Piezoelectric-Based Vibration Control: From Macro to Micro/Nano Scale Systems

518 Pages·2010·12.724 MB·English

by  Nader Jalili (auth.)

Piezoelectric-Based Vibration Control
Nader Jalili
Piezoelectric-Based Vibration
Control
From Macro to Micro/Nano Scale Systems
123
NaderJalili
DepartmentofMechanicalandIndustrialEngineering
373SnellEngineeringCenter
NortheasternUniversity
360HuntingtonAvenue
Boston,MA02115,USA
[email protected]
ISBN978-1-4419-0069-2 e-ISBN978-1-4419-0070-8
DOI10.1007/978-1-4419-0070-8
LibraryofCongressControlNumber:2009933099
(cid:2)c SpringerScience+BusinessMedia,LLC 2010
Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewritten
permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York,
NY10013, USA),except forbrief excerpts inconnection with reviews orscholarly analysis. Usein
connectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,
orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.
Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyare
notidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubject
toproprietaryrights.
Printedonacid-freepaper
SpringerispartofSpringerScience+BusinessMedia(www.springer.com)
To Jaleh,Paneed andPouya,
thelightsonmy journey,
To myparents,
fortheirunconditionalsupports,
Andto theonewho reignitedloveandhope
inme, and madethispossible.
Preface
Startingfromanelementarylevelinmechanicalvibrations,thisself-containedbook
providesreaderswithacomprehensiveunderstandingofphysicalprinciples,while
alsohighlightingrecentadvances,inpiezoelectricmaterialsandstructuresusedina
varietyofvibration-controlsystems.Thecontentsarecohesivelydividedintothree
majorparts,eachconsistingofseveralchapters.Thefirstpartofthebookitselfcan
serve as a single-source book on an introduction to mechanical vibrations which
startswiththerequiredpreliminaries,followedbyaunifiedapproachtovibrations
of discrete and continuoussystems. The second part presentsthe fundamentalsof
piezoelectric-basedsystemswithanemphasisontheirconstitutivemodelingaswell
asvibrationabsorptionandcontroltechniquesusingpiezoelectricactuatorsandsen-
sors.BuildingbaseduponPartsIandII,thelastpartofthebookprovidesreaders
with an insight into advanced topics in piezoelectric-based micro/nano actuators
andsensorswithapplicationsrangingfrommolecularmanufacturingandprecision
mechatronicstomolecularrecognitionandfunctionalnanostructures.
With its self-contained and single-source style, this book can serve as the pri-
maryreferenceinafirstcourseforseniorundergraduateandgraduatelevelstudents
as well as reference for research scientists in the mechanical, electrical, civil,
and aerospace engineering disciplines. Although a background in undergraduate
vibrations and dynamics is preferred, most fundamental concepts and required
mathematicaltoolsarebrieflyreviewedforthereaders’convenience.Suchaneasy-
to-follow formatmakes this book particularly usefulfor engineersworking in the
areas of vibration-control and piezoelectric systems, undergraduate students and
graduate students interested in the fundamentals of vibrations and control, and
researchersworkingonadvancedpiezoelectric-basedvibration-controlsystems.
Thematerialspresentedherearetheresultsofover10yearsofintensestudyand
research. Along this long journey, many individuals were instrumental in making
this book a success and I would like to acknowledgetheir help and support. First
andforemost,I wouldlike toexpressmy sinceregratitudeto myformeradvisors,
ProfessorEbrahimEsmailzadeh(MSthesis advisor)who taughtme fundamentals
of vibrationswithout such foundationsI would not be here today,as well as Pro-
fessor Nejat Olgac (PhD major advisor) who not only taught me the essence of
system dynamics and controls, but also taught me patiently and unselfishly many
real-life lessons that have become the guiding principles of my professional and
vii
viii Preface
personal life. I am also indebted to many of my former graduate students. With-
out their hardwork and dedication, this book would have not been even started.
