Watanabe Integral Transform Techniques for Green's Function

2. Auflage 2015
ISBN: 978-3-319-17455-6
Verlag: Springer Nature Switzerland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 76, 274 Seiten

Reihe: Lecture Notes in Applied and Computational Mechanics

This book describes mathematical techniques for integral transforms in a detailed but concise manner. The techniques are subsequently applied to the standard partial differential equations, such as the Laplace equation, the wave equation and elasticity equations. Green's functions for beams, plates and acoustic media are also shown, along with their mathematical derivations. The Cagniard-de Hoop method for double inversion is described in detail and 2D and 3D elastodynamic problems are treated in full.This new edition explains in detail how to introduce the branch cut for the multi-valued square root function. Further, an exact closed form Green's function for torsional waves is presented, as well as an application technique of the complex integral, which includes the square root function and an application technique of the complex integral.

Autoren/Hrsg.

Watanabe, Kazumi

Inhaltsverzeichnis

1;Preface to the Second Edition;7
2;Preface;8
3;Contents;11
4;1 Definition of Integral Transforms and Distributions;13
4.1;1.1 Integral Transforms;13
4.2;1.2 Distributions and Their Integration Formulas;18
4.3;1.3 Branch Cut and Argument of Square Root Functions;23
4.3.1;1.3.1 Square Root Function 1: \varvec{g}{(z)} = \sqrt {z - z_{0} };23
4.3.2;1.3.2 Square Root Function 2: \bi g(z) = \sqrt {z^{2} - z_{0}^{2} };26
4.4;1.4 Comments on Inversion Techniques and Integration Formulas;40
4.5;References;44
5;2 Green's Functions for Laplace and Wave Equations;45
5.1;2.1 1D Impulsive Source;45
5.2;2.2 1D Time-Harmonic Source;50
5.3;2.3 2D Static Source;56
5.4;2.4 2D Impulsive Source;61
5.5;2.5 2D Time-Harmonic Source;63
5.6;2.6 3D Static Source;80
5.7;2.7 3D Impulsive Source;82
5.8;2.8 3D Time-Harmonic Source;85
5.9;Appendix;88
5.10;References;88
6;3 Green's Dyadic for an Isotropic Elastic Solid;89
6.1;3.1 2D Impulsive Source;91
6.2;3.2 2D Time-Harmonic Source;99
6.3;3.3 2D Static Source;101
6.4;3.4 3D Impulsive Source;108
6.5;3.5 3D Time-Harmonic Source;119
6.6;3.6 3D Static Source;120
6.7;3.7 Torsional Source;121
6.7.1;3.7.1 Ring Source;122
6.7.2;3.7.2 Point Torque Source;125
6.8;Appendix;128
6.9;References;131
7;4 Acoustic Wave in a Uniform Flow;132
7.1;4.1 Compressive Viscous Fluid;132
7.2;4.2 Linearization;134
7.3;4.3 Viscous Acoustic Fluid;137
7.4;4.4 Wave Radiation in a Uniform Flow;140
7.5;4.5 Time-Harmonic Wave in a Uniform Flow;146
7.6;References;148
8;5 Green's Functions for Beam and Plate;149
8.1;5.1 An Impulsive Load on a Beam;149
8.2;5.2 A Moving Time-Harmonic Load on a Beam;152
8.3;5.3 An Impulsive Load on a Plate;155
8.4;5.4 A Time-Harmonic Load on a Plate;158
8.5;Appendix;162
8.6;References;162
9;6 Cagniard-de Hoop Technique;163
9.1;6.1 2D Anti-plane Deformation;164
9.2;6.2 2D In-plane Deformation;172
9.3;6.3 3D Dynamic Lamb's Problem;188
9.4;References;214
10;7 Miscellaneous Green's Functions;215
10.1;7.1 2D Static Green's Dyadic for an Orthotropic Elastic Solid;215
10.2;7.2 2D Static Green's Dyadic for an Inhomogeneous Elastic Solid;223
10.2.1;7.2.1 2D Kelvin's Solution for Homogeneous Media;231
10.3;7.3 Green's Function for Torsional Waves in a Monoclinic Material;232
10.4;7.4 Reflection of a Transient SH-Wave at a Moving Boundary;237
10.5;7.5 Wave Scattering by a Rigid Inclusion in an Inhomogeneous Elastic Solid;252
10.6;7.6 An Excellent Application of Cauchy Complex Integral;263
10.7;References;270
11;Index;271