Preface ...................................................... xvii
1 Historical Developments and Potential Applications: Smart
Materials and Structures ..................................... 1
1.1 Smart Structures ........................................ 3
1.1.1 Smart Material Actuators and Sensors ............. 4
1.1.2 Smart Actuators .................................. 7
1.1.3 Sensors .......................................... 8
1.1.4 Actuator-Sensor Synthesis ........................ 8
1.1.5 Control Methodologies ............................ 9
1.2 Manufacturing Issues ................................... 10
1.3 Piezoelectricity ....................................... 10
1.4 Shape Memory Alloys .................................... 14
1.5 Electrostrictives ...................................... 19
1.6 Magnetostrictives ...................................... 21
1.6.1 Terfenol-D ...................................... 22
1.6.2 Galfenol ........................................ 24
1.7 ER and MR Fluids ....................................... 25
1.8 Capability of Currently Available Smart Materials ...... 29
1.9 Smart Structures Programs .............................. 31
1.9.1 Space Systems ................................... 35
1.9.2 Fixed-Wing Aircraft ............................. 41
1.9.3 Jet Engines ..................................... 51
1.9.4 Rotary-Wing Aircraft ............................ 53
1.9.5 Civil Structures ................................ 61
1.9.6 Machine Tools ................................... 68
1.9.7 Automotive Systems .............................. 71
1.9.8 Marine Systems .................................. 75
1.9.9 Medical Systems ................................. 77
1.9.10 Electronics Equipment ........................... 86
1.9.11 Rail ............................................ 88
1.9.12 Robots .......................................... 89
1.9.13 Energy Harvesting ............................... 90
2 Piezoelectric Actuators and Sensors ........................ 113
2.1 Fundamentals of Piezoelectricity ...................... 113
2.2 Piezoceramics ......................................... 117
2.3 Soft and Hard Piezoelectric Ceramics .................. 119
2.4 Basic Piezoceramic Characteristics .................... 119
2.5 Electromechanical Constitutive Equations .............. 122
2.5.1 Piezoceramic Actuator Equations ................ 124
2.5.2 Piezoceramic Sensor Equations .................. 130
2.5.3 Alternate Forms of the Constitutive Equations .. 134
2.5.4 Piezoelectric Coupling Coefficients ............ 137
2.5.5 Actuator Performance and Load Line Analysis .... 140
2.6 Hysteresis and Nonlinearities in Piezoelectric
Materials ............................................. 145
2.7 Piezoceramic Actuators ................................ 146
2.7.1 Behavior under Static Excitation Fields ........ 147
2.7.2 Behavior under Dynamic Excitation Fields ....... 154
2.7.3 Depoling Behavior and Dielectric Breakdown ..... 161
2.7.4 Power Consumption .............................. 163
2.8 Equivalent Circuits to Model Piezoceramic Actuators ... 170
2.8.1 Curie Temperature .............................. 172
2.8.2 Cement-Based Piezoelectric Composites .......... 172
2.8.3 Shape Memory Ceramic Actuators ................. 172
2.9 Piezoelectric Sensors ................................. 173
2.9.1 Basic Sensing Mechanism ........................ 174
2.9.2 Bimorph as a Sensor ............................ 175
2.9.3 Signal-Conditioning Electronics ................ 176
2.9.4 Sensor Calibration ............................. 181
3 Shape Memory Alloys (SMAs) ................................. 194
3.1 Fundamentals of SMA Behavior .......................... 197
3.1.1 Phase Transformation ........................... 197
3.1.2 Lattice Structure and Deformation Mechanism .... 198
3.1.3 Low-Temperature Stress-Strain Curve ............ 200
3.1.4 Origin of the One-Way SME ...................... 201
3.1.5 Stress-Induced Martensite and
Pseudoelasticity ............................... 203
3.1.6 Two-Way SME .................................... 208
3.1.7 АН-Round SME ................................... 212
3.1.8 R-Phase Transformation ......................... 213
3.1.9 Porous SMA ..................................... 214
3.2 Constrained Behavior of SMA ........................... 214
3.2.1 Free Recovery .................................. 215
