive-off and passive-on forms respectively

52 Case (b) Designing Semiactive Hybrid Base IsolationSystem In this case the structure subjected to different scaledearthquakes and the semiactive base isolation system has beendesigned to be effective undermultiple excitations Forweighting

matrix Q defined in (9) different combinations of qaccels andqdrifts can be considered In this paper to evaluate the effect ofQrsquoselements on performance of hybrid control system six differentsets of qaccels and qdrifts have been defined as reported in Table 3which cover a wide range of qdriftsqaccels ratio In set (A-1) theacceleration and drift are weighted equally in the performanceindex function while in set (A-6) drift is weighted much morethan acceleration For each set the force weighting parameter rin (9) is determined to minimize the peak superstructure ac-celeration and base drift separately or simultaneously

e proposed method includes two steps first the struc-ture subjected to each earthquake separately and by usingdifferent sets of qaccels and qdrifts defined in Table 3 the peakacceleration of superstructure and base drift of isolatedstructure are determined through a sensitivity analysis fordifferent values of weighting parameter r As instance for sets(A-1) and (A-6) the peak response under different earthquakeshas been shown in Figures 3 and 4 For other sets of Q similartrends for response variation versus weighting parameter havebeen obtained aswell which because of space limitation has notbeen reported here en by using the results obtained in firststep for each ground motion the average of maximum re-sponses are calculated under all earthquakes for differentvalues of weighting parameter r and various sets of Q InFigure 5 the result of second step has been presented

According to the results it is clear that for the consideredstructure the changing pattern of the peak base drift and su-perstructure acceleration with r is almost similar under differentearthquakes Moreover for a specific structure according to theresults to have effective performance under multiple earth-quakes an appropriate range can be proposed to select r foreach design objective For example as shown in Figure 3(a) forset (A-1) the ranges (a) (b) and (c) are appropriate tominimizethe peak base drift base drift-acceleration and accelerationrespectively ese ranges are broken by the corner parametersr1 and r2 which are shown in Table 3 for each set of Q

Table 2 Peak response of structures under different earthquakes

EarthquakePeak acceleration (cms2) Peak interstory drift (cm) Peak base drift (cm)

F-B S-B-I P-Off P-On F-B S-B-I P-Off P-On S-B-I P-Off P-OnEl Centro (PGA 0348 g 1940) 1413 217 206 478 054 010 006 015 127 044 019Loma Prieta (PGA 0278 g 1989) 618 133 211 500 023 006 006 020 064 034 020Northridge (PGA 0535 g 1994) 678 176 186 237 030 009 004 007 109 029 018Petrolia (PGA 0163 g 1992) 324 146 136 164 013 007 004 005 090 026 015Parkfield California (PGA 035 g 1966) 564 90 323 370 015 003 005 007 026 0186 015Taft (PGA 018 g 1952) 529 77 179 279 021 003 004 007 037 025 017Average 688 140 207 338 026 006 005 010 076 029 017

Table 3 Various sets of Q and corner force weighting parameter

Various sets A-1 A-2 A-3 A-4 A-5 A-6qaccels 1 1 1 1 1 1qdrifts 1 102 104 106 108 1010

r1 10minus86 10minus86 10minus86 10minus83 10minus37 10minus15


rl-a 10minus58 10minus58 10minus58 10minus55 10minus23 10minus1


According to the results to havemore reduction in the averagesof maximum base drift and acceleration under multipleearthquakes it is recommended to select the force weightingparameter r from ranges (a) and (c) respectively For examplein this case study r 10minus14 and 10minus05 are selected from ranges(a) and (c) for minimizing the maximum base drift and ac-celeration of isolated structure respectively According toFigure 5 these values of r are the appropriate selections for allconsidered sets of Q to minimize the maximum base drift andacceleration If it is desired to control the acceleration and basedrift of the isolated structure simultaneously depending on therelative importance between the acceleration and base driftappropriate value for r can be selected from range (b) For eachset ofQ to control base drift and acceleration simultaneously in

this research the logarithmic average rl-a of corner parametersr1 and r2 has been selected and presented in Table 3 From theresults presented in Figure 5 it has been found that under allexcitations the minimum values for the peak base drift andsuperstructure acceleration of the isolated structure has beenachieved by using the sets (A-6) and (A-1) respectively eaverage of the peak base drift of the isolated structure and themaximum acceleration of the fixed-base structure under designrecords have been reduced about 79 and 70 for sets (A-6)and (A-1) respectively

e results obtained by using the proposed values for runder multiple records which has led to r 10minus14 r rl-a(Table 3) and r 10minus05 for the case study of the currentresearch regarding different design objectives have been

005

01

015

02

025

03

035

04

045

05

1E-17 1E-11

a b c

1E-05

Peak

bas

e dri

(cm

)

Weighting parameter (r)

r2r1

El CentroLoma PrietaNorthridge

PetroliaParkfield CaliforniaTa

(a)Pe

ak b

ase d

ri (c

m)

1E-17 1E-11 1E-0501

012

014

016

018

02

022

024

026




(b)

Figure 3 e peak base drift for sets (A-1) and (A-6) (a) A-1 (b) A-6

100

150

200

250

300

350

400

450

Peak

acce

lera

tion

(cm

s2 )

1E-17 1E-11 1E-05Weighting parameter (r)

(a)

100

150

200

250

300

350

400

450

500

550

600

1E-17 1E-11 1E-05

Peak

acce

lera

tion

(cm

s2 )


(b)

