Dynamics of Smart Structures

DYNAMICS OF SMART\nSTRUCTURES......Page 5
Contents......Page 9
Preface......Page 15
1.1.2 Structure and Classification of Polymers......Page 17
1.1.3 Characteristic Properties of Polymers......Page 18
1.2 Ceramics......Page 19
1.2.1 Properties of Ceramics......Page 20
1.3.1 Micro- and Macrocomposites......Page 21
1.3.4 Short-fibre Composites......Page 22
1.4.2 Electrostrictive, Magnetostrictive and Magnetoresistive......Page 23
1.4.3 The Shape Memory Effect......Page 24
1.5 Survey of Smart Polymeric Materials......Page 25
1.5.3 Electroactive Polymers......Page 26
1.6.2 Magnetically Activated Shape Memory Alloys......Page 27
1.7.2 Electro- and Magnetorheological Fluids......Page 28
1.9 Optical Fibres......Page 29
1.10 Smart Structures and Their Applications......Page 30
1.10.3 Structural Health Monitoring......Page 31
2.1 Introduction......Page 35
2.2.1 Resistive Transducers......Page 37
2.2.2 Inductive Transducers......Page 40
2.2.4 Cantilever-type Mechanical Resonator Transducers......Page 43
2.2.5 Eddy Current Transducer......Page 44
2.2.7 Transduction Mechanisms in Materials......Page 45
2.2.8 Hydrodynamic and Acoustic Transduction Mechanisms......Page 48
2.2.9 Transducer Sensitivities, Scaling Laws for Example Devices......Page 49
2.2.10 Modelling and Analysis of a Piezoelectric Transducer......Page 50
2.3 Actuation of Flexible Structures......Page 54
2.3.1 Pre-stressed Piezoelectric Actuators......Page 55
2.3.2 Shape Memory Material-based Actuators......Page 59
2.4.2 Analysis of a Typical Resonant Sensor......Page 60
2.4.3 Piezoelectric Accelerometers......Page 64
2.4.4 The Sensing of Rotational Motion......Page 67
2.4.5 The Coriolis Angular Rate Sensor......Page 69
2.5.2 Physical Principles of Fibre-optic Transducers......Page 71
2.5.3 Optical Fibres......Page 76
2.5.5 Fibre-optic Transducers for Structural Control......Page 80
3.2.1 Introduction to Time Domain Methods......Page 91
3.2.2 Transformations of State Variables......Page 93
3.2.3 Solution of the State Equations......Page 94
3.2.4 State Space and Transfer Function Equivalence......Page 96
3.2.5 State Space Realizations of Transfer Functions......Page 97
3.3.1 Stability, Eigenvalues and Eigenvectors......Page 98
3.3.2 Controllability and Observability......Page 99
3.3.4 Transformation of State Space Representations......Page 101
3.4 Shaping the Dynamic Response Using Feedback Control......Page 102
3.5 Modelling of the Transverse Vibration of Thin Beams......Page 104
3.5.1 Vibrations of Cantilever Beam......Page 110
3.5.2 Vibrations of Simply Supported, Slender Uniform Beam......Page 113
3.6 Externally Excited Motion of Beams......Page 114
3.7 Closed-loop Control of Flexural Vibration......Page 116
4.1.1 Nature of Acoustic Waves......Page 133
4.1.3 Features of Acoustic Waves......Page 134
4.2.1 Plane Waves......Page 135
4.2.2 Linear and Non-linear Waveforms......Page 138
4.2.3 Energy and Intensity......Page 139
4.2.5 Transmission and Reflection of Plane Waves at an Interface......Page 140
4.3.1 The Transmission Line......Page 141
4.3.2 The Ideal Transmission Line......Page 142
4.3.3 Matched Lines......Page 143
4.3.4 Reflection from the End of a Transmission Line: Standing Waves......Page 144
4.3.5 The Mechanical Transmission Line: An Electro-mechanical Analogy......Page 147
4.3.6 Dissipation of Waves in Transmission Lines......Page 148
4.4.1 Definition of Stress and Strain......Page 151
4.4.2 Linear Elastic Materials......Page 154
4.4.3 Equations of Wave Motion in an Elastic Medium......Page 158
4.4.4 Plane Waves in an Infinite Solid......Page 159
4.4.5 Spherical Waves in an Infinite Medium......Page 161
4.4.6 Transmission Line Model for Wave Propagation in Isotropic Solids......Page 162
4.4.7 Surface Waves in Semi-infinite Solids......Page 164
5.1 Flexural Vibrations of Plates......Page 177
5.2 The Effect of Flexure......Page 179
5.3 Vibrations in Plates of Finite Extent: Rectangular Plates......Page 184
5.4 Vibrations in Plates of Finite Extent: Circular Plates......Page 190
5.5 Vibrations of Membranes......Page 194
6.1 Introduction......Page 203
6.2 Piezoelectric Crystalline Media......Page 208
6.2.1 Electromechanically Active Piezopolymers......Page 212
6.3 Wave Propagation in Piezoelectric Crystals......Page 213
6.3.1 Normal Modes of Wave Propagation in Crystalline Media......Page 216