3.2.2 Constrained Recovery ........................... 215
3.2.3 Effective Load Lines of an SMA Wire Actuator ... 216
3.3 Constitutive Models ................................... 217
3.4 Quasi-Static Macroscopic Phenomenological
Constitutive Models ................................... 217
3.4.1 Tanaka Model ................................... 218
3.4.2 Liang and Rogers Model ......................... 220
3.4.3 Brinson Model .................................. 221
3.4.4 Boyd and Lagoudas Model ........................ 227
3.4.5 Other SMA Models ............................... 228
3.5 Testing of SMA Wires .................................. 229
3.5.1 Sample Preparation, Cycling, and Annealing ..... 229
3.5.2 Transformation Temperatures under Zero Stress .. 231
3.5.3 Variation of Transformation Temperatures with
Stress ......................................... 233
3.5.4 Stress-Strain Behavior at Constant
Temperature .................................... 236
3.5.5 Stress-Temperature Behavior at Constant
Strain ......................................... 238
3.5.6 Comparison of Resistive Heating and External
Heating ........................................ 241
3.6 Obtaining Critical Points and Model Parameters
from Experimental Data ................................ 243
3.7 Comparison of Constitutive Models with Experiments .... 246
3.8 Constrained Recovery Behavior (Stress versus
Temperature) at Constant Strain ....................... 249
3.8.1 Worked Example ................................. 251
3.8.2 Worked Example ................................. 253
3.9 Damping Capacity of SMA ............................... 256
3.10 Differences in Stress-Strain Behavior in Tension and
Compression ........................................... 258
3.11 Non-Quasi-Static Behavior ............................. 259
3.11.1 Stress-Relaxation .............................. 260
3.11.2 Effect of Strain Rate .......................... 261
3.11.3 Modeling Non-Quasi-Static Behavior ............. 261
3.11.4 Rate Form of Quasi-Static SMA Constitutive
Models ......................................... 263
3.11.5 Thermomechanical Energy Equilibrium ............ 264
3.11.6 Cyclic Loading ................................. 268
3.12 Power Requirements for SMA Activation ................. 269
3.12.1 Power Input: Resistance Behavior of SMA Wires .. 269
3.12.2 Heat Absorbed by the SMA Wire .................. 271
3.12.3 Heat Dissipation ............................... 272
3.13 Torsional Analysis of SMA Rods and Tubes .............. 272
3.13.1 Validation with Test Data ...................... 276
3.13.2 Constrained Recovery Behavior .................. 279
3.14 Composite Structures with Embedded SMA Wires .......... 281
3.14.1 Variable Stiffness Composite Beams ............. 282
3.14.2 SMA-in-Sleeve Concept .......................... 284
3.14.3 Beams with Embedded SMA Wires .................. 286
3.14.4 Power Requirements for Activation of SMA in
Structures ..................................... 289
3.14.5 Fabrication of Variable Stiffness Composite
Beams .......................................... 292
3.14.6 Experimental Testing of Variable Stiffness
Beams .......................................... 294
3.15 Concluding Remarks .................................... 297
4 Beam Modeling with Induced-Strain Actuation ................ 305
4.1 Material Elastic Constants ............................ 305
4.2 Basic Definitions: Stress, Strains, and
Displacements ......................................... 312
4.2.1 Beams .......................................... 315
4.2.2 Transverse Deflection of Uniform Isotropic
Beams .......................................... 318
4.3 Simple Blocked-Force Beam Model (Pin Force Model) ..... 320
4.3.1 Single Actuator Characteristics ................ 320
4.3.2 Dual Actuators: Symmetric Actuation ............ 321
4.3.3 Single Actuator: Asymmetric Actuation .......... 327
4.3.4 Unequal Electric Voltage (Vtop ≠ Vbottom) ....... 329
4.3.5 Dissimilar Actuators: Piezo Thickness (tCtop ≠
tCbottom) ....................................... 330
4.3.6 Dissimilar Actuators: Piezo Constants
(d31top ≠ d31bottom) ............................ 332
4.3.7 Worked Example ................................. 333
4.4 Uniform-Strain Model .................................. 337
4.4.1 Dual Actuators: Symmetric Actuation ............ 338
4.4.2 Single Actuator: Asymmetric Actuation .......... 347
