Piezoelectric Energy Harvesting

402 Pages·2011·27.23 MB·English

by  Alper Erturk

P1:OTE/OTE/SPH P2:OTE
fm JWST047-Erturk February8,2011 11:5 PrinterName:YettoCome
PIEZOELECTRIC ENERGY
HARVESTING
Piezoelectric Energy Harvesting, First Edition. Alper Erturk and Daniel J. Inman.
© 2011 John Wiley & Sons, Ltd. Published 2011 by John Wiley & Sons, Ltd. ISBN: 978-0-470-68254-8
P1:OTE/OTE/SPH P2:OTE
fm JWST047-Erturk February8,2011 11:5 PrinterName:YettoCome
PIEZOELECTRIC ENERGY
HARVESTING
AlperErturk
GeorgiaTech,USA
DanielJ.Inman
VirginiaTech,USA
A John Wiley and Sons, Ltd., Publication
P1:OTE/OTE/SPH P2:OTE
fm JWST047-Erturk February8,2011 11:5 PrinterName:YettoCome
Thiseditionfirstpublished2011
(cid:1)c 2011JohnWiley&Sons,Ltd
Registeredoffice
JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester,WestSussex,PO198SQ,UnitedKingdom
Fordetailsofourglobaleditorialoffices,forcustomerservicesandforinformationabouthowtoapplyforpermissionto
reusethecopyrightmaterialinthisbookpleaseseeourwebsiteatwww.wiley.com.
TherightoftheauthorstobeidentifiedastheauthorsofthisworkhasbeenassertedinaccordancewiththeCopyright,
DesignsandPatentsAct1988.
Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyform
orbyanymeans,electronic,mechanical,photocopying,recordingorotherwise,exceptaspermittedbytheUKCopyright,
DesignsandPatentsAct1988,withoutthepriorpermissionofthepublisher.
Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprintmaynotbeavailablein
electronicbooks.
Designationsusedbycompaniestodistinguishtheirproductsareoftenclaimedastrademarks.Allbrandnamesand
productnamesusedinthisbookaretradenames,servicemarks,trademarksorregisteredtrademarksoftheirrespective
owners.Thepublisherisnotassociatedwithanyproductorvendormentionedinthisbook.Thispublicationisdesignedto
provideaccurateandauthoritativeinformationinregardtothesubjectmattercovered.Itissoldontheunderstandingthat
thepublisherisnotengagedinrenderingprofessionalservices.Ifprofessionaladviceorotherexpertassistanceisrequired,
theservicesofacompetentprofessionalshouldbesought.
LibraryofCongressCataloging-in-PublicationData
Erturk,Alper.
Piezoelectricenergyharvesting/AlperErturk,DanielJ.Inman.
p.cm.
Includesbibliographicalreferencesandindex.
ISBN978-0-470-68254-8(hardback)
1.Piezoelectrictransducers. 2.Electricgenerators. 3.Piezoelectricity. I.Inman,D.J. II.Title.
TK7872.P54E782011
621.31(cid:1)3–dc22
2010046394
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
PrintISBN:978-0-470-68254-8
E-PDFISBN:978-1-119-99116-8
O-BookISBN:978-1-119-99115-1
E-PubISBN:978-1-119-99135-9
Setin10/12ptTimesbyAptaraInc.,NewDelhi,India
P1:OTE/OTE/SPH P2:OTE
fm JWST047-Erturk February8,2011 11:5 PrinterName:YettoCome
Theseoscillationsarisefreely,andIhavedeterminedvarious
conditions, andhaveperformedagreatmanybeautiful
experimentsontheposition oftheknotpointsandthepitchof
thetone,whichagreebeautifully withthetheory.
—DanielBernoulli (from alettertoLeonhardEuler)1
Wehavefoundanewmethodforthedevelopmentofpolar
electricityinthesesamecrystals,consistinginsubjectingthem
tovariationsinpressurealongtheirhemihedralaxes.
—PierreandPaul-JacquesCurie
(from thepaperannouncing theirdiscovery)2
1InTimoshenko,S.P.,1953,HistoryofStrengthofMaterials(withabriefaccountofthehistoryoftheoryof
elasticityandtheoryofstructures),McGraw-Hill,NewYork.
