Experimental Investigation on Effects of Positioning Pendulum Type Tuned Mass Damper on Different St

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Experimental Investigation on Effects of Positioning Pendulum Type Tuned Mass Damper on Different Storey Levels

1Post Graduate Student, Dept. of Civil Engineering, Datta Meghe College of Engineering Airoli, Navi Mumbai- 400708, India

2Professor, Dept. of Civil Engineering, Datta Meghe College of Engineering Airoli, Navi Mumbai- 400708, India

3Professor, Dept. of Civil Engineering, Datta Meghe College of Engineering Airoli, Navi Mumbai- 400708, India ***

Abstract - A PendulumtypeTunedMassDamper(PTMD)isapassivestructuralvibrationcontroldevicewhichconsistsofa movingsecondarymasswhichissuspendedfromthemainstructureandconnectedtoexternaldampers.PlacingPTMDattop ormiddleorbottomstoreylevelswillhavedifferenteffectsonvibrationresponseofthestructure.Inthecurrentinvestigation, effectsofpositioningPTMDondifferentstoreylevelsareexplored.Anactualmodelof3storiedframedstructureshasbeen fabricatedanditsresponseundersinusoidalbaseexcitationiscomparedwithPTMDsuspendedfromdifferentstoreylevels. DifferentPTMDfrequency,massandpositionswereconsideredandmodelistestedforbaseexcitationsusingshaketable analysis.ThePTMDwithoutdampingisusedandonlytheeffectofvariationinfrequencyratio,massratioandpositionis considered.TheresponseofthestructurewasexperimentallydeterminedandcomparedfordifferentPTMDlocations.The resultsshowsignificantreductioninaccelerationandmaximumdisplacementoftheactualmodelwhenthePTMDisplacedat thetopfloor.BestresultoccurswhenthePTMDisonthetopfloorandthefrequencyratiois1.WhenPTMDistunedforthe1st modal frequency, placing it on 2nd or 1st floor makes it very ineffective and in some case increases the acceleration and displacementresponseofthestructure.

Key Words: PendulumtypeTunedMassDamper,PTMDposition,Resonance,Seismicresistance,Shaketableanalysis

1. INTRODUCTION

Natural hazards like earthquake and wind presents an important problem of structural vibrations in tall and huge structures. Depending on their intensity, exterior vibrations can cause problems ranging from minor discomfort for the occupantstoseverestructuralharmorevencollapse[1].Latestdesignmethodsusetheinelasticdeformationstodissipatethe energyandmitigatethevibrationproblem.Manyolderstructuresmightnothavebeendesignedforresistingearthquakeloads. Henceexternalenergydissipationdevicesareusedtoaugmenttheperformanceofnewerandolderstructures.Oneofsuch deviceisaTunedMassDamper(TMD).TMDisapassivevibrationalcontroldevicewhichconsistsofanadditionalmassplaced insidethemainstructurewhichisconnectedtothemainstructureviaspringsanddampersthisallowsittomovewithrespect tothemainstructure.Whenthestructureisexcitedbytheexternalforces,italsoimpartsmotiontotheTMD,whichproduces restoringforceswhichareoutofphasewiththeexternalvibratingforcesduetowhichthestructuralvibrationresponseis reduced[2].TheTMDisusedtoavoidresonanceinthemainstructure.Resonanceoccurswhenthefrequencyofexternalforce issameasthenaturalfrequencyofthestructure[3]. ThusifthefrequencyoftheTMDiskeptneartothenaturalfrequencyof theprimarystructure,asignificantreductioninresponseofthestructureforthatforcingfrequencycanbeachieved[4].

