Piezoelectric-Based Vibration Control (eBook)

Nader Jalili is currently an Associate Professor of Mechanical and Industrial Engineering at Northeastern University. Previously he served as an Associate Professor of Mechanical Engineering at Clemson University. He received a Ph.D. degree in 1988, from the University of Connteticut. His present research works are chiefly on piezoelectric-based sensors/actuators, nanocomposites, piezoelectric-based nano-stager for microscopy applications, vibration control in automobiles, and e-textiles Founding Chair, Technical Committee on Vibration and Control of Smart Structures, ASME Dynamic Systems and Control Division (DSCD) . He’s currently Associate Editor, ASME Transactions on Dynamic Systems, Measurements and Control and the Technical Editor, IEEE/ASME Transaction on Mechatronics. He’s published over 45 journal articles and was a receipient of an NSF Young Investigator Career Award in 2003 for his work in the area of nanomanufacturing.

Preface 6
Contents 8
About this Book 14
Part I Introduction and Overview of Mechanical Vibrations 15
1 Introduction 16
1.1 A Brief Overview of Smart Structures 16
1.2 Concept of Vibration Control 18
1.2.1 Vibration Isolation vs. Vibration Absorption 19
1.2.2 Vibration Absorption vs. Vibration Control 20
1.2.3 Classifications of Vibration-Control Systems 21
1.3 Mathematical Models of Dynamical Systems 22
1.3.1 Linear vs. Nonlinear Models 22
1.3.2 Lumped-Parameters vs. Distributed-Parameters Models 24
2 An Introduction to Vibrations of Lumped-Parameters Systems 26
2.1 Vibration Characteristics of Linear Discrete Systems 26
2.2 Vibrations of Single-Degree-of-Freedom Systems 27
2.2.1 Time-domain Response Characteristics 28
2.2.2 Frequency Response Function 30
2.3 Vibrations of Multi-Degree-of-Freedom Systems 31
2.3.1 Eigenvalue Problem and Modal Matrix Representation 32
2.3.2 Classically Damped Systems 34
2.3.3 Non-proportional Damping 36
2.4 Illustrative Example from Vibration of Discrete Systems 38
3 A Brief Introduction to Variational Mechanics 47
3.1 An Overview of Calculus of Variations 47
3.1.1 Concept of Variation 48
3.1.2 Properties of Variational Operator 50
3.1.3 The Fundamental Theorem of Variation 51
3.1.4 Constrained Minimization of Functionals 55
3.2 A Brief Overview of Variational Mechanics 57
3.2.1 Work–Energy Theorem and Extended Hamilton's Principle 57
3.2.2 Application of Euler Equation in Analytical Dynamics 61
3.3 Steps in Deriving Equations of Motion via Analytical Method 63
4 A Unified Approach to Vibrations of Distributed-Parameters Systems 66
4.1 Equilibrium State and Kinematics of a Deformable Body 67
4.1.1 Differential Equations of Equilibrium 67
4.1.2 Strain–Displacement Relationships 69
4.1.3 Stress–Strain Constitutive Relationships 73
4.2 Virtual Work of a Deformable body 75
4.3 Illustrative Examples from Vibrations of Continuous Systems 80
4.3.1 Longitudinal Vibration of Bars 81
4.3.2 Transverse Vibration of Beams 85
4.3.3 Transverse Vibration of Plates 92
4.4 Eigenvalue Problem in Continuous Systems 97
4.4.1 Discretization of Equations and Separable Solution 98
4.4.2 Normal Modes Analysis 108
4.4.3 Method of Eigenfunctions Expansion 111
Part II Piezoelectric-Based Vibration-Control Systems 124
5 An Overview of Active Materials Utilized in Smart Structures 125
5.1 Piezoelectric Materials 126
5.1.1 Piezoelectricity Concept 126
5.1.2 Basic Behavior and Constitutive Modelsof Piezoelectric Materials 126
5.1.3 Practical Applications of Piezoelectric Materials 128
5.2 Pyroelectric Materials 129
5.2.1 Constitutive Model of Pyroelectric Materials 129
5.2.2 Common Pyroelectric Materials 130
5.3 Electrorheological and Magnetorheological Fluids 130
5.3.1 Electrorheological Fluids 130
5.3.2 Magnetorheological Fluids 131
5.4 Shape Memory Alloys (SMAs) 133
5.4.1 SMA Physical Principles and Properties 133
5.4.2 Commercial Applications of SMAs 134
