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

518 Pages·2010·12.724 MB·English
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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

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