The idea of TMD was originated by Frahm [5] who used a spring absorber then Den Hartog [6] first provided the optimizationmethodforundampedsystem.SincethenmanydifferenttypesofTMDhavebeendesigned.Oneofwhichisa Pendulum type Tuned Mass Damper (PTMD). PTMD works very similar to a TMD the only difference is that in TMD the secondarymasshastranslatingmotionbutinPTMDthesecondarymassissuspendedfromthemainstructurehenceitswings likeapendulum. DampersarealsoprovidedtothePTMDtodissipatethekineticenergyanditalsohelpsinreducingthe distancebywhichthePTMDmoves.Conventionally,thePTMDisprovidedatthetopstoreysofthestructurelikethePTMD fromthe92ndfloorintheTaipei101building[7].ThemainreasonofthisisthattheTMDshouldbeplacedatthelocation wherethemaximumamplitudeoftheparticularmodeshapeoccurs[2].ButifduetosomecircumstancesthePTMDisprovided onthemiddleorbottomstorylevels,andifitisnottunedproperly,thePTMDwillworkinadequatelyorevenworsenthe vibrationresponseofthestructure[8].

ThetuningofTMDisdonebyfindingoptimalparameterswhichareMassratio(μ),Frequencyratio(fr)andDampingratio (ζ),theseparametersaredefinedasfollows,

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μ= (1) fr = (2) ζ= (3)

AMultiDegreeofFreedom(MDOF)structurehasmultiplenaturalfrequenciesfordifferentmodeshapes[3].TheTMDis tunedtoaparticularmodalfrequencyandthismodalfrequencyisthedominantmodeofthestructurewhoseamplitudeis highestcomparedtoothermodes.ATMDwithoutdampercanbetunedtoreducetheresponseofthestructureforasingle naturalfrequencyofthedominantmode.ButwhenTMDisaddedtothestructure,itaddsanextradegreeoffreedominthe structureandduetothisthereisanadditionalmodalfrequencyatwhichresonanceofthestructurecanoccurs[9,10]henceto reducetheresponseofTMDandstructureatthisnewfrequency,theoptimaldampingisnecessaryotherwiseatthisfrequency theTMDwillbelesseffectivetoreducetheresponse.

AlthoughadamperisanimportantelementinTMD,inthecurrentwork,aPTMDisusedwithoutthedamper.Themain objectiveistoobservehowthestructuralresponsechangeswhenthePTMDwhichistunedtoreducethestructuralresponse atthe1stdominantmodeisprovidedondifferentstoreylevels.Forthisanactualmodelof3storiedframestructurewithPTMD istestedforthebaseexcitationshavingfrequencysameasdominantmodeofthestructureanddifferentmassratiosand frequencyratiosofthePTMDarealsoconsidered.

TillnowmultiplestudiesarecarriedouttodetermineoptimalparametersforPTMDandderiveequationforthesame. AbubakarandFarid(2009)[11]obtainedageneralizedequationfortunedmassdamperwasmadeconsideringthedampingin themainstructure,whichwasnotincludedinDenHartog’swork.YanhuiLiu,etal.(2020)[12]carriedoutnumericaland experimentalanalysistofindoptimalparametersforTMDforMDOFstructure.GinoB.Colherinhas,etal.(2019)[13],foundout optimalparametersforaMDOFstructurebyconsideringequivalentSDOFsystem.RafikR.GergesandBarryJ.Vickery(2005) [14],providedequationsforoptimalparametersfordifferentsystemswithandwithoutdampinghavingdifferentforcing conditions.TheyalsofoundoutPTMDtobemoreeffectiveforwindexcitationthanearthquakeexcitations.PedroL.Bernardes Júnior,MarcusV.G.deMorais,SuzanaM.Avila(2019)[15],ExperimentallyanalysedaninvertedPTMDandexperimentally foundoutoptimalparametersforMDOFstructureandwasabletoreducestructuralresponseforarangeoffrequencies

2. MATERIALS AND METHODS

In the current study, a 3 storied frame structure without infill wall was considered which was provided with PTMD suspendedfrom1st,2ndand3rdfloor(oneflooratatime).Anactualmodelofthestructurewasfabricatedwhichconsistsof3 rigidfloorslabssupportedby4columns.Thecolumnsarerigidlyfixedtothebase.Fig.1(a)andFig.1(b)arediagramshowing themodelelevationandplanrespectively.Table1showsthematerialproperties.ThemodelistestedwithPTMDsuspended fromdifferentfloorsforsinusoidal(harmonic)baseexcitationusingshaketabletesting.Thevibrationresponseofthestructure withandwithoutPTMDismeasuredandcompared.

