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This book features a comprehensive discussion of the mathematical foundations of ultrasonic nondestructive testing of materials. The authors include a brief description of the theory of acoustic and electromagnetic fields to underline the similarities and differences with respect to elastodynamics. They also cover vector, elastic plane, and Rayleigh surface waves as well as ultrasonic beams, inverse scattering, and ultrasonic nondestructive imaging. A coordinate-free notation system is used that is easier to understand and navigate than standard index notation.
Langenberg, Karl-Jörg; Marklein, René; Mayer, Klaus
Contents. Mathematical Foundations. Governing Equations of Elastodynamics. Constitutive Equations; Governing Equations; Elastodynamic Energy Conservation. Acoustics. Electromagnetism. Vector Wave Equations. Elastic Plane Waves in Homogeneous Materials. Reflection, Transmission and Mode Conversion of Elastic Plane Waves at Planar Boundaries between Homogeneous Non-Dissipative Materials. Rayleigh Surface Waves. Plane Wave Spatial Spectrum. Ultrasonic Beams and Wave Packets. Point Sources in Homogeneous Isotropic Infinite Space; Elastodynamic Source Fields. Force Density and Dilatation Rate Sources on Surfaces of Homogeneous Isotropic Half-Spaces; Radiation Fields of Piezoelectric Transducers. Scatterers in Homogeneous Isotropic Non-Dissipative Infinite Spaces. Inverse Scattering: US-NDT Imaging.