Figure 4 e peak acceleration for sets (A-1) and (A-6) (a) A-1 (b) A-6


01

015

02

025

03

035

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6

Peak

bas

e dri

(cm

)


(a)

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6


150

200

250

300

350

400

Peak

acce

lera

tion

(cm

s2 )

(b)

Figure 5 Average of the peak base drift and acceleration for various sets of Q (a) Peak base drift (b) Peak acceleration

Table 4 Peak response of structures under dierent earthquakes for set (A-1)


Optimal case r 10minus05 rl-a r 10minus14 r 10minus05 rl-a r 10minus14 r 10minus05 rl-a r 10minus14 Optimal caseEl Centro 208 209 272 392 0061 0067 0108 0438 0361 0368 0338Loma Prieta 213 213 312 400 0062 0067 0103 0335 0293 0290 0282Northridge 182 189 195 220 0045 0045 0054 0292 0269 0261 0261Petrolia 136 136 152 189 0037 0037 0039 0256 0211 0183 0182Parkeld California 321 323 328 348 0047 0053 0055 0182 0175 0169 0169Taft 179 179 201 227 0040 0051 0057 0255 0227 0202 0202




Table 6 Average of the peak responses for various sets of Q

Various setsPeak acceleration (cms2) Peak interstory drift (cm) Peak base drift (cm)

Optimal case r 10minus05 rl-a r 10minus14 r 10minus05 rl-a r 10minus14 r 10minus05 rl-a r 10minus14 Optimal caseA-1 207 208 243 296 0049 0053 0069 0293 0256 0245 0239A-2 207 208 243 296 0049 0053 0069 0293 0256 0245 0239A-3 207 208 243 296 0049 0053 0069 0293 0255 0244 0238A-4 207 208 263 325 0049 0060 0076 0293 0217 0212 0201A-5 210 212 283 357 0049 0069 0093 0289 0196 0158 0154A-6 295 295 306 343 0074 0084 0087 0182 0163 0158 0155


reported in Tables 4 and 5 for sets (A-1) and (A-6) as the bestsets for controlling the maximum superstructure accelerationand base drift for each excitationwhile the average values underall records are given in Table 6 for all considered sets of Q eresults show that the proposedmethod for designing semiactivebase isolation system has worked successfully under multipleexcitations regarding the design objectives Also to evaluate theefficiency of the proposed method the maximum responseunder each excitation for the case that the control system hasbeen designed optimally for each earthquake separately hasbeen given in Tables 4 and 5 for sets (A-1) and (A-6) too whilefor all sets of Q the average of corresponding values under alldesign records has been presented in Table 6 e results showthat the maximum responses and their averages obtained byusing r 10minus14 and r 10minus05 for mitigating the maximum basedrift and acceleration have been very close to the optimal caseunder each earthquake separately For example as shown inTable 6 for set (A-1) when the control system is designedoptimally for each earthquake separately the averages of thepeak accelerations and base drifts under design excitations are207 cms2 and 0239 cm while by using the proposed methodthe corresponding values have been 208 cms2 and 0245 cmwhich are very close together erefore the performance ofcontrol the system designed under multiple records by usingthe proposed method has been very close to the optimal caseunder each earthquake In addition if only one excitation isused for designing the control system the control systemmaynot have the most effective performance under multipleearthquakes As instance if only the Parkfield Californiaearthquake is considered as the design record r is determinedas 10minus46 regarding the objective of minimizing the peak basedrift as shown in Figure 3(a) For this r the average of the peakbase drifts under the considered earthquake records is equalto 0268 cm while by using the proposed design procedure inthis paper and considering the multiple earthquakes thecorresponding value has been 0245 cm erefore themultiple record-based design works better than the controlsystem designed based on only one excitation

Comparing the semiactive and passive forms of thehybrid control system (Tables 2 and 6) shows that in additionto using semiactive form using the passive-off and passive-on forms can be recommended respectively to minimizethe maximum acceleration and the maximum base driftHowever using the semiactive form because of its adapta-tion capability to different conditions is preferred

53 Case (c) Validating the Proposed Design Procedure underFilteredWhite Noise Excitations In Section 52 for designingthe control system under multiple earthquakes differentearthquake records were selected randomly as the design re-cords while selecting earthquake records based on seismicconditions of a specific site has been recommended by theseismic codes In this section it is shown that the resultsobtained in Section 52 are independent of the selectedearthquake record To this end the seismic load is simulated bypassing two different Gaussian white noises (WN) processesthrough the KanaindashTajimi filter [31 32] with the power spectraldensity function given by

s(ω) So

ω4g + 4ω2

gξ2gω2

ω2 minusω2g1113872 1113873

2+ 4ω2

gξ2gω2

⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦

So 003ξg

πωg 4ξ2g + 11113872 1113873

(17)

where So is the constant spectral density and ξg andωg are thedamping and frequency of the ground respectively echaracteristics of the KanaindashTajimi excitations used for thenumerical simulation are presented in Table 7 e peak basedrift and acceleration of structure subjected to the KanaindashTajimiexcitations are reported in Figures 6 and 7 for sets (A-1) and (A-6) and different values of r From the results it is clear that underthe KanaindashTajimi excitations the changing pattern of the peakbase drift with r is almost similar to the changing pattern shownin Section 52 for the selected earthquake records erefore itcan be concluded that the proposed designmethod and dividingr into three ranges regarding the design objectives are in-dependent of the selected earthquake record and if the designrecords are selected based on seismic conditions of a specific sitethe results are consistent with that of Section 52