4.4.3 Unequal Electric Voltage (Vtop ≠ Vbottom) ....... 354
4.4.4 Dissimilar Actuators: Piezo Thickness (tCtop ≠
tCbottom) ....................................... 355
4.4.5 Dissimilar Actuators: Piezo Constants (d31top ≠
d31bottom) ............................. 355
4.4.6 Worked Example ................................. 356
4.5 Euler-Bernoulli Beam Model ............................ 361
4.5.1 Dual Actuators: Symmetric Actuation ............ 361
4.5.2 Single Actuator: Asymmetric Actuation .......... 368
4.5.3 Unequal Electric Voltage (Vtop ≠ Vbottom) ....... 370
4.5.4 Dissimilar Actuators: Piezo Thickness (tCtop ≠
tCbottom) ....................................... 371
4.5.5 Dissimilar Actuators: Piezo Constants (d31top ≠
d31bottom) ...................................... 371
4.5.6 Worked Example ................................. 372
4.5.7 Bimorph Actuators .............................. 375
4.5.8 Induced Beam Response Using Euler-Bernoulli
Modeling ....................................... 377
4.5.9 Embedded Actuators ............................. 379
4.5.10 Worked Example ................................. 381
4.6 Testing of a Beam with Surface-Mounted
Piezoactuators ........................................ 383
4.6.1 Actuator Configuration ......................... 383
4.6.2 Beam Configuration and Wiring of Piezo ......... 383
4.6.3 Procedure ...................................... 384
4.6.4 Measurement of Tip Slope ....................... 384
4.6.5 Data Processing ................................ 385
4.7 Extension-Bending-Torsion Beam Model .................. 385
4.8 Beam Equilibrium Equations ............................ 391
4.9 Energy Principles and Approximate Solutions ........... 391
4.9.1 Energy Formulation: Uniform-Strain Model ....... 392
4.9.2 Energy Formulation: Euler-Bernoulli Model ...... 395
4.9.3 Galerkin Method ................................ 397
4.9.4 Worked Example ................................. 399
4.9.5 Worked Example ................................. 400
4.9.6 Rayleigh-Ritz Method ........................... 401
4.9.7 Worked Example ................................. 405
4.9.8 Worked Example ................................. 406
4.9.9 Energy Formulation: Dynamic Beam Governing
4 Equation Derived from Hamilton's Principle ................. 408
4.10 Finite Element Analysis with Induced-Strain
Actuation ............................................. 411
4.10.1 Behavior of a Single Element ................... 412
4.10.2 Assembly of Global Mass and Stiffness
Matrices ....................................... 415
4.10.3 Beam Bending with Induced-Strain Actuation ..... 416
4.10.4 Worked Example ................................. 418
4.11 First-Order Shear Deformation Theory (FSDT) for
Beams with Induced-Strain Actuation ................... 420
4.11.1 Formulation of the FSDT for a Beam ............. 421
4.11.2 Shear Correction Factor ........................ 423
4.11.3 Transverse Deflection of Uniform Isotropic
Beams Including Shear Correction ............... 424
4.11.4 Induced Beam Response Using Timoshenko Shear
Model .......................................... 426
4.11.5 Energy Formulation: FSDT ....................... 429
4.12 Layer-Wise Theories ................................... 431
4.13 Review of Beam Modeling ............................... 432
5 Plate Modeling with Induced-Strain Actuation ............... 446
5.1 Classical Laminated Plate Theory (CLPT) Formulation
without Actuation ..................................... 446
5.1.1 Stress-Strain Relations for a Lamina at an
Arbitrary Orientation .......................... 448
5.1.2 Macromechanical Behavior of a Laminate ......... 450
5.1.3 Resultant Laminate Forces and Moments .......... 452
5.1.4 Displacements-Based Governing Equations ........ 456
5.1.5 Boundary Conditions ............................ 458
5.2 Plate Theory with Induced-Strain Actuation ............ 460
5.2.1 Isotropic Plate: Symmetric Actuation
(Extension) .................................... 463
5.2.2 Isotropic Plate: Antisymmetric Actuation
(Bending) ...................................... 465
5.2.3 Worked Example ................................. 467
5.2.4 Single-Layer Specially Orthotropic Plate
(Extension) .................................... 469
5.2.5 Single-Layer Specially Orthotropic Plate
(Bending) ...................................... 471