5.5 Electrostrictive and Magnetostrictive Materials 135
5.5.1 Electrostrictive Materials 135
5.5.2 Magnetostrictive Materials 136
6 Physical Principles and Constitutive Models of Piezoelectric Materials 139
6.1 Fundamentals of Piezoelectricity 140
6.1.1 Polarization and Piezoelectric Effects 140
6.1.2 Crystallographic Structure of Piezoelectric Materials 142
6.2 Constitutive Models of Piezoelectric Materials 144
6.2.1 Preliminaries and Definitions 144
6.2.2 Constitutive Relations 145
6.2.3 Nonlinear Characteristics of Piezoelectric Materials 149
6.3 Piezoelectric Material Constitutive Constants 150
6.3.1 General Relationships 150
6.3.2 Piezoelectric Coefficients 152
6.4 Engineering Applications of Piezoelectric Materials and Structures 158
6.4.1 Application of Piezoceramics in Mechatronic Systems 159
6.4.2 Motion Magnification Strategies for Piezoceramic Actuation 159
6.4.3 Piezoceramic-Based High Precision Miniature Motors 160
6.5 Piezoelectric-Based Actuators and Sensors 161
6.5.1 Piezoelectric-Based Actuator/Sensor Configurations 161
6.5.2 Examples of Piezoelectric-Based Actuators/Sensors 164
6.6 Recent Advances in Piezoelectric-Based Systems 166
6.6.1 Piezoelectric-Based Micromanipulators 166
6.6.2 Piezoelectrically Actuated Microcantilevers 166
6.6.3 Piezoelectrically Driven Translational Nano-Positioners 168
6.6.4 Future Directions and Outlooks 168
7 Hysteretic Characteristics of Piezoelectric Materials 170
7.1 The Origin of Hysteresis 170
7.1.1 Rate-Independent and Rate-Dependent Hysteresis 171
7.1.2 Local versus Nonlocal Memories 172
7.2 Hysteresis Nonlinearities in Piezoelectric Materials 172
7.3 Hysteresis Modeling Frameworks for Piezoelectric Materials 173
7.3.1 Phenomenological Hysteresis Models 174
7.3.2 Constitutive-based Hysteresis Models 179
7.4 Hysteresis Compensation Techniques 188
8 Piezoelectric-Based Systems Modeling 191
8.1 Modeling Preliminaries and Assumptions 191
8.2 Modeling Piezoelectric Actuators in Axial (Stacked) Configuration 193
8.2.1 Piezoelectric Stacked Actuators under No External Load 194
8.2.2 Piezoelectric Stacked Actuators with External Load 197
8.2.3 Vibration Analysis of Piezoelectric Actuatorsin Axial Configuration – An Example Case Study 200
8.3 Modeling Piezoelectric Actuators in Transverse (Bender) Configuration 206
8.3.1 General Energy-based Modeling for Laminar Actuators 206
8.3.2 Vibration Analysis of a Piezoelectrically Actuated Active Probe"472 – An Example Case Study 213
8.3.3 Equivalent Bending Moment Actuation Generation 221
8.4 A Brief Introduction to Piezoelectric Actuation in 2D 227
8.4.1 General Energy-based Modeling for 2D Piezoelectric Actuation 227
8.4.2 Equivalent Bending Moment 2D Actuation Generation 232
8.5 Modeling Piezoelectric Sensors 234
8.5.1 Piezoelectric Stacked Sensors 235
8.5.2 Piezoelectric Laminar Sensors 237
8.5.3 Equivalent Circuit Models of Piezoelectric Sensors 238
9 Vibration Control Using Piezoelectric Actuators and Sensors 241
9.1 Notion of Vibration Control and Preliminaries 241
9.2 Active Vibration Absorption using Piezoelectric Inertial Actuators 243
9.2.1 Active Resonator Absorber 245
9.2.2 Delayed-Resonator Vibration Absorber 250
9.3 Piezoelectric-Based Active Vibration-Control Systems 259
9.3.1 Control of Piezoceramic Actuators in Axial Configuration 260
9.3.2 Vibration Control Using Piezoelectric Laminar Actuators 271
9.4 Piezoelectric-based Semi-active Vibration-Control Systems 292
9.4.1 A Brief Overview of Switched-Stiffness Vibration-Control Concept 294
9.4.2 Real-Time Implementation of Switched-Stiffness Concept 298
9.4.3 Switched-Stiffness Vibration Control using Piezoelectric Materials 301
9.4.4 Piezoelectric-Based Switched-Stiffness Experimentation 306
9.5 Self-sensing Actuation using Piezoelectric Materials 310
9.5.1 Preliminaries and Background 310
9.5.2 Adaptation Strategy for Piezoelectric Capacitance 312
9.5.3 Application of Self-sensing Actuation for Mass Detection 314
