Introduction

Contents Flow Chart

Mathematical Foundations

Scalar, Vector and Tensor Fields

Vektor and Tensor Analysis

Time and Spatial Spectral Analysis with Fourier Transforms

Delta Function

Governing Equations of Elastodynamics

NewtonCauchy Equation of Motion and Deformation Rate Equation in the

Time and Frequency Domain

Physical Foundations

Transition and Boundary Conditions

Constitutive Equations; Governing Equations; Elastodynamic Energy

Conservation

Materialgleichungen

Linear NonDissipative Materials: CauchyHooke Law

Elastodynamic Energy Conservation Theorem for NonDissipative

Materials in the Time and Frequency Domain

Linear Dissipative Materials

Piezoelectricity and Magnetostriction

Acoustics

Governing Equations of Acoustics

Transition and Boundary Conditions

Wave Equations in the Time and Frequency Domain

Solutions of the Homogeneous Acoustic Wave Equations in Homogeneous

Materials: Plane Longitudinal Pressure Waves

Acoustic Source Fields in Homogeneous Materials: Point Source

Synthesis with Green Functions

Hygens Principle for Acoustic Scattered Fields in Homogeneous

Materials

Electromagnetism

Maxwell Equations; Poynting Vector; Lorentz Force

Transition and Boundary Conditions

Constitutive Equations: Permittivity, Permeability; Dissipation:

Susceptibility Kernels, Conductivity

Wave Equations in the Time and Frequency Domain

Solutions of Homogeneous Electromagnetic Wave Equations in

Homogeneous Isotropic Materials: Plane Transverse Electromagnetic

Waves

Electromagnetic Source Fields in Homogeneous Isotropic Materials;

Tensor Electromagnetic Green Functions

Electromagnetic Scattered Fields; Electromagnetic Formulation of

Huygens Principle

TwoDimensional Electromagnetism: TM and TEDecoupling

Vector Wave Equations

Wave Equations for Anisotropic and Isotropic NonDissipative

Materials

Helmholtz Decomposition for Homogeneous Isotropic Materials: Pressure

and Shear Waves

Decoupling of Scalar SHWaves for Inhomogeneous Isotropic

TwoDimensional

Materials

Frequency Domain Wave Equations for NonDissipative and Dissipative

Materials

Elastic Plane Waves in Homogeneous Materials

Homogeneous Plane Waves in Isotropic NonDissipative Materials

Inhomogeneous Plane Waves in Isotropic NonDissipative Materials

Plane Waves in Anisotropic NonDissipative Materials

Plane Waves in Isotropic Dissipative Materials

Reflection, Transmission and Mode Conversion of Elastic Plane Waves at Planar Boundaries between Homogeneous NonDissipative Materials

StressFree Planar Boundary of a Homogeneous Isotropic

NonDissipative Elastic HalfSpace

Planar Boundary between Homogeneous Isotropic NonDissipative Elastic

HalfSpaces

Planar Boundary between a Homogeneous Isotropic NonDissipative and a

Homogeneous Transversely Isotropic NonDissipative HalfSpace and a

Homogeneous Transversely Isotropic NonDissipative Half Space

Rayleigh Surface Waves

Planar Surfaces

Slightly Curved Surfaces

Plane Wave Spatial Spectrum

Acoustic Plane Wave Spatial Spectrum

Elastic Plane Wave Spatial Spectrum

Ultrasonic Beams and Wave Packets

Gaussian Beams as Paraxial Approximation of a Spatial Plane Wave

Spectrum

Pulsed Beams as Exact Solutions of an Approximate Wave Equation

Pulsed Beams as Approximate Solutions of Eikonal and Transport Equations

Point Sources in Homogeneous Isotropic Infinite Space; Elastodynamic

Source Fields

Homogeneous Infinite Space Scalar Green Function

Homogeneous Isotropic Infinite Space Green Tensors of Elastodynamics

Two and ThreeDimensional Elastodynamic Source Fields

Elementary Spherical Waves and Plane Waves

Force Density and Dilatation Rate Sources on Surfaces of Homogeneous

Isotropic HalfSpaces; Radiation Fields of Piezoelectric Transducers

Acoustic HalfSpaces with Soft or Rigid Surfaces

StripLike Normal and Tangential Force Density Distributions on the

StressFree Surface of an elastic HalfSpace: Plane Wave Spectral

DecomposItion of the TwoDimensional Second Rank Green Tensor

Force Densities on the Surface of a StressFree HalfSpace

Circular Normal Force Force Density Distribution on the StressFree

Surface of an Elastic HalfSpace: Point Source Characteristic

Radiation Fields of Piezoelectric Transducers

Scatterers in Homogeneous Isotropic NonDissipative Infinite Spaces

Huygens' Principle

Integral Equations for Secondary Surface Deformation Sources on

Scatterers with StressFree Surfaces: Displacement Field Integral

Equation and Stress Field Integral Equation

Integral Equations for the Equivalent Sources of Penetrable

Scatterers

Scattering Tensor; FarFields

Inverse Scattering: USNDT Imaging

SAFT: Synthetic Aperture Focusing Technique

FTSAFT: Fourier Transform Synthetic Aperture Focusing Technique