5.2.6 Single-Layer Generally Orthotropic Plate
(Extension) .................................... 472
5.2.7 Single-Layer Generally Orthotropic Plate
(Bending) ...................................... 473
5.2.8 Multilayered Symmetric Laminate Plate .......... 474
5.2.9 Multilayered Antisymmetric Laminate Plate ...... 477
5.2.10 Summary of Couplings in Plate Stiffness
Matrices ....................................... 480
5.2.11 Worked Example ................................. 481
5.3 Classical Laminated Plate Theory (CLPT) Equations in
Terms of Displacements ................................ 486
5.4 Approximate Solutions Using Energy Principles ......... 488
5.4.1 Galerkin Method ................................ 489
5.4.2 Rayleigh-Ritz Method ........................... 490
5.4.3 Symmetric Laminated Plate Response ............. 492
5.4.4 Laminated Plate with Induced-Strain Actuation .. 494
5.4.5 Laminated Plate with Antisymmetric Layup:
Extension-Torsion Coupling ..................... 499
5.4.6 Laminated Plate with Symmetric Layup:
Bending-Torsion Coupling ....................... 502
5.4.7 Worked Example ................................. 506
5.4.8 Worked Example ................................. 512
5.4.9 Worked Example ................................. 517
5.5 Coupling Efficiency ................................... 521
5.5.1 Extension-Torsion Coupling Efficiency .......... 521
5.5.2 Bending-Torsion Coupling Efficiency ............ 523
5.5.3 Comparison of Extension-Torsion and
Bending-Torsion Coupling ....................... 524
5.6 Classical Laminated Plate Theory (CLPT) with
Induced-Strain Actuation for a Dynamic Case ........... 527
5.7 Refined Plate Theories ................................ 531
5.8 Classical Laminated Plate Theory (CLPT) for
Moderately Large Deflections .......................... 533
5.9 First-Order Shear Deformation Plate Theory (FSDT)
with Induced-Strain Actuation ......................... 538
5.10 Shear Correction Factors .............................. 542
5.11 Effect of Laminate Kinematic Assumptions on Global
Response .............................................. 545
5.11.1 Effect of Two-Dimensional Mesh Density on the
Computed Global Response ....................... 549
5.11.2 Pure-Extension Problem (Equal Voltages to Top
and Bottom Actuators) .......................... 550
5.11.3 Pure-Bending Problem (Actuators Subjected to
Equal but Opposite Voltages) ................... 552
5.12 Effect of Transverse Kinematic Assumptions on Global
Response .............................................. 554
5.12.1 Case I: Pure-Extension Actuation ............... 555
5.12.2 Case II: Pure-Bending Actuation ................ 559
5.13 Effect of Finite Thickness Adhesive Bond Layer ........ 562
5.13.1 Case I: Pure-Extension Actuation ............... 563
5.13.2 Case II: Pure-Bending Actuation ................ 565
5.14 Strain Energy Distribution ............................ 565
5.15 Review of Plate Modeling .............................. 573
6 Magnetostrictives and Electrostrictives .................... 581
6.1 Magnetostriction ...................................... 581
6.2 Review of Basic Concepts in Magnetism ................. 584
6.2.1 Magnetic Field В and the Biot-Savart Law ....... 585
6.2.2 Current Carrying Conductors .................... 586
6.2.3 Magnetic Flux Ф and Magnetic Field Intensity
H .............................................. 590
6.2.4 Interaction of a Current Carrying Conductor
and a Magnetic Field ........................... 591
6.2.5 Magnetization M, Permeability μ, and the
B-H Curve ...................................... 592
6.2.6 Demagnetization ................................ 595
6.2.7 Electrical Impedance ........................... 596
6.2.8 Systems of Units ............................... 596
6.2.9 Magnetic Circuits .............................. 597
6.3 Mechanism of Magnetostriction ......................... 599
6.3.1 Definition of Crystal Axes and Magnetic
Anisotropy ..................................... 599
6.3.2 Origin of the Magnetostrictive Effect .......... 601
6.3.3 Effect of Magnetic Field Polarity .............. 603
6.3.4 Effect of External Stresses .................... 605
6.3.5 Effect of Temperature .......................... 607
6.3.6 Strain Hysteresis .............................. 608
6.4 Constitutive Relations ................................ 609
6.4.1 Linear Piezomagnetic Equations ................. 611
