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E-raamat: Integral Transform Techniques for Green's Function

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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.

1 Definition of Integral Transforms and Distributions
1(32)
1.1 Integral Transforms
1(5)
1.2 Distributions and Their Integration Formulas
6(5)
1.3 Branch Cut and Argument of Square Root Functions
11(17)
1.3.1 Square Root Function 1: g(z) = √z - Z0
11(3)
1.3.2 Square Root Function 2: g(z) = √z2 - z20
14(14)
1.4 Comments on Inversion Techniques and Integration Formulas
28(5)
References
32(1)
2 Green's Functions for Laplace and Wave Equations
33(44)
2.1 1D Impulsive Source
33(5)
2.2 1D Time-Harmonic Source
38(6)
2.3 2D Static Source
44(5)
2.4 2D Impulsive Source
49(2)
2.5 2D Time-Harmonic Source
51(17)
2.6 3D Static Source
68(2)
2.7 3D Impulsive Source
70(3)
2.8 3D Time-Harmonic Source
73(4)
Appendix
76(1)
References
76(1)
3 Green's Dyadic for an Isotropic Elastic Solid
77(44)
3.1 2D Impulsive Source
79(8)
3.2 2D Time-Harmonic Source
87(2)
3.3 2D Static Source
89(7)
3.4 3D Impulsive Source
96(11)
3.5 3D Time-Harmonic Source
107(1)
3.6 3D Static Source
108(1)
3.7 Torsional Source
109(12)
3.7.1 Ring Source
110(3)
3.7.2 Point Torque Source
113(3)
Appendix
116(3)
References
119(2)
4 Acoustic Wave in a Uniform Flow
121(18)
4.1 Compressive Viscous Fluid
121(2)
4.2 Linearization
123(3)
4.3 Viscous Acoustic Fluid
126(3)
4.4 Wave Radiation in a Uniform Flow
129(6)
4.5 Time-Harmonic Wave in a Uniform Flow
135(4)
References
137(2)
5 Green's Functions for Beam and Plate
139(14)
5.1 An Impulsive Load on a Beam
139(3)
5.2 A Moving Time-Harmonic Load on a Beam
142(3)
5.3 An Impulsive Load on a Plate
145(3)
5.4 A Time-Harmonic Load on a Plate
148(5)
Appendix
152(1)
References
152(1)
6 Cagniard-de Hoop Technique
153(52)
6.1 2D Anti-plane Deformation
154(8)
6.2 2D In-plane Deformation
162(16)
6.3 3D Dynamic Lamb's Problem
178(27)
References
204(1)
7 Miscellaneous Green's Functions
205(56)
7.1 2D Static Green's Dyadic for an Orthotropic Elastic Solid
205(8)
7.2 2D Static Green's Dyadic for an Inhomogeneous Elastic Solid
213(9)
7.2.1 2D Kelvin's Solution for Homogeneous Media
221(1)
7.3 Green's Function for Torsional Waves in a Monoclinic Material
222(5)
7.4 Reflection of a Transient SH-Wave at a Moving Boundary
227(15)
7.5 Wave Scattering by a Rigid Inclusion in an Inhomogeneous Elastic Solid
242(11)
7.6 An Excellent Application of Cauchy Complex Integral
253(8)
References
260(1)
Index 261
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