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[资源] Piezoelectric-Based Vibration Control From Macro to Micro/Nano Scale Systems

Part I Introduction and Overview of Mechanical Vibrations
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 A Brief Overview of Smart Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Concept of Vibration Control .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1 Vibration Isolation vs. Vibration Absorption.. . . . . . . . . . . . . . . . 6
1.2.2 Vibration Absorption vs. Vibration Control . . . . . . . . . . . . . . . . . . 7
1.2.3 Classifications of Vibration-Control Systems . . . . . . . . . . . . . . . . 8
1.3 MathematicalModels of Dynamical Systems . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.1 Linear vs. NonlinearModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.2 Lumped-Parameters vs.
Distributed-ParametersModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 An Introduction to Vibrations of Lumped-Parameters Systems . . . . . . . . . 13
2.1 Vibration Characteristics of Linear Discrete Systems . . . . . . . . . . . . . . . . . 13
2.2 Vibrations of Single-Degree-of-FreedomSystems . . . . . . . . . . . . . . . . . . . . 14
2.2.1 Time-domain Response Characteristics . . . . . . . . . . . . . . . . . . . . . . 15
2.2.2 Frequency Response Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 Vibrations of Multi-Degree-of-FreedomSystems . . . . . . . . . . . . . . . . . . . . . 18
2.3.1 Eigenvalue Problem andModalMatrix Representation . . . . . 19
2.3.2 Classically Damped Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.3 Non-proportional Damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4 Illustrative Example from Vibration of Discrete Systems . . . . . . . . . . . . . 25
3 A Brief Introduction to VariationalMechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.1 An Overview of Calculus of Variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.1.1 Concept of Variation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.1.2 Properties of Variational Operator ı . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.1.3 The Fundamental Theorem of Variation. . . . . . . . . . . . . . . . . . . . . . 39
3.1.4 ConstrainedMinimization of Functionals .. . . . . . . . . . . . . . . . . . . 43
3.2 A Brief Overview of VariationalMechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
ix
x Contents
3.2.1 Work–Energy Theorem and Extended
Hamilton’s Principle.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2.2 Application of Euler Equation in Analytical Dynamics . . . . . 49
3.3 Steps in Deriving Equations ofMotion via AnalyticalMethod .. . . . . . 51
4 A Unified Approach to Vibrations
of Distributed-Parameters Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.1 Equilibrium State and Kinematics of a Deformable Body . . . . . . . . . . . . 56
4.1.1 Differential Equations of Equilibrium .. . . . . . . . . . . . . . . . . . . . . . . 56
4.1.2 Strain–Displacement Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.1.3 Stress–Strain Constitutive Relationships . . . . . . . . . . . . . . . . . . . . . 62
4.2 Virtual Work of a Deformable body .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.3 Illustrative Examples from Vibrations of Continuous Systems . . . . . . . 69
4.3.1 Longitudinal Vibration of Bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.3.2 Transverse Vibration of Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.3.3 Transverse Vibration of Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.4 Eigenvalue Problem in Continuous Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.4.1 Discretization of Equations and Separable Solution .. . . . . . . . 87
4.4.2 NormalModes Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.4.3 Method of Eigenfunctions Expansion . . . . . . . . . . . . . . . . . . . . . . . .100
Part II Piezoelectric-Based Vibration-Control Systems
5 An Overview of Active Materials Utilized in Smart Structures . . . . . . . . . .115
5.1 PiezoelectricMaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .116
5.1.1 Piezoelectricity Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .116