54 Case (d) Assessing the Performance of Designed ControlSystem under Testing Earthquakes To evaluate the perfor-mance of control systems designed in Section 53 under otherearthquakes that are different in the frequency content with thedesign records the designed semiactive base isolation systemshave been subjected to different scaled ground motions emaximum response of uncontrolled and controlled structuresunder testing records has been reported in Table 8 for differenttypes of passive control systems Also for the semiactive formthe average of the peak acceleration and base drift under testingearthquakes has been presented in Table 9 for r 10minus14 r rl-aand r 10minus05 obtained for controlling the maximum base driftbase drift-acceleration and acceleration under multiple designrecords As an instance the force-displacement curve of MRdamper force during Olympia (PGA 028 g 1949) earthquakehas been shown in Figure 8 for the P-Off and semiactive controlsystems Based on the results under testing records it is possibleto reduce the average of the maximum base drift of isolatedstructure up to 72 by using set (A-6) and r 10minus14 andmitigate the maximum acceleration of fixed-base structure upto 82by using set (A-1) and r 10minus05 Hence the effectivenessof the semiactive control system in reducing different responsesunder testing records has been proven as well

For better comparison the average of maximum re-sponse under testing excitations has been determined fordifferent values of r and shown in Figure 9 while the min-imum corresponding values are reported in Table 9 for eachset ofQ From the results it is clear that under testing records

Table 7 Characteristics of the KanaindashTajimi excitations

KanaindashTajimi excitation PGA (g) ξg ωg (rads)WN I 0475 03 373WN II 0432 04 60


025

03

035

04

045

05Pe

ak b

ase d

ri (c

m)

1E-17Weighting parameter (r)1E-11 1E-05

WN IWN II

(a)

02

022

024

026

028

03

Peak

bas

e dri

(cm

)


WN IWN II

(b)

Figure 6 e peak base drift under the KanaindashTajimi excitations for sets (A-1) and (A-6) (a) A-1 (b) A-6

150

200

250

300

350

400

Peak

acce

lera

tion

(cm

s2 )


WN IWN II

(a)

200

220

240

260

280

300

320

340

360

380

400

Peak

acce

lera

tion

(cm

s2 )


WN IWN II

(b)

Figure 7 e peak acceleration under the KanaindashTajimi excitations for sets (A-1) and (A-6) (a) A-1 (b) A-6

Table 8 Peak response of structures under testing earthquakes


F-B S-B-I P-O P-On F-B S-B-I P-O P-On S-B-I P-O P-OnOlympia (PGA 028 g 1949) 840 156 177 284 028 008 004 007 093 025 017San Helena Montana (PGA 0146 g 1935) 306 36 113 170 013 002 003 007 021 018 012Northridge (PGA 0344 g 1994) 1728 117 205 514 068 005 006 022 052 045 020Taft (PGA 0156 g 1952) 727 97 145 256 032 004 003 006 052 018 015Average 900 102 160 306 035 005 004 011 054 027 016


Table 9 Average of the peak responses for various sets of response weighting parameters under testing earthquakes

Various setsPeak Acceleration (cms2) Peak interstory drift (cm) Peak base drift (cm)


minus500

minus300

minus100

100

300

500

MR

dam

per f

orce

(N)

minus03 minus01 01 03Displacement (cm)

(a)

minus500

minus300

minus100

100

300

500

minus03 minus01 01 03

MR

dam

per f

orce

(N)

Displacement (cm)

(b)

Figure 8 Force-displacement curve of MR damper force under Olympia earthquake for the P-O and semiactive controls (a) P-O controlsystem (b) Semiactive control system (set A-6 r 10minus14)

012

014

016

018

02

022

024

026

028

Peak

bas

e dri

(cm

)

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6


(a)

50

100

150

200

250

300

350

400

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6


Peak

acce

lera

tion

(cm

s2 )

(b)

Figure 9 Average of the peak accelerations and base drifts under testing earthquakes for various sets of response weighting parameters(a) Peak base drift (b) Peak acceleration


too the changing pattern of the peak base drift and accel-eration with r is the same as design records and the ranges of(a) (b) and (c) are similar to the results shown in Figure 5 fordesign records Hence from this similarity the effectiveness ofthe semiactive control system under testing records has beenpredictable As shown in Table 9 under testing records toothe semiactive base isolation system designed by using themethod proposed in this research has worked the same asoptimal design for each record separately For example about72 reduction has been achieved in the average of maximumbase drift of the isolated structure when using set (A-6) andr 10minus14 while the corresponding value has been 72 for theoptimal case

6 Conclusion

In this paper a method has been presented for designinga semiactive control system composed of a low damping baseisolation system and a supplemental magnetorheological(MR) damper under multiple earthquake records to mitigatethe maximum superstructure acceleration and base drift ofthe isolated structure e H2linear quadratic Gaussian(LQG) and clipped-optimal control algorithms have beenused to determineMR damper force In the proposed methodwhere the main focus has been designing the semiactive baseisolation system to be effective under multiple design recordsfirst the appropriate range for the parameter of control systemhas been determined for each design objective under eachexcitation and then based on mitigating the average ofresponses under multiple earthquakes the control systemdesign parameters have been selected For numerical simu-lations a scaled three-story shear building base-isolated framesubjected to different scaled earthquakes and for different setsof response weighting matrix a semiactive base isolationsystem has been designed to mitigate the peak base drift andsuperstructure acceleration separately or simultaneously Inaddition to compare the performance of the semiactivecontrol system with that of the passive hybrid system theresponse of the base-isolated structure equipped with passive-off and passive-on MR dampers has been determined underdesign earthquakes According to the results of numericalsimulations the following can be concluded