Themodelissymmetricandthecenterofmasscoincideswiththecenterofstiffness.ThePTMDissuspendedfromthecenter ofmassoneachfloor.

Table -1: Modelproperties[16]

Structural Member DimensionandMaterialProperty

Material=Plywood,

Slab Properties

Dimensions:Length=360mm,Width=260mm,Thickness=12mm, Density=8.458KN/m3 , LongitudinalModulusofElasticity=10800MPa, LongitudinalPoisson'sratio=0.3, LongitudinalModulusofRigidity=4154MPa.

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Column Properties

Material=Aluminium, Dimensions:Width=19mm,Thickness=2mm, Density=27.1KN/m3 , ModulusofElasticity=70000MPa, Poisson'sratio=0.32, ModulusofRigidity=26516MPa.

Fig -1: FrameStructure3dView

3. FREE VIBRATION TEST

TheactualmodelshowninFig.4wasfabricatedwhichhadmassof3500gm.Tofindoutmodalfrequenciesofactualmodel, freevibrationtestwasconducted.Forfreevibrationtest,thebaseofthemodelwaskeptfixedandthetopfloorwasgivenan initialdisplacementalongthelongerspanofthemodel.Accelerationoftopfloorwasmeasuredduringthefreevibrationand FastFourierTransform(FFT)wascarriedoutontheaccelerationvstimedatatofindoutthenaturalfrequencies.Fig2andFig 3showsrecordedfreevibrationdataanditsFFTrespectively.

Fig -2: FreeVibrationAccelerationvsTimeGraph

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Fig -3: FourierTransformofAccelerationVsTimeData Fig -4: ActualModel

ThepeaksofFFTgraphshowsthenaturalfrequenciesofthestructurewhichwere1.2Hz,4Hzand6Hz,thesecorrespond tothe1st,2ndand3rdtranslationalmoderespectively.Thediagramsof1st,2ndand3rdtranslationalmodeshapesareshownin Figure5(a),Figure5(b)andFigure5(c)respectively. (a) (b) (c) Fig -5: ModeShapes

4. SHAKE TABLE TEST (WITHOUT PTMD)

To test the structure under resonant condition, the actual model was tested for sinusoidal base excitations having frequencies1.2Hz(1stmodalfrequency)and4Hz(2ndmodalfrequency).Forthis,shaketabletestingwasused.Theamplitude ofshaketableexcitationwaskeptas5mm.Forthesetestsmaximumamplitudeofdisplacementoccurredattopfloor.Hence accelerationoftopfloorandalsotheshaketableweremeasured.Fromtopflooraccelerationandshaketableacceleration, relativedisplacementbetweentopfloorandbasewascalculated.Figure6showsthegraphsofrelativedisplacementfor1.2Hz baseexcitationandFigure7showsrelativedisplacementfor4Hzbaseexcitation.Theobservedmaximumoftopfloorrelative displacementfor1.2Hzbaseexcitationwas78.86mmandfor4Hzbaseexcitationitwas18.88mm.