2In Cady, W.G., 1946, Piezoelectricity: An Introduction to the Theory and Applications of Electromechanical
PhenomenainCrystals,McGraw-Hill,NewYork.
P1:OTE/OTE/SPH P2:OTE
fm JWST047-Erturk February8,2011 11:5 PrinterName:YettoCome
Contents
AbouttheAuthors xvii
Preface xix
1 IntroductiontoPiezoelectricEnergyHarvesting 1
1.1 Vibration-BasedEnergyHarvestingUsingPiezoelectricTransduction 1
1.2 AnExampleofaPiezoelectricEnergyHarvestingSystem 4
1.3 MathematicalModelingofPiezoelectricEnergyHarvesters 6
1.4 SummaryoftheTheoryofLinearPiezoelectricity 9
1.5 OutlineoftheBook 12
References 14
2 BaseExcitationProblemforCantileveredStructuresandCorrectionof
theLumped-ParameterElectromechanicalModel 19
2.1 BaseExcitationProblemfortheTransverseVibrations
ofaCantileveredThinBeam 20
2.1.1 ResponsetoGeneralBaseExcitation 20
2.1.2 Steady-StateResponsetoHarmonicBaseExcitation 25
2.1.3 Lumped-ParameterModeloftheHarmonicBase
ExcitationProblem 26
2.1.4 ComparisonoftheDistributed-Parameterandthe
Lumped-ParameterModelPredictions 29
2.2 CorrectionoftheLumped-ParameterBaseExcitationModel
forTransverseVibrations 31
2.2.1 CorrectionFactorfortheLumped-ParameterModel 31
2.2.2 EffectofaTipMassontheCorrectionFactor 32
2.3 ExperimentalCaseStudiesforValidationoftheCorrectionFactor 35
2.3.1 CantileveredBeamwithoutaTipMassunderBaseExcitation 35
2.3.2 CantileveredBeamwithaTipMassunderBaseExcitation 39
2.4 BaseExcitationProblemforLongitudinalVibrationsandCorrectionof
itsLumped-ParameterModel 39
2.4.1 AnalyticalModalAnalysisandSteady-StateResponseto
HarmonicBaseExcitation 40
2.4.2 CorrectionFactorforLongitudinalVibrations 42
P1:OTE/OTE/SPH P2:OTE
fm JWST047-Erturk February8,2011 11:5 PrinterName:YettoCome
viii Contents
2.5 CorrectionFactorintheElectromechanicallyCoupled
Lumped-ParameterEquationsandaTheoreticalCaseStudy 43
2.5.1 AnElectromechanicallyCoupledLumped-ParameterModel
forPiezoelectricEnergyHarvesting 43
2.5.2 CorrectionFactorintheElectromechanicallyCoupled
Lumped-ParameterModelandaTheoreticalCaseStudy 45
2.6 Summary 46
2.7 ChapterNotes 46
References 47
3 AnalyticalDistributed-ParameterElectromechanicalModelingof
CantileveredPiezoelectricEnergyHarvesters 49
3.1 FundamentalsoftheElectromechanicallyCoupled
Distributed-ParameterModel 49
3.1.1 ModelingAssumptionsandBimorphConfigurations 49
3.1.2 CoupledMechanicalEquationandModalAnalysis
ofBimorphCantilevers 51
3.1.3 CoupledElectricalCircuitEquationofaThinPiezoceramic
LayerunderDynamicBending 57
3.2 SeriesConnectionofthePiezoceramicLayers 59
3.2.1 CoupledBeamEquationinModalCoordinates 60
3.2.2 CoupledElectricalCircuitEquation 60
3.2.3 Closed-FormVoltageResponseandVibrationResponse
atSteadyState 61
3.3 ParallelConnectionofthePiezoceramicLayers 63
3.3.1 CoupledBeamEquationinModalCoordinates 63
3.3.2 CoupledElectricalCircuitEquation 64
3.3.3 Closed-FormVoltageResponseandVibrationResponse
atSteadyState 64
3.4 EquivalentRepresentationoftheSeriesandtheParallel