(1) Changing pattern of the peak response with thedesign parameter of control algorithm has beensimilar under different real earthquakes and filteredwhite noise excitations Hence for a specific struc-ture and for each design objective a range can beproposed to the weighting parameter that is almostindependent from input earthquake

(2) e semiactive base isolation system designedaccording to the proposed method under multiplerecords has been effective in reducing the desiredresponses which in the current research up to 79and 70 reduction has been achieved in the averageof the peak base drift of the isolated structure and themaximum acceleration of the fixed-base structurerespectively

(3) e performance of semiactive base isolation sys-tems designed under multiple earthquakes to min-imize the peak base drift and acceleration have beenapproximately the same as passive-on and passive-off forms respectively

(4) e most reduction in the peak base drift has beenobtained when the assigned weight on drift in theperformance index is much more than the acceler-ation related weighting parameter and when driftand acceleration are weighted equally the maximumreduction in the peak acceleration is achieved

(5) Under testing earthquake records the average ofpeak base drift of isolated structure and the maxi-mum acceleration of fixed-base structure have beenreduced about 72 and 82 by using the proposeddesign method while the corresponding values havebeen 72 and 83 when the control system has beendesigned optimally for each earthquake separately

erefore the proposed method has been an efficientmethod for designing the semiactive base isolation systemunder multiple excitations which should be considered indesign procedure as per seismic design codes

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this article

References

[1] F Naeim and J M Kelly Design of Seismic Isolated StructureFrom eory to Practice Wiley New York NY USA 1999

[2] M C Constantinou M D Symans P Tsopelas andD P Taylor ldquoFluid dampers in applications of seismic energydissipation and seismic isolationrdquo in Proceedings of ATC-17-1Seminar on Seismic Isolation Passive Energy Dissipation andActive Control San Francisco CA USA March 1993

[3] T Kobori M Takahashi T Nasu N Niwa and K OgasawaraldquoSeismic response controlled structure with active variablestiffness systemrdquo Earthquake Engineering and StructuralDynamics vol 22 no 11 pp 925ndash941 1993

[4] J A Inaudi and J M Kelly ldquoHybrid isolation systems forequipment protectionrdquo Earthquake Engineering and Struc-tural Dynamics vol 22 no 4 pp 297ndash313 1993

[5] S Nagarajaiah M A Riley and A Reinhorn ldquoControl ofsliding-isolated bridge with absolute acceleration feedbackrdquoJournal of Engineering Mechanics vol 119 no 11 pp 2317ndash2332 1993

[6] J N Yang J C Wu A M Reinhorn and M Riley ldquoControlof sliding-isolated buildings using sliding-mode controlrdquoJournal of Structural Engineering vol 122 no 2 pp 179ndash1861996

[7] G J Madden M D Symans and N Wongprasert ldquoExper-imental verification of seismic response of building framewith adaptive sliding base-isolation systemrdquo Journal ofStructural Engineering vol 128 no 8 pp 1037ndash1045 2002

[8] N Wongprasert and M D Symans ldquoExperimental evaluationof adaptive elastomeric base-isolated structures usingvariable-orifice fluid dampersrdquo Journal of Structural Engi-neering vol 131 no 6 pp 867ndash877 2005


[9] S Narasimhan and S Nagarajaiah ldquoA STFT semiactivecontroller for base isolated buildings with variable stiffnessisolation systemsrdquo Engineering Structures vol 27 no 4pp 514ndash523 2005

[10] S Nagarajaiah and S Sahasrabudhe ldquoSeismic responsecontrol of smart sliding isolated buildings using variablestiffness systems an experimental and numerical studyrdquoEarthquake Engineering and Structural Dynamics vol 35no 2 pp 177ndash197 2006

[11] F Weber H Distl and C Braun ldquoSemi-active base isolationof civil engineering structures based on optimal viscousdamping and zero dynamic stiffnessrdquo in Proceedings of theIMACndashXXXV Conference and Exposition on Structural Dy-namics pp 1ndash9 Garden Grove CA USA February 2017

[12] Y Z Lin and R Christenson ldquoReal-time hybrid test validationof a MR damper controlled building with shake table testsrdquoAdvances in Structural Engineering vol 14 no 1 pp 79ndash922011

[13] S D Bharti S M Dumne and M K Shrimali ldquoEarthquakeresponse of asymmetric building with MR damperrdquo Earth-quake Engineering and Engineering Vibration vol 13 no 2pp 305ndash316 2014

[14] B Erkus and E A Johnson ldquoDissipativity analysis of the baseisolated benchmark structure with magnetorheological fluiddampersrdquo Smart Materials and Structures vol 20 no 10p 105001 2011

[15] Y Wang and S J Dyke ldquoModal-base LQG for smart baseisolation system design in seismic response controlrdquo Struc-tural Control and Health Monitoring vol 20 no 5pp 753ndash768 2013

[16] B Chen Y Z Sun Y L Li and S L Zhao ldquoControl of seismicresponse of a building frame by using hybrid system withmagnetorheological dampers and isolatorsrdquo Advances inStructural Engineering vol 17 no 8 pp 1199ndash1215 2014

[17] H S Kim and J W Kang ldquoMulti-objective fuzzy control ofsmart base isolated spatial structurerdquo International Journal ofSteel Structures vol 14 no 3 pp 547ndash556 2014

