Ultrasonic nondestructive testing of materials

Ultrasonic Nondestructive Testing of Materials: Theoretical Foundations explores the mathematical foundations and emerging applications of this testing process, which is based on elastic wave propagation in isotropic and anisotropic solids. In covering ultrasonic nondestructive testing methods, the book emphasizes the engineering point of view, yet it relies on the physics and mathematics aspects involved in elastic wave propagation theory.

As a result, this resource becomes a missing link in the literature by combining coverage of the theoretical aspects of testing and providing intuitive assessments of numerous standard problems to illustrate fundamental assertions. Content includes a brief description of the theory of acoustic and electromagnetic fields to underline the similarities and differences as compared to elastodynamics. It also covers vector algebra and analysis, elastic plane and Rayleigh surface waves, and ultrasonic beams, as well as transducer radiation, inverse scattering, and ultrasonic nondestructive imaging.

Although ultrasonic nondestructive testing can often be roughly understood in terms of plane waves and beams, this book addresses the key issues of transducer radiation and defect scattering and imaging, respectively. The authors physically formulate point source synthesis, and, in mathematical terms, they use representation integrals with Green functions, always including intuitive interpretations with mathematical evaluations.

Replacing cumbersome index notation with a coordinate-free version, this reference offers step-by-step documentation of relevant tensorial elastodynamic cases involving isotropic and anisotropic materials. It provides all necessary mathematical tools readers require to understand the mathematical and physical basis for ultrasonic nondestructive testing.

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