Themostinfluentialindividualswhohavedirectlycontributedtothisbookinclude
Dr.SaeidBashash(MS2005,PhD2008)forhismajorcontributionsonhysteresis
compensationsandcollectiveeffortsinmodelingandcontrolofpiezoelectric-based
systems with applications to MEMS and NEMS presented in Chaps. 7–10; Dr.
MohsenDadfarnia(MS2003)forhiscontributionsonpiezoelectric-basedvibration-
controlsystemsdiscussedmainlyinChap.9;Dr.AminSalehi-Khojin(PhD2008)
forhiscontributionsonpiezoelectric-basedmodelingofnanomechanicalcantilever
systems as well as nanoscopic properties of next-generation piezoelectric actua-
torsandsensorsgiveninChaps.8,9,and12;Dr.S.NimaMahmoodi(PhD2007)
forhiscontributionsonnonlinearmodelingof nanomechanicalcantileversystems
presented in Chap. 11; Ms. Mana Afshari (MS 2007) for her contributions on
nanomechanical cantilever systems with applications to biosensing discussed in
Chap.11;Dr.RezaSaeidpourazar(PhD2009)forhiscontributionsonmodelingand
control of microcantilever-based manipulation and imaging systems discussed in
Chap.10;andfinallyDr.MahmoudRezaHosseini(PhD2008)forhiscontributions
innanomaterials-basedsensorsmodelingandfabricationgiveninChap.12.Special
thanksalsogotothestaffatSpringer,Mr.StevenElliotandMr.AndrewLeighfor
theirencouragementtostartthisenterpriseandhelpthroughoutthisinterestingand
fruitfulexperience.
Boston,MA NaderJalili
Contents
PartI IntroductionandOverviewofMechanicalVibrations
1 Introduction.................................................................... 3
1.1 ABriefOverviewofSmartStructures................................. 3
1.2 ConceptofVibrationControl........................................... 5
1.2.1 VibrationIsolationvs.VibrationAbsorption................. 6
1.2.2 VibrationAbsorptionvs.VibrationControl.................. 7
1.2.3 ClassificationsofVibration-ControlSystems................ 8
1.3 MathematicalModelsofDynamicalSystems ......................... 9
1.3.1 Linearvs.NonlinearModels.................................. 9
1.3.2 Lumped-Parameters vs.
Distributed-ParametersModels............................... 11
2 AnIntroductiontoVibrationsofLumped-ParametersSystems......... 13
2.1 VibrationCharacteristicsofLinearDiscreteSystems................. 13
2.2 VibrationsofSingle-Degree-of-FreedomSystems .................... 14
2.2.1 Time-domainResponseCharacteristics ...................... 15
2.2.2 FrequencyResponseFunction................................ 17
2.3 VibrationsofMulti-Degree-of-FreedomSystems..................... 18
2.3.1 EigenvalueProblemandModalMatrixRepresentation..... 19
2.3.2 ClassicallyDampedSystems ................................. 21
2.3.3 Non-proportionalDamping ................................... 23
2.4 IllustrativeExamplefromVibrationofDiscreteSystems............. 25
3 ABriefIntroductiontoVariationalMechanics ............................ 35
3.1 AnOverviewofCalculusofVariations................................ 35
3.1.1 ConceptofVariation........................................... 36
3.1.2 PropertiesofVariationalOperatorı.......................... 38
3.1.3 TheFundamentalTheoremofVariation...................... 39
3.1.4 ConstrainedMinimizationofFunctionals.................... 43
3.2 ABriefOverviewofVariationalMechanics........................... 45
ix
x Contents
3.2.1 Work–EnergyTheorem and Extended
Hamilton’sPrinciple........................................... 45
3.2.2 ApplicationofEulerEquationinAnalyticalDynamics..... 49
3.3 StepsinDerivingEquationsofMotionviaAnalyticalMethod....... 51
4 A Unified Approach to Vibrations
ofDistributed-ParametersSystems.......................................... 55
4.1 EquilibriumStateandKinematicsofaDeformableBody............ 56
4.1.1 DifferentialEquationsofEquilibrium........................ 56
4.1.2 Strain–DisplacementRelationships........................... 58
4.1.3 Stress–StrainConstitutiveRelationships..................... 62