[18] M Mohebbi and H Dadkhah ldquoMulti-objective semi-activebase isolation systemrdquo International Journal of Optimizationin Civil Engineering vol 7 no 3 pp 319ndash338 2017

[19] J C Ramallo E A Johnson and B F Spencer ldquoSmart baseisolation systemsrdquo Journal of Engineering Mechanics vol 128no 10 pp 1088ndash1099 2002

[20] S Sahasrabudhe and S Nagarajaiah ldquoExperimental study ofsliding base-isolation buildings with magnetorheologicaldampers in near-fault earthquakerdquo Journal of StructuralEngineering vol 131 no 7 pp 1025ndash1034 2005

[21] E A Johnson J C Ramallo B F Spencer and M K SainldquoIntelligent base isolation systemsrdquo in Proceedings of 2ndWorld Conference on Structural Control pp 367ndash376 KyotoJapan June 1998

[22] H Yoshioka J C Ramallo and B F Spencer ldquoSmart baseisolation strategies employing magnetorheological dampersrdquoJournal of Engineering Mechanics vol 128 no 5 pp 540ndash5512002

[23] M Mohebbi H Dadkhah and K Shakeri ldquoOptimal hybridbase isolation and MR damperrdquo International Journal ofOptimization in Civil Engineering vol 5 no 4 pp 493ndash5092015

[24] S F Ali and A Ramaswamy ldquoHybrid structural control usingmagnetorheological dampers for base isolated structuresrdquoSmart Materials and Structures vol 18 no 5 p 055011 2009

[25] Y F Du X Zhu H Li and G H Wang ldquoCollapse simulationof plan irregular isolation structures subjected to near-fault

seismic motionrdquo Applied Mechanics and Materials vol 433ndash435 pp 2290ndash2294 2013

[26] S J Dyke B F Spencer M K Sain and J D CarlsonldquoModeling and control of magnetorheological dampers forseismic response reductionrdquo Smart Materials and Structuresvol 5 no 5 pp 565ndash575 1996

[27] B F Spencer S J Dyke M K Sain and J D CarlsonldquoPhenomenological model for magnetorheological dampersrdquoJournal of Engineering Mechanics vol 123 no 3 pp 230ndash2381997

[28] L M Jansen and S J Dyke ldquoSemi-active control strategies forMR damper a comparative studyrdquo Journal of EngineeringMechanics vol 126 no 8 pp 795ndash803 2000

[29] M Mohebbi and A Joghataie ldquoDesigning optimal tuned massdampers for nonlinear frames by distributed genetic algo-rithmsrdquo Structural Design of Tall and Special Buildings vol 21no 1 pp 57ndash76 2012

[30] R Villaverde Fundamental Concepts of Earthquake Engi-neering Taylor and Francis Group New York NY USA2009

[31] H Tajimi ldquoA statistical method of determining the maximumresponse of a building structure during an earthquakerdquo inProceedings of 2nd World Conference in Earthquake Engi-neering pp 781ndash797 Tokyo Japan July 1960

[32] K Kanai ldquoAn empirical formula for the spectrum of strongearthquake motionsrdquo in Bulletin Earthquake Research In-stitute University of Tokyo Tokyo Japan vol 39 pp 85ndash951961


International Journal of

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Shock and Vibration


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wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

require high external power supplies semiactive systemshave been proposed to replace them Several semiactivemechanisms have been examined in combination withthe base isolation system such as variable orifice damper[7 8] and variable stiffness system [9 10] Weber et al[11] studied the performance of structure equipped witha semiactive friction pendulum against the seismicloading and determined the optimal friction coefficientof isolation system for minimizing the structure accel-eration Magnetorheological (MR) damper is also an-other effective semiactive control system consideredseparately [12 13] or together with the base isolationsystem for controlling the structural response [14ndash18]Ramallo et al [19] demonstrated the effectiveness ofadding a MR damper to conventional isolated structuresby achieving notable decreases in base drifts comparedto passive systems Sahasrabudhe and Nagarajaiah [20]proved experimentally the effectiveness of the semiactivebase isolation system in reducing the base drift and otherresponse of the superstructure under near-fieldearthquakes

In previous researches mostly only one excitation hasbeen used in the design procedure of semiactive controlsystem while the characteristics of earthquakes maystrongly affect its performance As examples for de-signing a semiactive base isolation system Johnson et al[21] designed the control system under one excitationand Yoshioka et al [22] used the H2LQG algorithm tominimize the peak acceleration under only the El Centroearthquake Also Mohebbi et al [23] determined theoptimal weighting parameter of semiactive base isolationsystem under one excitation with design objective ofminimizing the peak base drift However althoughRamallo et al [19] designed the control system to reducethe base drift without increasing acceleration based onthe results of four historical earthquakes they de-termined the design variables of the control algorithmbased on try and error