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Fig -6: Top(3rd)floorandbottomfloor(base) Fig -8: Top(3rd)floorandbottomfloor(base) accelerations(1.2Hzbaseexcitation) accelerations(4Hzbaseexcitation)

5. SHAKE TABLE TEST (WITH PTMD)

ThePTMDsetupconsistedofaweightsuspendedfrombottomofthefloorusingarelativelymasslessrod.ThePTMDwas suspendedfrom3rd,2nd,and1stflooroneflooratatimeasshowninFigure8(a),Figure8(b)andFigure8(c)respectively,and differentmassratio=0.05,0.1,0.15anddifferentfrequencyratio=0.8,1,1.3wereconsideredandtestedforsinusoidalbase excitationfortwodifferentfrequencies1.2Hzand4Hzkeepingtheamplitude5mm.Theaccelerationoftopfloorandshake tableweremeasuredforthetestswith1.2Hzbaseexcitation.Forthetestswherethebaseexcitationfrequencywas4Hzand PTMDwasattopfloor,themaximumdisplacementwasoccurringonthe2ndfloorhencetheaccelerationof2ndfloorand shaketableweremeasuredforthosetests.Relativedisplacementdatawascalculatedfromaccelerationreadings.

Although for high rise buildings, mass ratio is limited to 5% [17], larger mass ratios were considered for the test to determineeffectofchangeinmassratio.

Fig -8: PTMDAttachedon3rd,2ndand1stFloor Thegraphsofrelativedisplacementoftopfloorwithrespecttothebaseofseveraltestsareasfollows.

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(Theapplicationofbaseexcitationsbeginsat10secondmarkandthevibrationsafterthe10secondmarkareconsideredfor thestructuralresponse).

Fig -9: Relativedisplacement(PTMDon3rd

Fig -10: Relativedisplacement(PTMDon2nd floor)(1.2Hzbasefrequency)(μ=0.05,fr=1) floor)(1.2Hzbasefrequency)(μ=0.05,fr=1)

Fig -11: Relativedisplacement(PTMDon1st

Fig -12: Relativedisplacement(PTMDon1st floor)(1.2Hzbasefrequency)(μ=0.05,fr=1) floor)(1.2Hzbasefrequency)(μ=0.05,fr=1.3)

Fig -13: Relativedisplacement(PTMDon2nd

Fig -14: Relativedisplacementof floor)(1.2Hzbasefrequency)(μ=0.05,fr=1.3) 2ndfloorw.r.t.base(PTMDon3rdfloor) (4Hzbasefrequency)(μ=0.05,fr=1)

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Fig -15: Relativedisplacement(PTMDon2nd

Fig-16: Relativedisplacement(PTMDon1st floor)(4Hzbasefrequency)(μ=0.05,fr=1) floor)(4Hzbasefrequency)(μ=0.05,fr=1)

6. RESULTS AND DISCUSSION

Followingarethemaximumrelativedisplacements.(MaximumdisplacementwithoutPTMDfor1.2Hzexcitationwas 78.86mmandfor4Hzitwas18.88mm)

Table -2: MaximumDisplacementofTopFloor(mm)(PTMDPosition3rdFloor)(1.2Hzbaseexcitation)

μ fr

0.05 0.1 0.15 0.8 42.94 27.81 20.1 1 16.97 13.08 11.93 1.3 67.15 31.93 24.41

Table -3: MaximumDisplacementofTopFloor(mm)(PTMDPosition2ndFloor)(1.2Hzbaseexcitation)

μ fr

0.05 0.1 0.15 0.8 49.32 41.54 31.13 1 29.65 16.82 14.38 1.3 124 50.38 37.78

Table -4: MaximumDisplacementofTopFloor(mm)(PTMDPosition1stFloor)(1.2Hzbaseexcitation)

μ fr

0.05 0.1 0.15

0.8 67.12 64.92 61.05 1 68.88 43.34 27.02 1.3 102.2 131.1 144.4

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Table -5: MaximumDisplacementof2ndFloor(mm)(PTMDPosition3rdFloor)(4Hzbaseexcitation)

μ fr

0.05 0.1 0.15

0.8 14.36 13.99 12.86 1 13.83 13.38 12.71 1.3 14.01 13.73 12.48

Table -6: MaximumDisplacementofTopFloor(mm)(PTMDPosition2ndFloor)(4Hzbaseexcitation)

