About the Book
The book provides a pedagogical approach that emphasizes the physical processes of active materials and the design and control of engineering systems. It will also be a reference text for practicing engineers who might understand the basic principles of active materials but have an interest in learning more about specific applications. The text includes a number of worked examples, design problems, and homework problems (with a solutions manual) that will be useful for both instructors and practicing engineers.
Table of Contents:
Preface xiii
1 Introduction to Smart Material Systems 1
1.1 Types of Smart Materials, 2
1.2 Historical Overview of Piezoelectric Materials, Shape Memory Alloys, and Electroactive Polymers, 5
1.3 Recent Applications of Smart Materials and Smart Material Systems, 6
1.4 Additional Types of Smart Materials, 11
1.5 Smart Material Properties, 12
1.6 Organization of the Book, 16
1.7 Suggested Course Outlines, 19
1.8 Units, Examples, and Nomenclature, 20
Problems, 22
Notes, 22
2 Modeling Mechanical and Electrical Systems 24
2.1 Fundamental Relationships in Mechanics and Electrostatics, 24
2.1.1 Mechanics of Materials, 25
2.1.2 Linear Mechanical Constitutive Relationships, 32
2.1.3 Electrostatics, 35
2.1.4 Electronic Constitutive Properties of Conducting and Insulating Materials, 43
2.2 Work and Energy Methods, 48
2.2.1 Mechanical Work, 48
2.2.2 Electrical Work, 54
2.3 Basic Mechanical and Electrical Elements, 56
2.3.1 Axially Loaded Bars, 56
2.3.2 Bending Beams, 58
2.3.3 Capacitors, 64
2.3.4 Summary, 66
2.4 Energy-Based Modeling Methods, 67
2.4.1 Variational Motion, 68
2.5 Variational Principle of Systems in Static Equilibrium, 70
2.5.1 Generalized State Variables, 72
2.6 Variational Principle of Dynamic Systems, 78
2.7 Chapter Summary, 84
Problems, 85
Notes, 89
3 Mathematical Representations of Smart Material Systems 91
3.1 Algebraic Equations for Systems in Static Equilibrium, 91
3.2 Second-Order Models of Dynamic Systems, 92
3.3 First-Order Models of Dynamic Systems, 97
3.3.1 Transformation of Second-Order Models to First-Order Form, 98
3.3.2 Output Equations for State Variable Models, 99
3.4 Input–Output Models and Frequency Response, 101
3.4.1 Frequency Response, 103
3.5 Impedance and Admittance Models, 109
3.5.1 System Impedance Models and Terminal Constraints, 113
3.6 Chapter Summary, 118
Problems, 118
Notes, 121
4 Piezoelectric Materials 122
4.1 Electromechanical Coupling in Piezoelectric Devices: One-Dimensional Model, 122
4.1.1 Direct Piezoelectric Effect, 122
4.1.2 Converse Effect, 124
4.2 Physical Basis for Electromechanical Coupling in Piezoelectric Materials, 126
4.2.1 Manufacturing of Piezoelectric Materials, 127
4.2.2 Effect of Mechanical and Electrical Boundary Conditions, 131
4.2.3 Interpretation of the Piezoelectric Coupling Coefficient, 133
4.3 Constitutive Equations for Linear Piezoelectric Material, 135
4.3.1 Compact Notation for Piezoelectric Constitutive Equations, 137
4.4 Common Operating Modes of a Piezoelectric Transducer, 141
4.4.1 33 Operating Mode, 142
4.4.2 Transducer Equations for a 33 Piezoelectric Device, 147
4.4.3 Piezoelectric Stack Actuator, 150
4.4.4 Piezoelectric Stack Actuating a Linear Elastic Load, 152
4.5 Dynamic Force and Motion Sensing, 157
4.6 31 Operating Mode of a Piezoelectric Device, 160
4.6.1 Extensional 31 Piezoelectric Devices, 162
4.6.2 Bending 31 Piezoelectric Devices, 166
4.6.3 Transducer Equations for a Piezoelectric Bimorph, 172
4.6.4 Piezoelectric Bimorphs Including Substrate Effects, 175
4.7 Transducer Comparison, 178
4.7.1 Energy Comparisons, 182
4.8 Electrostrictive Materials, 184
4.8.1 One-Dimensional Analysis, 186
4.8.2 Polarization-Based Models of Electrostriction, 188
4.8.3 Constitutive Modeling, 192
4.8.4 Harmonic Response of Electrostrictive Materials, 196
4.9 Chapter Summary, 199
Problems, 200
Notes, 203
5 Piezoelectric Material Systems 205
5.1 Derivation of the Piezoelectric Constitutive Relationships, 205
5.1.1 Alternative Energy Forms and Transformation of the Energy Functions, 208
5.1.2 Development of the Energy Functions, 210
5.1.3 Transformation of the Linear Constitutive Relationships, 212
5.2 Approximation Methods for Static Analysis of Piezolectric Material Systems, 217
5.2.1 General Solution for Free Deflection and Blocked Force, 221
5.3 Piezoelectric Beams, 223