Part III Piezoelectric-Based Micro/Nano Sensors and Actuators 318
10 Piezoelectric-Based Micro- and Nano-Positioning Systems 319
10.1 Classification of Control and Manipulation at the Nanoscale 319
10.1.1 Scanning Probe Microscopy-Based Control and Manipulation 321
10.1.2 Nanorobotic Manipulation-Based Control and Manipulation 325
10.2 Piezoelectrically Driven Micro- and Nano-Positioning Systems 327
10.2.1 Piezoelectric Actuators Used in STM Systems 328
10.2.2 Modeling Piezoelectric Actuators Used in STM Systems 328
10.3 Control of Single-Axis Piezoelectric Nano-positioning Systems 334
10.3.1 Feedforward Control Strategies 336
10.3.2 Feedback Control Strategies 338
10.4 Control of Multiple-Axis Piezoelectric Nano-positioning Systems 342
10.4.1 Modeling and Control of Coupled Parallel Piezo-Flexural Nano-Positioning Stages 342
10.4.2 Modeling and Control of Three-Dimensional Nano-Positioning Systems 357
11 Piezoelectric-Based Nanomechanical Cantilever Sensors 365
11.1 Preliminaries and Overview 366
11.1.1 Fundamental Operation of Nanomechanical Cantilever Sensors 366
11.1.2 Linear vs. Nonlinear and Small-scale vs. Large-scale Vibrations 369
11.1.3 Common Methods of Signal Transduction in NMCS 369
11.1.4 Engineering Applications and Recent Developments 372
11.2 Modeling Frameworks for NanomechanicalCantilever Sensors 374
11.2.1 Linear and Nonlinear Vibration Analyses of Piezoelectrically-driven NMCS 374
11.2.2 Coupled Flexural-Torsional Vibration Analysis of NMCS 394
11.3 Ultrasmall Mass Sensing and MaterialsCharacterization using NMCS 405
11.3.1 Biological Species Detection using NMCS 407
11.3.2 Ultrasmall Mass Detection using Active Probes 417
12 Nanomaterial-Based Piezoelectric Actuators and Sensors 424
12.1 Piezoelectric Properties of Nanotubes (CNT and BNNT) 425
12.1.1 A Brief Overview of Nanotubes 425
12.1.2 Piezoelectricity in Nanotubes and Nanotube-Based Materials 426
12.2 Nanotube-Based Piezoelectric Sensors and Actuators 428
12.2.1 Actuation and Sensing Mechanism in Multifunctional Nanomaterials 428
12.2.2 Fabrication of Nanotube-Based Piezoelectric Film Sensors 431
12.2.3 Piezoelectric Properties Measurement of Nanotube-Based Sensors 437
12.3 Structural Damping and Vibration Control Using Nanotubes-Based Composites 439
12.3.1 Fabrication of Nanotube-Based Composites for Vibration Damping and Control 439
12.3.2 Free Vibration Characterization of Nanotube-Based Composites 441
12.3.3 Forced Vibration Characterization of Nanotube-Based Composites 446
12.4 Piezoelectric Nanocomposites with Tunable Properties 451
12.4.1 A Brief Overview of Interphase Zone Control 451
12.4.2 Molecular Dynamic Simulations for Nanotube-Based Composites 453
12.4.3 Continuum Level Elasticity Model of Nanotube-Based Composites 456
12.4.4 Numerical Results and Discussions of Nanotube-Based Composites 456
12.5 Electronic Textiles Comprised of Functional Nanomaterials 460
12.5.1 The Concept of Electronic Textiles 460
12.5.2 Fabrication of Nonwoven CNT-based Composite Fabrics 460
12.5.3 Experimental Characterization of CNT-based Fabric Sensors 464
Mathematical Preliminaries 467
A.1 Preliminaries and Definitions 467
A.2 Indicial Notation and Summation Convention 470
A.2.1 Indicial Notation Convention 470
A.2.2 The Kronecker Delta 471
A.3 Equilibrium States and Stability 472
A.3.1 Equilibrium Points or States 472
A.3.2 Concept of Stability 473
A.4 A Brief Overview of Fundamental Stability Theorems 475
A.4.1 Lyapunov Local and Global Stability Theorems 475
A.4.2 Local and Global Invariant Set Theorems 478
Proofs of Selected Theorems 480
B.1 Proof of Theorem9.1 (Dadfarnia et al. 2004a) 480
B.2 Proof of Theorem9.2 (Dadfarnia et al. 2004b) 483
B.3 Proof of Theorem 9.3 (Ramaratnam and Jalili 2006a) 485
B.4 Proof of Theorem10.1 (Bashash and Jalili 2009) 486
B.5 Proof of Theorem10.2 (Bashash and Jalili 2009) 487
References 489
Index 507