μ fr

0.05 0.1 0.15 0.8 18.23 16.39 15.14 1 17.46 16.93 19.93 1.3 18.34 21.41 15.93

Table -7: MaximumDisplacementofTopFloor(mm)(PTMDPosition1stFloor)(4Hzbaseexcitation)

μ fr

0.05 0.1 0.15 0.8 22.01 17.09 16.04 1 16.33 16.03 16.11 1.3 18.5 17.25 16.19

Followingarethegraphsofdisplacementvsfrequencyratioanddisplacementvsmassratio. (a) (b)

Chart -1: MaximumDisplacementofTopFloor(mm)(PTMDon3rdFloor)(1.2Hzbaseexcitation)

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(a) (b)

Chart -2: MaximumDisplacementofTopFloor(mm)(PTMDon2nd Floor)(1.2Hzbaseexcitation)

(a) (b)

Chart -3: MaximumDisplacementofTopFloor(mm)(PTMDon1st Floor)(1.2Hzbaseexcitation)

(a) (b)

Chart -4: MaximumDisplacementof2nd Floor(mm)(PTMDon3rd Floor)(4Hzbaseexcitation)

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(a) (b)

Chart -5: MaximumDisplacementofTopFloor(mm)(PTMDon2nd Floor)(4Hzbaseexcitation)

(a) (b)

Chart -6: MaximumDisplacementofTopFloor(mm)(PTMDon1st Floor)(4Hzbaseexcitation)

6.1 Discussion of the results

Following are the graphs of acceleration response of the structure with and without PTMD for 1.2Hz and 4Hz base excitation(PTMDlocatedon3rd floor).

Chart -7: Accelerationresponseof3rd floor

Chart -8: Accelerationresponseof2nd floor withandwithoutPTMD(1.2Hzexcitation) withandwithoutPTMD(4Hzexcitation)

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PTMD location 3rd floor

At1.2Hzexcitationfrequencyresonancewasobserved,hencethePTMDwastunedforthisfrequency.Fromtheresultsitis observedthatwhenthePTMDfrequencyratioof1issuspendedfromthe3rdfloor,significantreductionintheresponseofthe structureoccursforthe1.2Hzbaseexcitationsasshowninchart7.Thisisbecauseforthemodeshapeat1.2Hzbaseexcitation, themaximumamplitudeofvibrationoccursonthe3rd floorandasstatedearlier,thePTMDshouldbesuspendedfromthe pointofmaximumamplitudeforoptimalresults.AlsoduetoPTMD,resonancewaspreventedandasteadystateresponseof thestructurewasachieved.ThePTMDsuspendedfromthe3rd floorhavingμ=0.05,fr=1gives78.4%reductioninmaximum displacement.Thereductioninmaximumdisplacementiscalculatedfromfollowingequation.

%Reductionindisplacement= ˟100

FromChart1(a)itisobservedthatfr=1givesthebestresults.Whenincreasingordecreasingthefrequencyratiofrom1,it makesPTMDlesseffectiveinreducingthedisplacementfor1.2Hzexcitation.

FromdisplacementvsmassratiodataitisobservedthatIncreasingmassratiofrom0.05to0.1givessomeimprovementin reducingthemaximumdisplacement.Butincreasingmassratiofrom0.1to0.15,givesonlyaslightimprovementinreducing themaximumdisplacement.

Forthetestswithbaseexcitationfrequencyof4Hz,changingthefrequencyratiofrom0.8to1andfrom1to1.3doesnot provideanysignificantdifferenceinreducingthemaximumdisplacement.Andwhenthemassratioischangedfrom0.5to0.15, onlya slightimprovementisobservedin reducing the maximumdisplacement. ThePTMDwith μ=0.05,fr=1gives26.7% reductioninmaximumdisplacement.

