Elastic Waves in Solids, Volume 2

Tony Valier-Brasier is a lecturer at the Jean Le Rond d’Alembert Institute at Sorbonne University in Paris, France. His research focuses on the propagation of elastic waves in multiple scattering media, as well as on guided waves. Daniel Royer is a visiting professor at the Institut Langevin (Ondes et Images) in Paris, France. His research focuses on the propagation of guided elastic waves and their generation and detection by optical methods.

Preface vii

List of Main Symbols xi

Chapter 1. Radiation of Elastic Waves 1

1.1. Acoustic radiation in a fluid 1

1.1.1. Integral formulation of the Helmholtz equation 3

1.1.2. Rayleigh integral 5

1.1.3. Rayleigh–Sommerfeld integral 8

1.1.4. Harmonic case 8

1.1.5. Impulse diffraction 20

1.2. Generation of elastic waves by a surface source 32

1.2.1. Solid with orthotropic symmetry 34

1.2.2. Far field 36

1.2.3. Generation in a plate 48

1.3. Radiation of elementary spherical sources 52

1.3.1. Pulsating sphere 53

1.3.2. Oscillating sphere with a rotational motion 54

1.3.3. Oscillating sphere with a translational motion 55

Chapter 2. Scattering of Elastic Waves 59

2.1. Acoustic scattering by an immersed cylinder 63

2.1.1. Scattering by a rigid cylinder 65

2.1.2. Scattering by an elastic cylinder 68

2.1.3. Circumferential waves 71

2.2. Scattering of elastic waves by a cylinder 73

2.3. Scattering of elastic waves by a spherical particle 77

2.3.1. General formulation of the problem 77

2.3.2. Scattering of a longitudinal plane wave 78

2.3.3. Scattering of a transverse plane wave 85

2.4. Scattering by a set of particles 92

2.4.1. Scalar theory of multiple scattering 93

2.4.2. Velocity and attenuation of coherent waves 100

Chapter 3. Generation and Detection 105

3.1. Piezoelectric transducer for bulk waves 106

3.1.1. Materials and structures 106

3.1.2. One-dimensional model, equivalent circuits 110

3.1.3. Frequency and impulse responses – emitted power 117

3.1.4. Electrical impedance, efficiency 122

3.2. Piezoelectric transducer for surface waves 125

3.2.1. Operating principle 126

3.2.2. Impulse response model 132

3.2.3. Three-port circuit (hexapole): scattering matrix 139

3.2.4. Coupled modes method 143

3.3. Generation by laser impact 154

3.3.1. Thermoelastic regime 156

3.3.2. Ablation regime 166

3.4. Optical measurement of mechanical displacements 169

3.4.1. Non-interferometric methods 169

3.4.2. Interferometric methods 172

3.4.3. Doppler velocimetry 177

3.4.4. Picosecond acoustics 181

Appendix 1 185

Appendix 2 195

References 201

Index 207