6.4.2 Refined Magnetostrictive Models ................ 613
6.4.3 Preisach Model ................................. 614
6.4.4 Energy Methods ................................. 615
6.5 Material Properties ................................... 616
6.5.1 Magnetomechanical Coupling ..................... 617
6.5.2 Worked Example ................................. 621
6.5.3 Delta-E Effect ................................. 622
6.5.4 Magnetostrictive Composites .................... 624
6.6 Magnetostrictive Actuators ............................ 625
6.6.1 Generation of the Magnetic Field ............... 627
6.6.2 Construction of a Typical Actuator ............. 627
6.6.3 Measurement of Magnetic Field .................. 628
6.6.4 DC Bias Field .................................. 629
6.6.5 Design of the Magnetic Field Generator for
a Magnetostrictive Actuator .................... 630
6.6.6 Worked Example: Design of a Magnetic Field
Generator for a Magnetostrictive Actuator ...... 634
6.6.7 Power Consumption and Eddy Current Losses ...... 636
6.6.8 Magnetostrictive Particulate Actuators ......... 639
6.7 Magnetostrictive Sensors .............................. 639
6.7.1 Worked Example ................................. 640
6.8 Iron-Gallium Alloys ................................... 641
6.9 Magnetic Shape Memory Alloys .......................... 643
6.9.1 Basic Mechanism ................................ 644
6.9.2 Effect of an External Magnetic Field ........... 645
6.9.3 Effect of an External Stress ................... 645
6.9.4 Behavior under a Combination of Magnetic
Field and Compressive Stress ................... 646
6.9.5 Dynamic Response ............................... 649
6.9.6 Comparison with SMAs ........................... 649
6.9.7 Experimental Behavior .......................... 651
6.9.8 MSMA Constitutive Modeling ..................... 653
6.9.9 Linear Actuator ................................ 655
6.9.10 Design of the Magnetic Field Generator
(E-Frame) ...................................... 656
6.9.11 Worked Example: Design of a Magnetic Field
Generator (E-Frame) ............................ 659
6.10 Electrostrictives ..................................... 662
6.10.1 Constitutive Relations ......................... 666
6.10.2 Behavior under Static Excitation Fields ........ 670
6.10.3 Behavior under Dynamic Excitation Fields ....... 673
6.10.4 Effect of Temperature .......................... 676
6.11 Polarization .......................................... 677
6.12 Young's Modulus ....................................... 678
6.13 Summary and Conclusions ............................... 678
7 Electrorheological and Magnetorheological Fluids ........... 685
7.1 Fundamental Composition and Behavior of ER/MR Fluids .. 686
7.1.1 Compostion of ER/MR Fluids ..................... 687
7.1.2 Viscosity ...................................... 687
7.1.3 Origin of the Change in Viscosity .............. 688
7.1.4 Yield Behavior ................................. 690
7.1.5 Temperature Dependence ......................... 692
7.1.6 Dynamic Behavior and Long-Term Effects ......... 692
7.1.7 Comparison of ER and MR Fluids ................. 693
7.2 Modeling of ER/MR Fluid Behavior and Device
Performance ........................................... 694
7.2.1 Equivalent Viscous Damping ..................... 695
7.2.2 Bingham Plastic Model .......................... 696
7.2.3 Herschel-Bulkley Model ......................... 697
7.2.4 Biviscous Model ................................ 697
7.2.5 Hysteretic Biviscous ........................... 698
7.2.6 Other Models ................................... 699
7.3 ER and MR Fluid Dampers ............................... 700
7.4 Modeling of ER/MR Fluid Dampers ....................... 704
7.4.1 Rectangular Flow Passage ....................... 705
7.4.2 Worked Example: Herschel-Bulkley Fluid Model ... 718
7.4.3 Worked Example: Bingham Biplastic Fluid Model .. 721
7.4.4 Annular Flow Passage ........................... 725
7.4.5 Squeeze Mode ................................... 734
7.5 Summary and Conclusions ............................... 735
8 Applications of Active Materials in Integrated Systems ..... 739
8.1 Summary of Applications ............................... 739
8.1.1 Space Systems .................................. 741
8.1.2 Fixed-Wing Aircraft and Rotorcraft ............. 741
