Ultrasonic Nondestructive Testing of Materials

Contents 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 Newton-Cauchy 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 Non-Dissipative Materials: Cauchy-Hooke Law Elastodynamic Energy Conservation Theorem for Non-Dissipative 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 Two-Dimensional Electromagnetism: TM- and TE-Decoupling Vector Wave Equations Wave Equations for Anisotropic and Isotropic Non-Dissipative Materials Helmholtz Decomposition for Homogeneous Isotropic Materials: Pressure and Shear Waves Decoupling of Scalar SH-Waves for Inhomogeneous Isotropic Two-Dimensional Materials Frequency Domain Wave Equations for Non-Dissipative and Dissipative Materials Elastic Plane Waves in Homogeneous Materials Homogeneous Plane Waves in Isotropic Non-Dissipative Materials Inhomogeneous Plane Waves in Isotropic Non-Dissipative Materials Plane Waves in Anisotropic Non-Dissipative Materials Plane Waves in Isotropic Dissipative Materials Reflection, Transmission and Mode Conversion of Elastic Plane Waves at Planar Boundaries between Homogeneous Non-Dissipative Materials Stress-Free Planar Boundary of a Homogeneous Isotropic Non-Dissipative Elastic Half-Space Planar Boundary between Homogeneous Isotropic Non-Dissipative Elastic HalfSpaces Planar Boundary between a Homogeneous Isotropic Non-Dissipative and a Homogeneous Transversely Isotropic Non-Dissipative Half-Space and a Homogeneous Transversely Isotropic Non-Dissipative 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 Three-Dimensional Elastodynamic Source Fields Elementary Spherical Waves and Plane Waves Force Density and Dilatation Rate Sources on Surfaces of Homogeneous Isotropic Half-Spaces; Radiation Fields of Piezoelectric Transducers Acoustic Half-Spaces with Soft or Rigid Surfaces Strip-Like Normal and Tangential Force Density Distributions on the StressFree Surface of an elastic Half-Space: Plane Wave Spectral DecomposItion of the Two-Dimensional Second Rank Green Tensor Force Densities on the Surface of a Stress-Free Half-Space Circular Normal Force Force Density Distribution on the Stress-Free Surface of an Elastic Half-Space: Point Source Characteristic Radiation Fields of Piezoelectric Transducers Scatterers in Homogeneous Isotropic Non-Dissipative Infinite Spaces Huygens' Principle Integral Equations for Secondary Surface Deformation Sources on Scatterers with Stress-Free Surfaces: Displacement Field Integral Equation and Stress Field Integral Equation Integral Equations for the Equivalent Sources of Penetrable Scatterers Scattering Tensor; Far-Fields Inverse Scattering: US-NDT Imaging SAFT: Synthetic Aperture Focusing Technique FT-SAFT: Fourier Transform Synthetic Aperture Focusing Technique