ConnectionCases 65
3.4.1 ModalElectromechanicalCouplingTerms 66
3.4.2 EquivalentCapacitanceforSeriesandParallelConnections 66
3.4.3 EquivalentRepresentationoftheElectromechanicalEquations 67
3.5 Single-ModeElectromechanicalEquationsforModalExcitations 68
3.6 Multi-modeandSingle-ModeElectromechanicalFRFs 69
3.6.1 Multi-modeElectromechanicalFRFs 70
3.6.2 Single-ModeElectromechanicalFRFs 71
3.7 TheoreticalCaseStudy 71
3.7.1 PropertiesoftheBimorphCantilever 72
3.7.2 FrequencyResponseoftheVoltageOutput 73
3.7.3 FrequencyResponseoftheCurrentOutput 76
3.7.4 FrequencyResponseofthePowerOutput 78
3.7.5 FrequencyResponseoftheRelativeTipDisplacement 81
3.7.6 ParallelConnectionofthePiezoceramicLayers 83
3.7.7 Single-ModeFRFs 87
P1:OTE/OTE/SPH P2:OTE
fm JWST047-Erturk February8,2011 11:5 PrinterName:YettoCome
Contents ix
3.8 Summary 90
3.9 ChapterNotes 90
References 94
4 ExperimentalValidationoftheAnalyticalSolutionfor
BimorphConfigurations 97
4.1 PZT-5HBimorphCantileverwithoutaTipMass 97
4.1.1 ExperimentalSetupandGuidelinesforTestinganEnergyHarvester 97
4.1.2 ValidationoftheElectromechanicalFRFsforaSetofResistors 103
4.1.3 ElectricalPerformanceDiagramsattheFundamental
Short-CircuitandOpen-CircuitResonanceFrequencies 107
4.1.4 VibrationResponseDiagramsattheFundamental
Short-CircuitandOpen-CircuitResonanceFrequencies 110
4.2 PZT-5HBimorphCantileverwithaTipMass 111
4.2.1 ExperimentalSetup 111
4.2.2 ValidationoftheElectromechanicalFRFsforaSetofResistors 113
4.2.3 ElectricalPerformanceDiagramsattheFundamental
Short-CircuitandOpen-CircuitResonanceFrequencies 114
4.2.4 VibrationResponseDiagramsattheFundamental
Short-CircuitandOpen-CircuitResonanceFrequencies 119
4.2.5 ModelPredictionswiththePointMassAssumption 119
4.2.6 PerformanceComparisonofthePZT-5HBimorphwithand
withouttheTipMass 121
4.3 PZT-5ABimorphCantilever 122
4.3.1 ExperimentalSetup 122
4.3.2 ValidationoftheElectromechanicalFRFsforaSetofResistors 124
4.3.3 ComparisonoftheSingle-ModeandMulti-mode
ElectromechanicalFRFs 125
4.4 Summary 128
4.5 ChapterNotes 128
References 130
5 DimensionlessEquations,AsymptoticAnalyses,andClosed-Form
RelationsforParameterIdentificationandOptimization 131
5.1 DimensionlessRepresentationoftheSingle-Mode
ElectromechanicalFRFs 132
5.1.1 ComplexForms 132
5.1.2 Magnitude–PhaseForms 132
5.1.3 DimensionlessForms 133
5.2 AsymptoticAnalysesandResonanceFrequencies 134
5.2.1 Short-CircuitandOpen-CircuitAsymptotesoftheVoltageFRF 134
5.2.2 Short-CircuitandOpen-CircuitAsymptotesoftheTip
DisplacementFRF 135
5.2.3 Short-CircuitandOpen-CircuitResonanceFrequenciesof
theVoltageFRF 136
P1:OTE/OTE/SPH P2:OTE
fm JWST047-Erturk February8,2011 11:5 PrinterName:YettoCome
x Contents
5.2.4 Short-CircuitandOpen-CircuitResonanceFrequenciesof
theTipDisplacementFRF 136
5.2.5 ComparisonoftheShort-CircuitandOpen-Circuit
ResonanceFrequencies 137
5.3 IdentificationofMechanicalDamping 138
5.3.1 IdentificationoftheModalMechanicalDampingRatiofrom