PTMD location 2nd floor

PTMDsuspendedfrom2ndfloorislesseffectiveatdisplacementreductionthanPTMDpositionedon3rdfloorfor1.2Hzbase excitation.For1.2HzexcitationandPTMDon2nd floor,frequencyratioof1isbetterthanfrequencyratioof0.8and1.3.And reducingthefrequencyratiofrom1makesPTMDlesseffective.AlsoworstcaseoccurswhenPTMDhasμ=0.05,fr=1.3,Forthis caseThemaximumdisplacementobserved is124mm whichisgreaterthanthemaximumdisplacementof the structure without the PTMD. Forthis case,resonance ofthestructureisobserved for 1.2Hz excitation, whichisfarworse than the structurewithoutPTMD.Forthiscase,increasingthemassratioto0.1givessomeimprovement.

Steadystateresponseisobservedfor1.2HzexcitationwhenPTMDshasfrequencyratioof0.8and1.Forthesecases,when increasing mass ratio from 0.05 to 0.1, a slight improvement is observed in reducing the maximum displacement. Also increasingmassratiofrom0.1to0.15providednegligibleimprovement.

ConsideringthePTMDwithμ=0.15,fr=1,for4Hzbaseexcitation,themaximumdisplacementwasmorethanthemaximum displacementofthestructurewithoutPTMD.ChangingthePTMDparametersdidnotprovideanysignificantimprovement.

PTMD location 1st floor

The PTMD suspended from 1st floor was observed to have the worst performance. When the frequency ratio is 1.3, resonanceofthestructureisobservedfor1.2HzexcitationandthemaximumdisplacementswithPTMDaremorethanthe maximumdisplacementofstructurewithoutPTMD,alsoincreasingthemassratioworsentheperformancewhenfr=1.3.When frequencyratiois1,increasingthemassratiohelpsinreducingthemaximumdisplacement.

For4Hzbaseexcitation,thePTMDdoesnotprovideeffectiveresultsandthemaximumdisplacementofstructurewith PTMDforseveralcombinationsofparametersismorethanthemaximumdisplacementofstructurewithoutPTMD.

7. CONCLUSIONS

A3storiedstructurewastestedforharmonicbaseexcitationshavingfrequency1.2Hzand4Hz.PTMDwasprovidedonthe structurehavingdifferentparametersanddifferentpositions,thedisplacementofthestructurewascalculatedfrommeasured data and performance of PTMD in reducing the maximum displacement was determined and compared for different parameters.Followingconclusionscanbemadefromtheobservations.

1. ThePTMDwhichistunedforthespecificfrequencywasparticularlyeffectiveatloweringtheresponseofthestructure whentheexcitationisprovidedatthatspecificfrequency.

2. PTMDsuspendedfromthe3rd(top)floorproducedthebestresultsinloweringthedisplacementofthestructureand avoidingresonancefor1.2Hzbaseexcitation.

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3. TheeffectivenessofPTMDonthesecond(middle)floorwasinferiortothatofPTMDonthetopfloorinminimizingthe structuralresponse.Furthermore,whenPTMDwasgivenafrequencyratioof1.3,resonanceofthestructurewas observed,and the maximumdisplacement ofstructure withPTMDwasgreater thanthe maximumdisplacement withoutPTMD.

4. When PTMD was provided on the 1st (bottom) floor, it was ineffective at reducing the response of the structure. Additionally,resonanceofthestructurewasobservedforamajorityofparametercombinations,andthemaximum displacementofstructurewithPTMDwasmuchgreaterthanthedisplacementofthestructurewithoutPTMD.

5. For4Hzbaseexcitation,PTMDlocatedontopfloorprovidessomereductioninthemaximumdisplacementofthe structure.PTMDlocatedon2nd floorand1st floorhavelittletonoeffectinreducingtheresponsefor4Hzexcitation. Andinsomecasescanincreasethedisplacementofthestructure.

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