4.2 VirtualWorkofaDeformablebody.................................... 64
4.3 IllustrativeExamplesfromVibrationsofContinuousSystems....... 69
4.3.1 LongitudinalVibrationofBars ............................... 70
4.3.2 TransverseVibrationofBeams ............................... 74
4.3.3 TransverseVibrationofPlates................................ 81
4.4 EigenvalueProbleminContinuousSystems........................... 86
4.4.1 DiscretizationofEquationsandSeparableSolution......... 87
4.4.2 NormalModesAnalysis....................................... 97
4.4.3 MethodofEigenfunctionsExpansion........................100
PartII Piezoelectric-BasedVibration-ControlSystems
5 AnOverviewofActiveMaterialsUtilizedinSmartStructures..........115
5.1 PiezoelectricMaterials..................................................116
5.1.1 PiezoelectricityConcept ......................................116
5.1.2 BasicBehaviorandConstitutiveModels
ofPiezoelectricMaterials.....................................116
5.1.3 PracticalApplicationsofPiezoelectricMaterials............118
5.2 PyroelectricMaterials...................................................119
5.2.1 ConstitutiveModelofPyroelectricMaterials................119
5.2.2 CommonPyroelectricMaterials..............................120
5.3 ElectrorheologicalandMagnetorheologicalFluids....................120
5.3.1 ElectrorheologicalFluids......................................120
5.3.2 MagnetorheologicalFluids....................................121
5.4 ShapeMemoryAlloys(SMAs).........................................123
5.4.1 SMAPhysicalPrinciplesandProperties.....................123
5.4.2 CommercialApplicationsofSMAs ..........................124
5.5 ElectrostrictiveandMagnetostrictiveMaterials .......................125
5.5.1 ElectrostrictiveMaterials......................................125
5.5.2 MagnetostrictiveMaterials....................................126
6 Physical Principles and Constitutive Models
ofPiezoelectricMaterials.....................................................129
6.1 FundamentalsofPiezoelectricity.......................................130
6.1.1 PolarizationandPiezoelectricEffects........................130
Contents xi
6.1.2 CrystallographicStructureofPiezoelectricMaterials.......132
6.2 ConstitutiveModelsofPiezoelectricMaterials........................134
6.2.1 PreliminariesandDefinitions.................................134
6.2.2 ConstitutiveRelations.........................................135
6.2.3 NonlinearCharacteristicsofPiezoelectricMaterials ........139
6.3 PiezoelectricMaterialConstitutiveConstants .........................140
6.3.1 GeneralRelationships.........................................140
6.3.2 PiezoelectricCoefficients .....................................142
6.4 EngineeringApplicationsofPiezoelectricMaterialsandStructures.148
6.4.1 ApplicationofPiezoceramicsinMechatronicSystems .....149
6.4.2 Motion Magnification Strategies for
PiezoceramicActuation.......................................149
6.4.3 Piezoceramic-BasedHighPrecisionMiniatureMotors .....150
6.5 Piezoelectric-BasedActuatorsandSensors............................151
6.5.1 Piezoelectric-BasedActuator/SensorConfigurations........151
6.5.2 ExamplesofPiezoelectric-BasedActuators/Sensors........154
6.6 RecentAdvancesinPiezoelectric-BasedSystems.....................156
6.6.1 Piezoelectric-BasedMicromanipulators......................156
6.6.2 PiezoelectricallyActuatedMicrocantilevers.................156
6.6.3 PiezoelectricallyDrivenTranslationalNano-Positioners....158
6.6.4 FutureDirectionsandOutlooks...............................158
7 HystereticCharacteristicsofPiezoelectricMaterials .....................161
7.1 TheOriginofHysteresis................................................161
7.1.1 Rate-IndependentandRate-DependentHysteresis ..........162
