Integral Transform Techniques for Green's Function (eBook)

Preface to the Second Edition 7
Preface 8
Contents 11
1 Definition of Integral Transforms and Distributions 13
1.1 Integral Transforms 13
1.2 Distributions and Their Integration Formulas 18
1.3 Branch Cut and Argument of Square Root Functions 23
1.3.1 Square Root Function 1: /varvec{g}{(z)} = /sqrt {z - z_{0} } 23
1.3.2 Square Root Function 2: /bi g(z) = /sqrt {z^{2} - z_{0}^{2} } 26
1.4 Comments on Inversion Techniques and Integration Formulas 40
References 44
2 Green's Functions for Laplace and Wave Equations 45
2.1 1D Impulsive Source 45
2.2 1D Time-Harmonic Source 50
2.3 2D Static Source 56
2.4 2D Impulsive Source 61
2.5 2D Time-Harmonic Source 63
2.6 3D Static Source 80
2.7 3D Impulsive Source 82
2.8 3D Time-Harmonic Source 85
Appendix 88
References 88
3 Green's Dyadic for an Isotropic Elastic Solid 89
3.1 2D Impulsive Source 91
3.2 2D Time-Harmonic Source 99
3.3 2D Static Source 101
3.4 3D Impulsive Source 108
3.5 3D Time-Harmonic Source 119
3.6 3D Static Source 120
3.7 Torsional Source 121
3.7.1 Ring Source 122
3.7.2 Point Torque Source 125
Appendix 128
References 131
4 Acoustic Wave in a Uniform Flow 132
4.1 Compressive Viscous Fluid 132
4.2 Linearization 134
4.3 Viscous Acoustic Fluid 137
4.4 Wave Radiation in a Uniform Flow 140
4.5 Time-Harmonic Wave in a Uniform Flow 146
References 148
5 Green's Functions for Beam and Plate 149
5.1 An Impulsive Load on a Beam 149
5.2 A Moving Time-Harmonic Load on a Beam 152
5.3 An Impulsive Load on a Plate 155
5.4 A Time-Harmonic Load on a Plate 158
Appendix 162
References 162
6 Cagniard-de Hoop Technique 163
6.1 2D Anti-plane Deformation 164
6.2 2D In-plane Deformation 172
6.3 3D Dynamic Lamb's Problem 188
References 214
7 Miscellaneous Green's Functions 215
7.1 2D Static Green's Dyadic for an Orthotropic Elastic Solid 215
7.2 2D Static Green's Dyadic for an Inhomogeneous Elastic Solid 223
7.2.1 2D Kelvin's Solution for Homogeneous Media 231
7.3 Green's Function for Torsional Waves in a Monoclinic Material 232
7.4 Reflection of a Transient SH-Wave at a Moving Boundary 237
7.5 Wave Scattering by a Rigid Inclusion in an Inhomogeneous Elastic Solid 252
7.6 An Excellent Application of Cauchy Complex Integral 263
References 270
Index 271