theVoltageFRF 138
5.3.2 IdentificationoftheModalMechanicalDampingRatiofrom
theTipDisplacementFRF 139
5.4 IdentificationoftheOptimumElectricalLoadforResonanceExcitation 139
5.4.1 ElectricalPowerFRF 139
5.4.2 OptimumValuesofLoadResistanceattheShort-Circuitand
Open-CircuitResonanceFrequenciesoftheVoltageFRF 140
5.5 IntersectionoftheVoltageAsymptotesandaSimpleTechniqueforthe
ExperimentalIdentificationoftheOptimumLoadResistance 141
5.5.1 OntheIntersectionoftheVoltageAsymptotesfor
ResonanceExcitation 141
5.5.2 ASimpleTechniquefortheExperimentalIdentificationofthe
OptimumLoadResistance 142
5.6 VibrationAttenuation/AmplificationfromtheShort-Circuitto
Open-CircuitConditions 143
5.7 ExperimentalValidationforaPZT-5HBimorphCantilever 144
5.7.1 IdentificationofMechanicalDamping 144
5.7.2 FundamentalShort-CircuitandOpen-Circuit
ResonanceFrequencies 145
5.7.3 MagnitudeandPhaseoftheVoltageFRF 145
5.7.4 VoltageAsymptotesforResonanceExcitation 146
5.7.5 Powervs.LoadResistanceDiagramsandtheOptimumLoads 147
5.7.6 CommentontheOptimumLoadResistanceObtainedfrom
theSimplifiedCircuitRepresentationsofaPiezoceramicLayer 147
5.8 Summary 148
5.9 ChapterNotes 149
References 150
6 ApproximateAnalyticalDistributed-ParameterElectromechanical
ModelingofCantileveredPiezoelectricEnergyHarvesters 151
6.1 UnimorphPiezoelectricEnergyHarvesterConfiguration 152
6.2 ElectromechanicalEuler–BernoulliModelwithAxialDeformations 153
6.2.1 Distributed-ParameterElectromechanicalEnergyFormulation 153
6.2.2 SpatialDiscretizationoftheEnergyEquations 157
6.2.3 ElectromechanicalLagrangeEquations 159
6.2.4 SolutionoftheElectromechanicalLagrangeEquations 163
6.3 ElectromechanicalRayleighModelwithAxialDeformations 166
6.3.1 Distributed-ParameterElectromechanicalEnergyFormulation 166
6.3.2 SpatialDiscretizationoftheEnergyEquations 167
P1:OTE/OTE/SPH P2:OTE
fm JWST047-Erturk February8,2011 11:5 PrinterName:YettoCome
Contents xi
6.3.3 ElectromechanicalLagrangeEquations 167
6.3.4 SolutionoftheElectromechanicalLagrangeEquations 168
6.4 ElectromechanicalTimoshenkoModelwithAxialDeformations 168
6.4.1 Distributed-ParameterElectromechanicalEnergyFormulation 168
6.4.2 SpatialDiscretizationoftheEnergyEquations 171
6.4.3 ElectromechanicalLagrangeEquations 174
6.4.4 SolutionoftheElectromechanicalLagrangeEquations 178
6.5 ModelingofSymmetricConfigurations 181
6.5.1 Euler–BernoulliandRayleighModels 181
6.5.2 TimoshenkoModel 182
6.6 PresenceofaTipMassintheEuler–Bernoulli,Rayleigh,and
TimoshenkoModels 183
6.7 CommentsontheKinematicallyAdmissibleTrialFunctions 185
6.7.1 Euler–BernoulliandRayleighModels 185
6.7.2 TimoshenkoModel 186
6.8 ExperimentalValidationoftheAssumed-ModesSolutionfor
aBimorphCantilever 187
6.8.1 PZT-5HBimorphCantileverwithoutaTipMass 187
6.8.2 PZT-5HBimorphCantileverwithaTipMass 189
6.9 ExperimentalValidationforaTwo-SegmentCantilever 191
6.10 Summary 194
6.11 ChapterNotes 195
References 196