5.3.1 Cantilevered Bimorphs, 223
5.3.2 Pinned–Pinned Bimorphs, 227
5.4 Piezoelectric Material Systems: Dynamic Analysis, 232
5.4.1 General Solution, 233
5.5 Spatial Filtering and Modal Filters in Piezoelectric Material Systems, 235
5.5.1 Modal Filters, 239
5.6 Dynamic Response of Piezoelectric Beams, 241
5.6.1 Cantilevered Piezoelectric Beam, 249
5.6.2 Generalized Coupling Coefficients, 263
5.6.3 Structural Damping, 264
5.7 Piezoelectric Plates, 268
5.7.1 Static Analysis of Piezoelectric Plates, 269
5.7.2 Dynamic Analysis of Piezoelectric Plates, 281
5.8 Chapter Summary, 289
Problems, 290
Notes, 297
6 Shape Memory Alloys 298
6.1 Properties of Thermally Activated Shape Memory Materials, 298
6.2 Physical Basis for Shape Memory Properties, 300
6.3 Constitutive Modeling, 302
6.3.1 One-Dimensional Constitutive Model, 302
6.3.2 Modeling the Shape Memory Effect, 307
6.3.3 Modeling the Pseudoelastic Effect, 311
6.4 Multivariant Constitutive Model, 320
6.5 Actuation Models of Shape Memory Alloys, 326
6.5.1 Free Strain Recovery, 327
6.5.2 Restrained Recovery, 327
6.5.3 Controlled Recovery, 329
6.6 Electrical Activation of Shape Memory Alloys, 330
6.7 Dynamic Modeling of Shape Memory Alloys for
Electrical Actuation, 335
6.8 Chapter Summary, 341
Problems, 342
Notes, 345
7 Electroactive Polymer Materials 346
7.1 Fundamental Properties of Polymers, 347
7.1.1 Classification of Electroactive Polymers, 349
7.2 Dielectric Elastomers, 355
7.3 Conducting Polymer Actuators, 362
7.3.1 Properties of Conducting Polymer Actuators, 363
7.3.2 Transducer Models of Conducting Polymers, 367
7.4 Ionomeric Polymer Transducers, 369
7.4.1 Input–Output Transducer Models, 369
7.4.2 Actuator and Sensor Equations, 375
7.4.3 Material Properties of Ionomeric Polymer Transducers, 377
7.5 Chapter Summary, 382
Problems, 383
Notes, 384
8 Motion Control Applications 385
8.1 Mechanically Leveraged Piezoelectric Actuators, 386
8.2 Position Control of Piezoelectric Materials, 391
8.2.1 Proportional–Derivative Control, 392
8.2.2 Proportional–Integral–Derivative Control, 396
8.3 Frequency-Leveraged Piezoelectric Actuators, 402
8.4 Electroactive Polymers, 409
8.4.1 Motion Control Using Ionomers, 409
8.5 Chapter Summary, 412
Problems, 413
Notes, 414
9 Passive and Semiactive Damping 416
9.1 Passive Damping, 416
9.2 Piezoelectric Shunts, 419
9.2.1 Inductive–Resistive Shunts, 425
9.2.2 Comparison of Shunt Techniques, 431
9.3 Multimode Shunt Techniques, 432
9.4 Semiactive Damping Methods, 440
9.4.1 System Norms for Performance Definition, 441
9.4.2 Adaptive Shunt Networks, 443
9.4.3 Practical Considerations for Adaptive Shunt Networks, 447
9.5 Switched-State Absorbers and Dampers, 448
9.6 Passive Damping Using Shape Memory Alloy Wires, 453
9.6.1 Passive Damping via the Pseudoelastic Effect, 454
9.6.2 Parametric Study of Shape Memory Alloy Passive Damping, 460
9.7 Chapter Summary, 464
Problems, 465
Notes, 466
10 Active Vibration Control 467
10.1 Second-Order Models for Vibration Control, 467
10.1.1 Output Feedback, 468
10.2 Active Vibration Control Example, 471
10.3 Dynamic Output Feedback, 475
10.3.1 Piezoelectric Material Systems with Dynamic Output Feedback, 480
10.3.2 Self-Sensing Actuation, 483
10.4 Distributed Sensing, 486
10.5 State-Space Control Methodologies, 488
10.5.1 Transformation to First-Order Form, 488
10.5.2 Full-State Feedback, 491
10.5.3 Optimal Full-State Feedback: Linear Quadratic Regulator Problem, 496
10.5.4 State Estimation, 505
10.5.5 Estimator Design, 507
10.6 Chapter Summary, 508
Problems, 509
Notes, 510
11 Power Analysis for Smart Material Systems 511
11.1 Electrical Power for Resistive and Capacitive Elements, 511
11.2 Power Amplifier Analysis, 520
11.2.1 Linear Power Amplifiers, 520
11.2.2 Design of Linear Power Amplifiers, 524
11.2.3 Switching and Regenerative Power Amplifiers, 530
11.3 Energy Harvesting, 533
11.4 Chapter Summary, 542
Problems, 543
Notes, 544
References 545
Index 553
About the Author :
Donald J. Leo is a professor in the mechanical engineering department of Virginia Polytechnic Institute and State University. Professor Leo has worked in the field of smart materials as a graduate student, a practicing engineer, and, most recently, a faculty member at Virginia Tech. He is the Associate Director for one of the leading centers of study in this area, the Center for Intelligent Material Systems and Structures.