Hence in previous researches which use only oneexcitation in designing semiactive base isolation systemsthe effect of earthquake characteristics on designing andperformance of semiactive base isolation has not beenstudied in detail On the other hand according to regu-lations of seismic design codes to take into account theeffect of different earthquake characteristics in designoutput and design a structure to be resistant under dif-ferent excitations it is recommended to consider multipledesign records in a design procedure where the designrecords are selected based on site seismic conditionerefore following this recommendation and extendingit in designing control system to be effective under dif-ferent earthquakes in this paper it has been decided todesign the semiactive base isolation system based onconsidering multiple earthquakes in the design procedurethat the earthquake records have been selected randomlyHowever in addition to considering the randomly se-lected earthquake records the filtered white noise

excitations are considered in this paper If the obtainedresults based on the selected earthquakes are satisfiedunder the filtered white noise excitations it can beconcluded that the results are valid for a wide range ofearthquakes as well as sits Also instead of trial-and-errormethod a systematic procedure is explained to design thesemiactive base isolation system According to the seismicdesign codes the acceleration and drift have been knownas the proper criteria of designing structure that re-spectively represent the criteria of the occupant comfortability and the structure safety In most previous researches ithas been seen that the maximum acceleration of isolatedstructure increases when adding the supplemental MRdamper to the base isolation system which can causeproblems regarding occupant comfort ability criterion[23 24] Hence in this research controlling the base driftand superstructure acceleration separately or simulta-neously under multiple records has been considered asdesign objectives For numerical simulations a three-story frame subjected to different earthquakes and fordifferent design objectives the parameters of controlsystem have been determined based on minimizing theaverage of responses obtained under several excitationsIn addition the performance of control system designedbased on using multiple records in the design procedurehas been evaluated under different test records

2 System Model

Assuming that the performance of the hybrid base isolationand MR damper system is adequate to keep the structure inthe linear region the equation of motion of the semiactivebase isolation system can be written as

Ms eurox + Cs _x + Ksx ΓfminusMsΛeuroxg (1)

where Γ [minus1 0itimes1]T which indicates the position of MRdampers Λ is the vector that all of its components areunity f is the force of the MR damper euroxg is the groundacceleration x is the vector of the displacements of thestructure relative to the ground andMs Ks and Cs are themass stiffness and damping matrices of controlledstructure respectively

e state-space form of the equation of motion is given by

_Z AZ + Bf + E euroxg(2)

y CZ + Df + ] (3)

where Z is the state vector (Z [x _x]T) ] is the mea-surement noise vector y is the vector of measured outputsand A B C D and E are the system matrices Defining y asthe vector that includes the acceleration of the base iso-lation floor accelerations of the isolated structure and thedisplacement of the base isolation (ie y [ eurox1 euroxn x1])the system matrices of (2) and (3) for a system with ndegrees of freedom can be written as


A 0ntimesn Intimesn





[ ]

D Mminus1s Γ

0[ ]

(4)

3 MR Damper Model




or equivalently



_y 1


(6)




(7)




4 Control Algorithm



τ

0yT(t)Qy(t) + rf2

c( )dt[ ] (9)


Q qaccelsI 0

0 qdriftsI[ ] (10)



τ

0qaccels sum

N

i1eurox2i + eurox2b

+ qdriftx2b + rf

2cdt

(11)


fc minuskcz


c1

c0

k1

k0

y x

f

BoucminusWen




kc BprimePr

L (CS)prime

(13)



+ CprimeQC 0


(14)




5 Numerical Example



Ms

m0 0 0 0

0 m1 0 0

0 0 m2 0

0 0 0 m3

Cs

c0 + c1 minusc1 0 0



Ks

k0 + k1 minusk1 0 0



(16)


c1

m1

k1

c0

m0

k0

c2

m2

k2

c3

m3


k3

c1

m1

k1

c2

m2

k2

c3

m3k3

MR damper



























005

01

015

02

025

03

035

04

045

05

1E-17 1E-11

a b c

1E-05

Peak

bas

e dri

(cm

)


r2r1



(a)Pe

ak b

ase d

ri (c

m)

1E-17 1E-11 1E-0501

012

014

016

018

02

022

024

026




(b)


100

150

200

250

300

350

400

450

Peak

acce

lera

tion

(cm

s2 )


(a)

100

150

200

250

300

350

400

450

500

550

600

1E-17 1E-11 1E-05

Peak

acce

lera

tion

(cm

s2 )


(b)



01

015

02

025

03

035

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6

Peak

bas

e dri

(cm

)


(a)

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6


150

200

250

300

350

400

Peak

acce

lera

tion

(cm

s2 )

(b)















s(ω) So

ω4g + 4ω2

gξ2gω2

ω2 minusω2g1113872 1113873

2+ 4ω2

gξ2gω2

⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦

So 003ξg

πωg 4ξ2g + 11113872 1113873

(17)







025

03

035

04

045

05Pe

ak b

ase d

ri (c

m)


WN IWN II

(a)

02

022

024

026

028

03

Peak

bas

e dri

(cm

)


WN IWN II

(b)


150

200

250

300

350

400

Peak

acce

lera

tion

(cm

s2 )


WN IWN II

(a)

200

220

240

260

280

300

320

340

360

380

400

Peak

acce

lera

tion

(cm

s2 )


WN IWN II

(b)









minus500

minus300

minus100

100

300

500

MR

dam

per f

orce

(N)


(a)

minus500

minus300

minus100

100

300

500


MR

dam

per f

orce

(N)

Displacement (cm)

(b)


012

014

016

018

02

022

024

026

028

Peak

bas

e dri

(cm

)

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6


(a)

50

100

150

200

250

300

350

400

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6


Peak

acce

lera

tion

(cm

s2 )

(b)




6 Conclusion










References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


A 0ntimesn Intimesn





[ ]

D Mminus1s Γ

0[ ]

(4)

3 MR Damper Model




or equivalently



_y 1


(6)




(7)




4 Control Algorithm



τ

0yT(t)Qy(t) + rf2

c( )dt[ ] (9)


Q qaccelsI 0

0 qdriftsI[ ] (10)