8.1.3 Civil Structures ............................... 741
8.1.4 Machine Tools .................................. 742
8.1.5 Automotive ..................................... 742
8.1.6 Marine Systems ................................. 742
8.1.7 Medical Systems ................................ 742
8.1.8 Electronic Equipment ........................... 742
8.1.9 Rail ........................................... 743
8.1.10 Robots ......................................... 743
8.1.11 Energy Harvesting .............................. 743
8.2 Solid-State Actuation and Stroke Amplification ........ 743
8.2.1 Amplification by Means of Special Geometry or
Arrangement of the Active Material ............. 744
8.2.2 Amplification by External Leverage Mechanisms .. 755
8.2.3 Torsional Actuators ............................ 758
8.3 Double-Lever (L-L) Actuator ........................... 761
8.3.1 Positioning of the Hinges ...................... 761
8.3.2 Actuation Efficiency: Stiffness of the
Actuator, Support, and Linkages ................ 762
8.4 Energy Density ........................................ 769
8.4.1 Worked Example ................................. 770
8.5 Stroke Amplification Using Frequency Rectification:
The Piezoelectric Hybrid Hydraulic Actuator ........... 772
8.5.1 Inchworm Motors ................................ 773
8.5.2 Ultrasonic Piezoelectric Motors ................ 774
8.5.3 Hybrid Hydraulic Actuation Concept ............. 775
8.5.4 Operating Principles ........................... 778
8.5.5 Active Material Load Line ...................... 779
8.5.6 Pumping Cycle .................................. 780
8.5.7 Energy Transfer ................................ 782
8.5.8 Work Done Per Cycle ............................ 785
8.5.9 Maximum Output Work ............................ 786
8.5.10 Prototype Actuator ............................. 787
8.5.11 Experimental Testing ........................... 790
8.5.12 Modeling Approaches ............................ 796
8.5.13 Transmission-Line Approach ..................... 804
8.6 Smart Helicopter Rotor ................................ 810
8.6.1 Model-Scale Active Rotors ...................... 812
8.6.2 Full-Scale Active Rotors ....................... 817
8.6.3 Adaptive Controllers for Smart Rotors .......... 819
8.7 SMA Actuated Tracking Tab for a Helicopter Rotor ...... 823
8.7.1 Actuator Design Goals .......................... 824
8.7.2 Construction and Operating Principle ........... 825
8.7.3 Blade Section Assembly ......................... 828
8.7.4 Modeling of the Device ......................... 828
8.7.5 Parametric Studies and Actuator Design ......... 831
8.7.6 Results of Parametric Studies .................. 832
8.7.7 Testing and Performance of the System .......... 834
8.8 Tuning of Composite Beams ............................. 837
8.8.1 Fabrication of Composite Beams with SMA in
Embedded Sleeves ............................... 837
8.8.2 Dynamic Testing of Composite Beams with SMA
Wires .......................................... 838
8.8.3 Free Vibration Analysis of Composite Beams
with SMA Wires ................................. 838
8.8.4 Calculation of the Spring Coefficient of SMA
Wire under Tension ............................. 840
8.8.5 Correlation with Test Data ..................... 841
8.9 Shunted Piezoelectrics ................................ 842
8.9.1 Principle of Operation ......................... 843
8.9.2 Types of Shunt Circuits ........................ 847
8.9.3 Worked Example ................................. 858
8.9.4 Worked Example ................................. 859
8.9.5 Worked Example ................................. 860
8.10 Energy Harvesting ..................................... 863
8.10.1 Vibration-Based Energy Harvesters .............. 863
8.10.2 Wind-Based Energy Harvesters ................... 864
8.10.3 Modeling of Piezoelectric Energy Harvesters .... 864
8.10.4 Worked Example ................................. 870
8.10.5 Worked Example ................................. 872
8.10.6 Worked Example ................................. 876
8.11 Constrained Layer Damping ............................. 877
8.11.1 Active Constrained Layer Damping ............... 880
8.12 Interior Noise Control ................................ 884
Index ......................................................... 897
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