7 ModelingofPiezoelectricEnergyHarvestingforVariousFormsof
DynamicLoading 199
7.1 GoverningElectromechanicalEquations 199
7.2 PeriodicExcitation 202
7.2.1 FourierSeriesRepresentationofPeriodicBaseAcceleration 202
7.2.2 PeriodicElectromechanicalResponse 203
7.3 WhiteNoiseExcitation 204
7.3.1 RepresentationoftheBaseAcceleration 205
7.3.2 SpectralDensityandAutocorrelationFunctionofthe
VoltageResponse 206
7.3.3 ExpectedValueofthePowerOutput 206
7.4 ExcitationDuetoMovingLoads 208
7.4.1 CantileveredPiezoelectricEnergyHarvesterLocatedonaBridge 208
7.4.2 ThinPiezoelectricLayerCoveringaRegionontheBridge 212
7.5 LocalStrainFluctuationsonLargeStructures 214
7.5.1 PowerOutputtoGeneralStrainFluctuations 215
7.5.2 Steady-StatePowerOutputtoHarmonicStrainFluctuations 216
7.5.3 StrainGageMeasurementsandStrainTransformations 217
7.6 NumericalSolutionforGeneralTransientExcitation 218
7.6.1 InitialConditionsinModalCoordinates 219
7.6.2 State-SpaceRepresentationoftheElectromechanicalEquations 219
P1:OTE/OTE/SPH P2:OTE
fm JWST047-Erturk February8,2011 11:5 PrinterName:YettoCome
xii Contents
7.7 CaseStudies 221
7.7.1 PeriodicExcitationofaBimorphEnergyHarvesterona
MechanismLink 222
7.7.2 AnalysisofaPiezoceramicPatchforSurfaceStrain
FluctuationsofaBridge 226
7.8 Summary 230
7.9 ChapterNotes 231
References 232
8 ModelingandExploitingMechanicalNonlinearitiesinPiezoelectric
EnergyHarvesting 233
8.1 PerturbationSolutionofthePiezoelectricEnergyHarvestingProblem:
theMethodofMultipleScales 234
8.1.1 LinearSingle-ModeEquationsofaPiezoelectricEnergyHarvester 234
8.1.2 ExactSolution 234
8.1.3 ResonanceApproximationoftheExactSolution 235
8.1.4 PerturbationSolution 236
8.2 MonostableDuffingOscillatorwithPiezoelectricCoupling 239
8.2.1 AnalyticalExpressionsBasedonthePerturbationSolution 239
8.2.2 State-SpaceRepresentationoftheGoverningEquationsfor
NumericalSolution 241
8.2.3 TheoreticalCaseStudy 242
8.3 BistableDuffingOscillatorwithPiezoelectricCoupling:the
PiezomagnetoelasticEnergyHarvester 247
8.3.1 Lumped-ParameterElectromechanicalEquations 247
8.3.2 Time-DomainSimulationsoftheElectromechanicalResponse 249
8.3.3 PerformanceComparisonofthePiezomagnetoelasticandthe
PiezoelasticConfigurationsinthePhaseSpace 250
8.3.4 ComparisonoftheChaoticResponseandtheLarge-Amplitude
PeriodicResponse 252
8.4 ExperimentalPerformanceResultsoftheBistablePiezomagnetoelastic
EnergyHarvester 253
8.4.1 ExperimentalSetup 253
8.4.2 PerformanceResultsofthePiezomagnetoelasticConfiguration 254
8.4.3 ComparisonofthePiezomagnetoelasticandthePiezoelastic
ConfigurationsforVoltageGeneration 256
8.4.4 OntheChaoticandtheLarge-AmplitudePeriodicRegionsof
theResponse 256
8.4.5 BroadbandPerformanceComparison 258
8.4.6 VerticalExcitationofthePiezomagnetoelasticEnergyHarvester 260
8.5 ABistablePlateforPiezoelectricEnergyHarvesting 262
8.5.1 NonlinearPhenomenaintheBistablePlate 262
8.5.2 BroadbandPowerGenerationPerformance 265
8.6 Summary 267
8.7 ChapterNotes 268
References 270