Electromagneto-Mechanics of Material Systems and Structures

About the Author ix

Preface xi

Acknowledgments xiii

1 Introduction 1

References 2

2 Conducting Material Systems and Structures 5

2.1 Basic Equations of Dynamic Magnetoelasticity 5

2.2 Magnetoelastic Plate Vibrations and Waves 7

2.2.1 Classical Plate Bending Theory 9

2.2.2 Mindlin's Theory of Plate Bending 13

2.2.3 Classical Plate Bending Solutions 16

2.2.4 Mindlin Plate Bending Solutions 23

2.2.5 Plane Strain Plate Solutions 26

2.3 Dynamic Magnetoelastic Crack Mechanics 32

2.4 Cracked Materials Under Electromagnetic Force 40

2.5 Summary 45

References 45

3 Dielectric/Ferroelectric Material Systems and Structures 47

Part 3.1 Dielectrics 47

3.1 Basic Equations of Electroelasticity 48

3.2 Static Electroelastic Crack Mechanics 49

3.2.1 Infinite Dielectric Materials 49

3.2.2 Dielectric Strip 57

3.3 Electroelastic Vibrations and Waves 60

3.4 Dynamic Electroelastic Crack Mechanics 68

3.5 Summary 72

Part 3.2 Piezoelectricity 72

3.6 Piezomechanics and Basic Equations 73

3.6.1 Linear Theory 73

3.6.2 Model of Polarization Switching 77

3.6.3 Model of Domain Wall Motion 80

3.6.4 Classical Lamination Theory 82

3.7 Bending of Piezoelectric Laminates 90

3.7.1 Bimorphs 90

3.7.2 Functionally Graded Bimorphs 100

3.7.3 Laminated Plates 111

3.8 Electromechanical Field Concentrations 113

3.8.1 Laminates 113

3.8.2 Disk Composites 123

3.8.3 Fiber Composites 126

3.8.4 MEMS Mirrors 136

3.9 Cryogenic and High-Temperature Electromechanical Responses 140

3.9.1 Cryogenic Electromechanical Response 140

3.9.2 High-Temperature Electromechanical Response 147

3.10 Electric Fracture and Fatigue 149

3.10.1 Fracture Mechanics Parameters 150

3.10.2 Cracked Rectangular Piezoelectric Material 173

3.10.3 Indentation Fracture Test 185

3.10.4 Modified Small Punch Test 189

3.10.5 Single-Edge Precracked Beam Test 193

3.10.6 Double Torsion Test 201

3.10.7 Fatigue of SEPB Specimens 203

3.11 Summary 212

References 213

4 Ferromagnetic Material Systems and Structures 219

Part 4.1 Ferromagnetics 219

4.1 Basic Equations of Magnetoelasticity 220

4.1.1 Soft Ferromagnetic Materials 220

4.1.2 Magnetically Saturated Materials 221

4.1.3 Electromagnetic Materials 222

4.2 Magnetoelastic Instability 224

4.2.1 Buckling of Soft Ferromagnetic Material 225

4.2.2 Buckling of Magnetically Saturated Material 228

4.2.3 Bending of Soft Ferromagnetic Material 231

4.3 Magnetoelastic Vibrations and Waves 233

4.3.1 Vibrations and Waves of Soft Ferromagnetic Material 233

4.3.2 Vibrations and Waves of Magnetically Saturated Material 243

4.4 Magnetic Moment Intensity Factor 250

4.4.1 Simply Supported Plate Under Static Bending 251

4.4.2 Fixed-End Plate Under Static Bending 252

4.4.3 Infinite Plate Under Dynamic Bending 255

4.5 Tensile Fracture and Fatigue 256

4.5.1 Cracked Rectangular Soft Ferromagnetic Material 257

4.5.2 Fracture Test 261

4.5.3 Fatigue Crack Growth Test 263

4.6 Summary 265

Part 4.2 Magnetostriction 265

4.7 Basic Equations of Magnetostriction 265

4.8 Nonlinear Magneto-Mechanical Response 267

4.8.1 Terfenol-D/Metal Laminates 267

4.8.2 Terfenol-D/PZT Laminates 270

4.9 Magnetoelectric Response 272

4.10 Summary 273

References 273

Index 277

Yasuhide Shindo, Tohoku University, Japan