Ultrasound and Elastic Waves (eBook)

Cover 1
Contents 8
List of Figures 12
Preface 18
Acknowledgments 22
Chapter 1. Introduction 24
What is Ultrasonics? 24
How has UT Technology Progressed? 24
What Are Some Current Industrial/Manufacturing Applications of UT? 25
What Are the Major Medical Applications of UT? 28
What Are Some Unique Applications of UT? 30
Chapter 2. Definitions and Background 32
What is a Wave? 32
What are the Quantitative Measures of a Wave? 37
What is Elasticity? 40
What are the Units of Elasticity, Density, and Wavespeed? 45
Chapter 3. Wave Propagation Concepts 48
What are the Types of Elastic Waves? 48
What is a UT Beam? 58
How Does a Propagating Wave Change? 63
Chapter 4. Wave Interactions 68
How Do Two or More Waves Interact? 68
How Does a Wave Interact with a Nonuniform Object? 84
Chapter 5. Hardware: Equipment Concepts 88
Chapter 6. Software: Data Processing 108
What Does Software Do? 108
A. What are the Types of Time-Domain Analyses? 109
B. What Are the Types of Spectral Analysis? 124
C. What Statistical Measurements Are Taken? 131
D. What Is Imaging? 140
Appendix 1. Stress, Strain, and Elasticity (Also Vectors and Tensors) 144
A. Elasticity 144
B. Stress 145
C. Strain 151
D. Alternative Indicial Notation 153
Appendix 2. The Generalized Hooke's Law 154
A. Hooke's Law 154
B. Stiffness in Rotated Axes 155
C. Special Classes of Elastic Materials 156
Appendix 3. States of Stress or Strain in Waves 162
A. States of Uniaxial Stress or Strain 162
B. Uniaxial Stress–Strain Relationships 166
Appendix 4. Balance of Forces and Newton's Law of Inertia 170
A. One-Dimensional System 171
B. Three-Dimensional Systems 171
Appendix 5. Theory of Wave Propagation 174
A. One-Dimensional Systems 174
B. Three–Dimensional Systems 177
C. Wave Excitations 178
Appendix 6. Solutions to the Wave Equations 182
A. Fundamental Solution Types 182
B. Separation of Variables 186
C. Plane Waves in Two or Three Dimensions 186
D. Plane Wave Solutions 188
Appendix 7. Dispersion, Group Velocity 192
A. Wave Propagation in Viscoelastic Media 193
B. Wave Propagation in a Thick Rod 194
C. Bending Waves 195
Appendix 8. Transducer Beam Forming 198
A. Simplified Analysis of Beam Forming 198
B. Analysis of Radial Variation over Beam 199
C. Analysis of Axial Variation of BeamStrength 203
Appendix 9. Solutions for Anisotropy 206
A. Wavespeed 207
B. Material (Particle) Motion and the Principal Directions (Vectors) 209
C. Special Cases 210
D. Group Velocity 214
Appendix 10. Oblique Interactions between Waves and Boundaries 218
A. Oblique Free-Surface Reflection of a Longitudinal Wave 218
B. Oblique Free Surface Reflection of a Transverse Wave 221
C. Refraction (Oblique Transmission) of a Longitudinal or Transverse Wave 223
D. Rayleigh Waves 224
Appendix 11. Lateral Stress and Strain in Rods under Axial Loads 228
A. Simple Approximation for Thin Rods 228
B. The Mindlin–Herrmann Approximation 229
Appendix 12 Bending Waves in Beams and Plates 234
A. Bending of Beams 234
B. Thin Plates 240
Appendix 13 Time-Domain Analysis 244
A. The Hilbert Transform and the Analytic Envelope and Phase 244
B. Time-Domain Signal Conditioning 246
References 252
Index 254