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  SPECIFICATION
ULTRASONIC NONDESTRUCTIVE TESTING OF MATERIALS (hb)2012
Author: KARL JORG LANGENBERG
ISBN: 9781439855881
Year: 2012
Publisher: TAYLOR & FRANCIS BOOK LTD.
Category: MATHEMATICS
Edition: 1
Format: Hard Cover
Language: English
 ABOUT THE TITLE
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.

Includes numerical computations to explain wave propagation phenomena and compare results of analytical formulations

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.

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 TABLE OF 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
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