τ

0qaccels sum

N

i1eurox2i + eurox2b

+ qdriftx2b + rf

2cdt

(11)


fc minuskcz


c1

c0

k1

k0

y x

f

BoucminusWen




kc BprimePr

L (CS)prime

(13)



+ CprimeQC 0


(14)




5 Numerical Example



Ms

m0 0 0 0

0 m1 0 0

0 0 m2 0

0 0 0 m3

Cs

c0 + c1 minusc1 0 0



Ks

k0 + k1 minusk1 0 0



(16)


c1

m1

k1

c0

m0

k0

c2

m2

k2

c3

m3


k3

c1

m1

k1

c2

m2

k2

c3

m3k3

MR damper



























005

01

015

02

025

03

035

04

045

05

1E-17 1E-11

a b c

1E-05

Peak

bas

e dri

(cm

)


r2r1



(a)Pe

ak b

ase d

ri (c

m)

1E-17 1E-11 1E-0501

012

014

016

018

02

022

024

026




(b)


100

150

200

250

300

350

400

450

Peak

acce

lera

tion

(cm

s2 )


(a)

100

150

200

250

300

350

400

450

500

550

600

1E-17 1E-11 1E-05

Peak

acce

lera

tion

(cm

s2 )


(b)



01

015

02

025

03

035

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6

Peak

bas

e dri

(cm

)


(a)

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6


150

200

250

300

350

400

Peak

acce

lera

tion

(cm

s2 )

(b)















s(ω) So

ω4g + 4ω2

gξ2gω2

ω2 minusω2g1113872 1113873

2+ 4ω2

gξ2gω2

⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦

So 003ξg

πωg 4ξ2g + 11113872 1113873

(17)







025

03

035

04

045

05Pe

ak b

ase d

ri (c

m)


WN IWN II

(a)

02

022

024

026

028

03

Peak

bas

e dri

(cm

)


WN IWN II

(b)


150

200

250

300

350

400

Peak

acce

lera

tion

(cm

s2 )


WN IWN II

(a)

200

220

240

260

280

300

320

340

360

380

400

Peak

acce

lera

tion

(cm

s2 )


WN IWN II

(b)









minus500

minus300

minus100

100

300

500

MR

dam

per f

orce

(N)


(a)

minus500

minus300

minus100

100

300

500


MR

dam

per f

orce

(N)

Displacement (cm)

(b)


012

014

016

018

02

022

024

026

028

Peak

bas

e dri

(cm

)

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6


(a)

50

100

150

200

250

300

350

400

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6


Peak

acce

lera

tion

(cm

s2 )

(b)




6 Conclusion










References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



kc BprimePr

L (CS)prime

(13)



+ CprimeQC 0


(14)




5 Numerical Example



Ms

m0 0 0 0

0 m1 0 0

0 0 m2 0

0 0 0 m3

Cs

c0 + c1 minusc1 0 0



Ks

k0 + k1 minusk1 0 0



(16)


c1

m1

k1

c0

m0

k0

c2

m2

k2

c3

m3


k3

c1

m1

k1

c2

m2

k2

c3

m3k3

MR damper



























005

01

015

02

025

03

035

04

045

05

1E-17 1E-11

a b c

1E-05

Peak

bas

e dri

(cm

)


r2r1



(a)Pe

ak b

ase d

ri (c

m)

1E-17 1E-11 1E-0501

012

014

016

018

02

022

024

026




(b)


100

150

200

250

300

350

400

450

Peak

acce

lera

tion

(cm

s2 )


(a)

100

150

200

250

300

350

400

450

500

550

600

1E-17 1E-11 1E-05

Peak

acce

lera

tion

(cm

s2 )


(b)



01

015

02

025

03

035

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6

Peak

bas

e dri

(cm

)


(a)

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6


150

200

250

300

350

400

Peak

acce

lera

tion

(cm

s2 )

(b)















s(ω) So

ω4g + 4ω2

gξ2gω2

ω2 minusω2g1113872 1113873

2+ 4ω2

gξ2gω2

⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦

So 003ξg

πωg 4ξ2g + 11113872 1113873

(17)







025

03

035

04

045

05Pe

ak b

ase d

ri (c

m)


WN IWN II

(a)

02

022

024

026

028

03

Peak

bas

e dri

(cm

)


WN IWN II

(b)


150

200

250

300

350

400

Peak

acce

lera

tion

(cm

s2 )


WN IWN II

(a)

200

220

240

260

280

300

320

340

360

380

400

Peak

acce

lera

tion

(cm

s2 )


WN IWN II

(b)









minus500

minus300

minus100

100

300

500

MR

dam

per f

orce

(N)


(a)

minus500

minus300

minus100

100

300

500


MR

dam

per f

orce

(N)

Displacement (cm)

(b)


012

014

016

018

02

022

024

026

028

Peak

bas

e dri

(cm

)

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6


(a)

50

100

150

200

250

300

350

400

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6


Peak

acce

lera

tion

(cm

s2 )

(b)




6 Conclusion










References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






















005

01

015

02

025

03

035

04

045

05

1E-17 1E-11

a b c

1E-05

Peak

bas

e dri

(cm

)


r2r1



(a)Pe

ak b

ase d

ri (c

m)

1E-17 1E-11 1E-0501

012

014

016

018

02

022

024

026




(b)


100

150

200

250

300

350

400

450

Peak

acce

lera

tion

(cm

s2 )


(a)

100

150

200

250

300

350

400

450

500

550

600

1E-17 1E-11 1E-05

Peak

acce

lera

tion

(cm

s2 )