5.1.2 Basic Behavior and Constitutive Models
of PiezoelectricMaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .116
5.1.3 Practical Applications of PiezoelectricMaterials . . . . . . . . . . . .118
5.2 PyroelectricMaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .119
5.2.1 Constitutive Model of Pyroelectric Materials . . . . . . . . . . . . . . . .119
5.2.2 Common PyroelectricMaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .120
5.3 Electrorheological andMagnetorheological Fluids. . . . . . . . . . . . . . . . . . . .120
5.3.1 Electrorheological Fluids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .120
5.3.2 Magnetorheological Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121
5.4 ShapeMemory Alloys (SMAs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .123
5.4.1 SMA Physical Principles and Properties . . . . . . . . . . . . . . . . . . . . .123
5.4.2 Commercial Applications of SMAs . . . . . . . . . . . . . . . . . . . . . . . . . .124
5.5 Electrostrictive andMagnetostrictiveMaterials . . . . . . . . . . . . . . . . . . . . . . .125
5.5.1 ElectrostrictiveMaterials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .125
5.5.2 MagnetostrictiveMaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .126
6 Physical Principles and Constitutive Models
of PiezoelectricMaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .129
6.1 Fundamentals of Piezoelectricity .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .130
6.1.1 Polarization and Piezoelectric Effects . . . . . . . . . . . . . . . . . . . . . . . .130
Contents xi
6.1.2 Crystallographic Structure of PiezoelectricMaterials . . . . . . .132
6.2 Constitutive Models of Piezoelectric Materials . . . . . . . . . . . . . . . . . . . . . . . .134
6.2.1 Preliminaries and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .134
6.2.2 Constitutive Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .135
6.2.3 Nonlinear Characteristics of PiezoelectricMaterials . . . . . . . .139
6.3 Piezoelectric Material Constitutive Constants . . . . . . . . . . . . . . . . . . . . . . . . .140
6.3.1 General Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .140
6.3.2 Piezoelectric Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .142
6.4 Engineering Applications of Piezoelectric Materials and Structures .148
6.4.1 Application of Piezoceramics inMechatronic Systems . . . . .149
6.4.2 Motion Magnification Strategies for
Piezoceramic Actuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .149
6.4.3 Piezoceramic-Based High PrecisionMiniatureMotors . . . . .150
6.5 Piezoelectric-Based Actuators and Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . .151
6.5.1 Piezoelectric-Based Actuator/Sensor Configurations .. . . . . . .151
6.5.2 Examples of Piezoelectric-Based Actuators/Sensors . . . . . . . .154
6.6 Recent Advances in Piezoelectric-Based Systems. . . . . . . . . . . . . . . . . . . . .156
6.6.1 Piezoelectric-BasedMicromanipulators .. . . . . . . . . . . . . . . . . . . . .156
6.6.2 Piezoelectrically Actuated Microcantilevers . . . . . . . . . . . . . . . . .156
6.6.3 Piezoelectrically Driven Translational Nano-Positioners .. . .158
6.6.4 Future Directions and Outlooks.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .158
7 Hysteretic Characteristics of PiezoelectricMaterials . . . . . . . . . . . . . . . . . . . . .161
7.1 The Origin of Hysteresis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .161
7.1.1 Rate-Independent and Rate-Dependent Hysteresis . . . . . . . . . .162
7.1.2 Local versus NonlocalMemories . . . . . . . . . . . . . . . . . . . . . . . . . . . . .163
7.2 Hysteresis Nonlinearities in Piezoelectric Materials . . . . . . . . . . . . . . . . . .163
7.3 HysteresisModeling Frameworks for PiezoelectricMaterials . . . . . . . .164
7.3.1 PhenomenologicalHysteresisModels . . . . . . . . . . . . . . . . . . . . . . . .165
7.3.2 Constitutive-based Hysteresis Models . . . . . . . . . . . . . . . . . . . . . . . .170
7.4 Hysteresis Compensation Techniques .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .179
8 Piezoelectric-Based Systems Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .183