7.1.2 LocalversusNonlocalMemories.............................163
7.2 HysteresisNonlinearitiesinPiezoelectricMaterials ..................163
7.3 HysteresisModelingFrameworksforPiezoelectricMaterials........164
7.3.1 PhenomenologicalHysteresisModels........................165
7.3.2 Constitutive-basedHysteresisModels........................170
7.4 HysteresisCompensationTechniques..................................179
8 Piezoelectric-BasedSystemsModeling......................................183
8.1 ModelingPreliminariesandAssumptions .............................183
8.2 ModelingPiezoelectricActuatorsinAxial(Stacked)Configuration.185
8.2.1 PiezoelectricStackedActuatorsunderNo
ExternalLoad..................................................186
8.2.2 PiezoelectricStackedActuatorswithExternalLoad ........189
8.2.3 VibrationAnalysisofPiezoelectricActuators
inAxialConfiguration–AnExampleCaseStudy...........192
8.3 Modeling Piezoelectric Actuators in Transverse
(Bender)Configuration .................................................198
8.3.1 GeneralEnergy-basedModelingforLaminarActuators....198
8.3.2 VibrationAnalysis of a Piezoelectrically
ActuatedActiveProbe(cid:2)–AnExampleCaseStudy.........205
xii Contents
8.3.3 EquivalentBendingMomentActuationGeneration.........213
8.4 ABriefIntroductiontoPiezoelectricActuationin2D ................219
8.4.1 GeneralEnergy-basedModelingfor 2D
PiezoelectricActuation........................................219
8.4.2 EquivalentBendingMoment2DActuationGeneration.....224
8.5 ModelingPiezoelectricSensors ........................................226
8.5.1 PiezoelectricStackedSensors.................................227
8.5.2 PiezoelectricLaminarSensors................................229
8.5.3 EquivalentCircuitModelsofPiezoelectricSensors.........230
9 VibrationControlUsing PiezoelectricActuatorsand
Sensors .........................................................................233
9.1 NotionofVibrationControlandPreliminaries........................233
9.2 ActiveVibrationAbsorptionusingPiezoelectricInertialActuators..235
9.2.1 ActiveResonatorAbsorber ...................................237
9.2.2 Delayed-ResonatorVibrationAbsorber......................242
9.3 Piezoelectric-BasedActiveVibration-ControlSystems...............251
9.3.1 ControlofPiezoceramicActuatorsinAxialConfiguration .252
9.3.2 VibrationControlUsingPiezoelectricLaminarActuators..263
9.4 Piezoelectric-basedSemi-activeVibration-ControlSystems..........284
9.4.1 A Brief Overviewof Switched-Stiffness
Vibration-ControlConcept....................................286
9.4.2 Real-Time Implementation of
Switched-StiffnessConcept...................................290
9.4.3 Switched-StiffnessVibrationControlusing
PiezoelectricMaterials........................................293
9.4.4 Piezoelectric-BasedSwitched-StiffnessExperimentation...298
9.5 Self-sensingActuationusingPiezoelectricMaterials.................302
9.5.1 PreliminariesandBackground................................302
9.5.2 AdaptationStrategyforPiezoelectricCapacitance ..........304
9.5.3 ApplicationofSelf-sensingActuationforMassDetection..306
PartIII Piezoelectric-BasedMicro/NanoSensorsandActuators
10 Piezoelectric-BasedMicro-andNano-PositioningSystems...............313
10.1 ClassificationofControlandManipulationattheNanoscale.........313
10.1.1 ScanningProbeMicroscopy-BasedControl
andManipulation..............................................315
10.1.2 NanoroboticManipulation-BasedControl
andManipulation..............................................319
10.2 PiezoelectricallyDrivenMicro-andNano-PositioningSystems .....321
10.2.1 PiezoelectricActuatorsUsedinSTMSystems ..............322
10.2.2 ModelingPiezoelectricActuatorsUsedinSTMSystems...322
10.3 ControlofSingle-AxisPiezoelectricNano-positioningSystems.....328
10.3.1 FeedforwardControlStrategies...............................330