(b)



01

015

02

025

03

035

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6

Peak

bas

e dri

(cm

)


(a)

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6


150

200

250

300

350

400

Peak

acce

lera

tion

(cm

s2 )

(b)















s(ω) So

ω4g + 4ω2

gξ2gω2

ω2 minusω2g1113872 1113873

2+ 4ω2

gξ2gω2

⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦

So 003ξg

πωg 4ξ2g + 11113872 1113873

(17)







025

03

035

04

045

05Pe

ak b

ase d

ri (c

m)


WN IWN II

(a)

02

022

024

026

028

03

Peak

bas

e dri

(cm

)


WN IWN II

(b)


150

200

250

300

350

400

Peak

acce

lera

tion

(cm

s2 )


WN IWN II

(a)

200

220

240

260

280

300

320

340

360

380

400

Peak

acce

lera

tion

(cm

s2 )


WN IWN II

(b)









minus500

minus300

minus100

100

300

500

MR

dam

per f

orce

(N)


(a)

minus500

minus300

minus100

100

300

500


MR

dam

per f

orce

(N)

Displacement (cm)

(b)


012

014

016

018

02

022

024

026

028

Peak

bas

e dri

(cm

)

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6


(a)

50

100

150

200

250

300

350

400

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6


Peak

acce

lera

tion

(cm

s2 )

(b)




6 Conclusion










References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


01

015

02

025

03

035

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6

Peak

bas

e dri

(cm

)


(a)

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6


150

200

250

300

350

400

Peak

acce

lera

tion

(cm

s2 )

(b)















s(ω) So

ω4g + 4ω2

gξ2gω2

ω2 minusω2g1113872 1113873

2+ 4ω2

gξ2gω2

⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦

So 003ξg

πωg 4ξ2g + 11113872 1113873

(17)







025

03

035

04

045

05Pe

ak b

ase d

ri (c

m)


WN IWN II

(a)

02

022

024

026

028

03

Peak

bas

e dri

(cm

)


WN IWN II

(b)


150

200

250

300

350

400

Peak

acce

lera

tion

(cm

s2 )


WN IWN II

(a)

200

220

240

260

280

300

320

340

360

380

400

Peak

acce

lera

tion

(cm

s2 )


WN IWN II

(b)









minus500

minus300

minus100

100

300

500

MR

dam

per f

orce

(N)


(a)

minus500

minus300

minus100

100

300

500


MR

dam

per f

orce

(N)

Displacement (cm)

(b)


012

014

016

018

02

022

024

026

028

Peak

bas

e dri

(cm

)

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6


(a)

50

100

150

200

250

300

350

400

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6


Peak

acce

lera

tion

(cm

s2 )

(b)




6 Conclusion










References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





s(ω) So

ω4g + 4ω2

gξ2gω2

ω2 minusω2g1113872 1113873

2+ 4ω2

gξ2gω2

⎡⎢⎢⎢⎢⎢⎣⎤⎥⎥⎥⎥⎥⎦

So 003ξg

πωg 4ξ2g + 11113872 1113873

(17)







025

03

035

04

045

05Pe

ak b

ase d

ri (c

m)


WN IWN II

(a)

02

022

024

026

028

03

Peak

bas

e dri

(cm

)


WN IWN II

(b)


150

200

250

300

350

400

Peak

acce

lera

tion

(cm

s2 )


WN IWN II

(a)

200

220

240

260

280

300

320

340

360

380

400

Peak

acce

lera

tion

(cm

s2 )


WN IWN II

(b)









minus500

minus300

minus100

100

300

500

MR

dam

per f

orce

(N)


(a)

minus500

minus300

minus100

100

300

500


MR

dam

per f

orce

(N)

Displacement (cm)

(b)


012

014

016

018

02

022

024

026

028

Peak

bas

e dri

(cm

)

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6


(a)

50

100

150

200

250

300

350

400

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6


Peak

acce

lera

tion

(cm

s2 )

(b)




6 Conclusion










References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


025

03

035

04

045

05Pe

ak b

ase d

ri (c

m)


WN IWN II

(a)

02

022

024

026

028

03

Peak

bas

e dri

(cm

)


WN IWN II

(b)


150

200

250

300

350

400

Peak

acce

lera

tion

(cm

s2 )


WN IWN II

(a)

200

220

240

260

280

300

320

340

360

380

400

Peak

acce

lera

tion

(cm

s2 )


WN IWN II

(b)









minus500

minus300

minus100

100

300

500

MR

dam

per f

orce

(N)


(a)

minus500

minus300

minus100

100

300

500


MR

dam

per f

orce

(N)

Displacement (cm)

(b)


012

014

016

018

02

022

024

026

028

Peak

bas

e dri

(cm

)

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6


(a)

50

100

150

200

250

300

350

400

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6


Peak

acce

lera

tion

(cm

s2 )

(b)




6 Conclusion










References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





minus500

minus300

minus100

100

300

500

MR

dam

per f

orce

(N)


(a)

minus500

minus300

minus100

100

300

500


MR

dam

per f

orce

(N)

Displacement (cm)

(b)


012

014

016

018

02

022

024

026

028

Peak

bas

e dri

(cm

)

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6


(a)

50

100

150

200

250

300

350

400

1E-17 1E-11 1E-05

A-1A-2A-3

A-4A-5A-6


Peak

acce

lera

tion

(cm

s2 )

(b)




6 Conclusion










References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



6 Conclusion










References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


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