8.1 Modeling Preliminaries and Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .183
8.2 Modeling Piezoelectric Actuators in Axial (Stacked) Configuration .185
8.2.1 Piezoelectric Stacked Actuators under No
External Load .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .186
8.2.2 Piezoelectric Stacked Actuators with External Load . . . . . . . .189
8.2.3 Vibration Analysis of Piezoelectric Actuators
in Axial Configuration – An Example Case Study.. . . . . . . . . .192
8.3 Modeling Piezoelectric Actuators in Transverse
(Bender) Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .198
8.3.1 General Energy-basedModeling for Laminar Actuators . . . .198
8.3.2 Vibration Analysis of a Piezoelectrically
Actuated Active Probe – An Example Case Study.. . . . . . . .205
xii Contents
8.3.3 Equivalent BendingMoment Actuation Generation . . . . . . . . .213
8.4 A Brief Introduction to Piezoelectric Actuation in 2D . . . . . . . . . . . . . . . .219
8.4.1 General Energy-based Modeling for 2D
Piezoelectric Actuation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .219
8.4.2 Equivalent BendingMoment 2D Actuation Generation .. . . .224
8.5 Modeling Piezoelectric Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .226
8.5.1 Piezoelectric Stacked Sensors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .227
8.5.2 Piezoelectric Laminar Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .229
8.5.3 Equivalent Circuit Models of Piezoelectric Sensors . . . . . . . . .230
9 Vibration Control Using Piezoelectric Actuators and
Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .233
9.1 Notion of Vibration Control and Preliminaries . . . . . . . . . . . . . . . . . . . . . . . .233
9.2 Active Vibration Absorption using Piezoelectric Inertial Actuators . .235
9.2.1 Active Resonator Absorber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .237
9.2.2 Delayed-Resonator Vibration Absorber . . . . . . . . . . . . . . . . . . . . . .242
9.3 Piezoelectric-Based Active Vibration-Control Systems . . . . . . . . . . . . . . .251
9.3.1 Control of Piezoceramic Actuators in Axial Configuration .252
9.3.2 Vibration Control Using Piezoelectric Laminar Actuators . .263
9.4 Piezoelectric-based Semi-active Vibration-Control Systems. . . . . . . . . .284
9.4.1 A Brief Overview of Switched-Stiffness
Vibration-Control Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .286
9.4.2 Real-Time Implementation of
Switched-Stiffness Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .290
9.4.3 Switched-Stiffness Vibration Control using
PiezoelectricMaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .293
9.4.4 Piezoelectric-Based Switched-Stiffness Experimentation .. .298
9.5 Self-sensing Actuation using PiezoelectricMaterials . . . . . . . . . . . . . . . . .302
9.5.1 Preliminaries and Background .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .302
9.5.2 Adaptation Strategy for Piezoelectric Capacitance . . . . . . . . . .304
9.5.3 Application of Self-sensing Actuation for Mass Detection..306
Part III Piezoelectric-BasedMicro/Nano Sensors and Actuators
10 Piezoelectric-BasedMicro- and Nano-Positioning Systems . . . . . . . . . . . . . . .313
10.1 Classification of Control andManipulation at the Nanoscale . . . . . . . . .313
10.1.1 Scanning Probe Microscopy-Based Control
andManipulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .315
10.1.2 Nanorobotic Manipulation-Based Control
andManipulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .319
10.2 Piezoelectrically DrivenMicro- and Nano-Positioning Systems . . . . .321
10.2.1 Piezoelectric Actuators Used in STMSystems . . . . . . . . . . . . . .322
10.2.2 Modeling Piezoelectric Actuators Used in STM Systems . . .322
10.3 Control of Single-Axis Piezoelectric Nano-positioning Systems . . . . .328
10.3.1 Feedforward Control Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .330
Contents xiii
10.3.2 Feedback Control Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .332
10.4 Control of Multiple-Axis Piezoelectric
Nano-positioning Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .336
10.4.1 Modeling and Control of Coupled Parallel
Piezo-Flexural Nano-Positioning Stages . . . . . . . . . . . . . . . . . . . . .336