6.3.2 Surface Wave Propagation in Piezoelectric Crystalline Media......Page 218
6.3.3 Influence of Coordinate Transformations on Elastic Constants......Page 219
6.3.4 Determination of Piezoelectric Stiffened Coefficients......Page 223
6.4.1 Transmission Line Model for Wave Propagation in Non-piezoelectric Crystalline Solids......Page 226
6.4.2 Transmission Line Model for Wave Propagation in Piezoelectric Crystalline Solids......Page 229
6.5 Discrete Element Model of Thin Piezoelectric Transducers......Page 230
6.5.1 One-port Modelling of Thin Piezoelectric Transducers......Page 234
6.5.2 Two-port Modelling of a Piezoelectric Diaphragm Resting on a Cavity......Page 235
6.5.3 Modelling of a Helmholtz-type Resonator Driven by a Piezoelectric Disc Transducer......Page 236
6.5.4 Modelling of Ultrasonic Wave Motors......Page 239
6.6 The Generation of Acoustic Waves......Page 242
6.6.1 Launching and Sensing of SAWs in Piezoelectric Media......Page 245
6.6.2 Wave Propagation in Periodic Structures......Page 248
7.1 Mechanics of Composite Laminated Media......Page 257
7.1.2 Orthotropic, Transverse Isotropic and Isotropic Elastic Laminae......Page 258
7.1.3 Axis Transformations......Page 261
7.1.4 Laminate Constitutive Relationships......Page 262
7.1.5 Dynamics of Laminated Structures......Page 266
7.1.6 Equations of Motion of an Orthotropic Thin Plate......Page 267
7.1.7 First-order Shear Deformation Theory......Page 270
7.1.8 Composite Laminated Plates: First-order Zig-zag Theory......Page 271
7.1.9 Elastic Constants Along Principal Directions......Page 275
7.2 Failure of Fibre Composites......Page 277
7.3 Flexural Vibrations in Laminated Composite Plates......Page 280
7.3.1 Equations of Motion of Continuous Systems in Principal Coordinates: The Energy Method......Page 281
7.3.2 Energy Methods Applied to Composite Plates......Page 284
7.4 Dynamic Modelling of Flexible Structures......Page 285
7.4.2 Equivalent Circuit Modelling......Page 286
7.5.1 Frequency Domain Modelling for Control......Page 287
7.5.2 Design for Controllability......Page 293
8.1.1 Basic Thermodynamic Concepts......Page 307
8.2 The Shape Memory Effect: The Phase-transformation Kinetics......Page 309
8.2.1 Pseudo-elasticity......Page 310
8.2.3 One-way and Two-way Shape Memory Effects......Page 312
8.2.4 Superelasticity......Page 313
8.3 Non-linear Constitutive Relationships......Page 314
8.3.1 The Shape Memory Alloy Constitutive Relationships......Page 315
8.4 Thermal Control of Shape Memory Alloys......Page 317
8.5.1 The Nature of Hysteresis......Page 318
8.5.3 Hysteresis Modelling: The Hysteron......Page 319
8.5.4 Modelling the Martensite Fraction–temperature Hysteresis......Page 324
8.5.5 Decomposition of Hysteretic Systems......Page 325
8.6 Constitutive Relationships for Non-linear and Hysteretic Media......Page 326
8.7.1 Simulation and Inverse Modelling of Shape Memory Alloy Actuators......Page 328
8.7.2 Control of Shape Memory Alloy Actuators......Page 330
9.2 Controller Synthesis for Structural Control......Page 337
9.2.1 Problems Encountered in Structural Control: Spillover, Model Uncertainty, Non-causal Compensators and Sensor Noise......Page 338
9.2.2 Concepts of Stability......Page 339
9.2.3 Passive Controller Synthesis......Page 343
9.2.4 Active Controller Synthesis and Compensation......Page 346
9.2.5 Reduced-order Modelling: Balancing......Page 352
9.2.6 Zero-spillover Controller Synthesis......Page 354
9.3.1 The Basis for Performance Metric Optimization-based Controller Synthesis......Page 356
9.3.2 Optimal H  Control: Problem Definition and Solution......Page 360
9.3.3 Optimal Control Synthesis: Linear Matrix Inequalities......Page 362
9.4 Optimal Design of Structronic Systems......Page 366
9.4.1 Optimal Robust Design of Controlled Structures......Page 367
9.4.2 Optimum Placement and Co-location of the Sensor and Actuators: The Active Clamp......Page 373
9.4.3 Optimal Controller Design Applied to Smart Composites......Page 377
9.4.4 Optimal Robust Stabilization of Smart Structures......Page 386
9.5 Design of an Active Catheter......Page 391
9.6 Modelling and Control of Machine Tool Chatter......Page 392
9.6.1 Stability Analysis of Machine Tool Chatter......Page 396
9.6.2 Feedback Control of Machine Tool Chatter......Page 398
Index......Page 405