10.4.2 Modeling and Control of Three-Dimensional
Nano-Positioning Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .351
11 Piezoelectric-Based Nanomechanical Cantilever Sensors . . . . . . . . . . . . . . . . .359
11.1 Preliminaries and Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .360
11.1.1 Fundamental Operation of Nanomechanical
Cantilever Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .360
11.1.2 Linear vs. Nonlinear and Small-scale vs.
Large-scale Vibrations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .363
11.1.3 Common Methods of Signal Transduction in NMCS. . . . . . . .363
11.1.4 Engineering Applications and Recent Developments.. . . . . . .366
11.2 Modeling Frameworks for Nanomechanical
Cantilever Sensors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .368
11.2.1 Linear and Nonlinear Vibration Analyses
of Piezoelectrically-drivenNMCS. . . . . . . . . . . . . . . . . . . . . . . . . . . .368
11.2.2 Coupled Flexural-Torsional Vibration Analysis
of NMCS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .388
11.3 Ultrasmall Mass Sensing and Materials
Characterization using NMCS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .399
11.3.1 Biological Species Detection using NMCS . . . . . . . . . . . . . . . . . .401
11.3.2 UltrasmallMass Detection using Active Probes . . . . . . . . . . . . .411
12 Nanomaterial-Based Piezoelectric Actuators and Sensors . . . . . . . . . . . . . . . .419
12.1 Piezoelectric Properties of Nanotubes (CNT and BNNT). . . . . . . . . . . . .420
12.1.1 A Brief Overview of Nanotubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .420
12.1.2 Piezoelectricity in Nanotubes
and Nanotube-BasedMaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .421
12.2 Nanotube-Based Piezoelectric Sensors and Actuators . . . . . . . . . . . . . . . .423
12.2.1 Actuation and Sensing Mechanism
in Multifunctional Nanomaterials. . . . . . . . . . . . . . . . . . . . . . . . . . . . .423
12.2.2 Fabrication of Nanotube-Based Piezoelectric
Film Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .426
12.2.3 Piezoelectric Properties Measurement
of Nanotube-Based Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .432
12.3 Structural Damping and Vibration Control Using
Nanotubes-Based Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .434
12.3.1 Fabrication of Nanotube-Based Composites
for Vibration Damping and Control . . . . . . . . . . . . . . . . . . . . . . . . . .434
12.3.2 Free Vibration Characterization
of Nanotube-Based Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .436
xiv Contents
12.3.3 Forced Vibration Characterization
of Nanotube-Based Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .441
12.4 Piezoelectric Nanocomposites with Tunable Properties. . . . . . . . . . . . . . .446
12.4.1 A Brief Overview of Interphase Zone Control . . . . . . . . . . . . . . .446
12.4.2 Molecular Dynamic Simulations
for Nanotube-Based Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . .448
12.4.3 Continuum Level Elasticity Model
of Nanotube-Based Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .451
12.4.4 Numerical Results and Discussions
of Nanotube-Based Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .451
12.5 Electronic Textiles Comprised of Functional Nanomaterials . . . . . . . . .455
12.5.1 The Concept of Electronic Textiles . . . . . . . . . . . . . . . . . . . . . . . . . . .455
12.5.2 Fabrication of Nonwoven CNT-based
Composite Fabrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .455
12.5.3 Experimental Characterization of CNT-based
Fabric Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .459
Mathematical Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .463
A.1 Preliminaries and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .463
A.2 Indicial Notation and Summation Convention .. . . . . . . . . . . . . . . . . . . . . . . .466
A.2.1 Indicial Notation Convention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .466
A.2.2 The Kronecker Delta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .467
A.3 Equilibrium States and Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .468
A.3.1 Equilibrium Points or States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .468
A.3.2 Concept of Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .469
A.4 A Brief Overview of Fundamental Stability Theorems . . . . . . . . . . . . . . .471
A.4.1 Lyapunov Local and Global Stability Theorems .. . . . . . . . . . . .471
A.4.2 Local and Global Invariant Set Theorems .. . . . . . . . . . . . . . . . . . .474
Proofs of Selected Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .477
B.1 Proof of Theorem 9.1 (Dadfarnia et al. 2004a) . . . . . . . . . . . . . . . . . . . . . . . .477
B.2 Proof of Theorem 9.2 (Dadfarnia et al. 2004b) . . . . . . . . . . . . . . . . . . . . . . . .480
B.3 Proof of Theorem 9.3 (Ramaratnam and Jalili 2006a) . . . . . . . . . . . . . . . .482
B.4 Proof of Theorem 10.1 (Bashash and Jalili 2009) . . . . . . . . . . . . . . . . . . . . .483
B.5 Proof of Theorem 10.2 (Bashash and Jalili 2009) . . . . . . . . . . . . . . . . . . . . .484

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