Elastic Waves at High Frequencies: Techniques

John G. Harris intended to explain in this book the special techniques required to model the radiation and diffraction of elastic and surface waves. Sadly, he died before he could fulfil this ambition, but his plan has been brought to fruition by a team of his distinguished collaborators. The book begins with the basic underlying equations for wave motion and then builds upon this foundation by solving a number of fundamental scattering problems. The remaining chapters provide a thorough introduction to modern techniques that have proven essential to understanding radiation and diffraction at high frequencies. Graduate students, researchers and professionals in applied mathematics, physics and engineering will find that the chapters increase in complexity, beginning with plane-wave propagation and spectral analyses. Other topics include elastic wave theory, the WienerHopf technique, the effects of viscosity on acoustic diffraction, and the phenomenon of channelling of wave energy along guided structures.

Foreword	p. ix
Linear elastic waves	p. 1
Model equations	p. 1
Continuity and boundary conditions	p. 6
Flux of energy	p. 6
The Fourier and Laplace transforms	p. 9
A wave is not a vibration	p. 12
Dispersive propagation	p. 15
General references	p. 20
Canonical acoustic-wave problems	p. 23
Radiation from a piston in an infinite baffle	p. 23
Diffraction of an acoustic plane wave by an edge	p. 40
Summary	p. 50
Canonical elastic-wave problems	p. 52
The scattering of a spherical wave from a fluid-solid interface	p. 52
Rayleigh-Lamb modes and Rayleigh surface waves	p. 62
Radiation and impedance	p. 71
Reciprocity	p. 71
Green's tensor	p. 72
Reciprocity revisited	p. 78
Force on a particle from an elastic wave	p. 79
Integral equations for crack scattering	p. 81
Formulation	p. 81
A hypersingular integral equation	p. 84
Low-frequency scattering	p. 86
Some strategies	p. 88
Flat cracks as a special case	p. 88
Flat cracks: direct approach	p. 89
Flat cracks: how to compute [u]	p. 91
Curved cracks	p. 93
Scanned acoustic imaging	p. 96
Scanned, reflection acoustic microscope	p. 97
Fresnel and F number	p. 99
Converging spherical wave	p. 99
Focused acoustic beam	p. 101
Scattered focused beam	p. 103
An electromechanical reciprocity relation	p. 109
Measurement model	p. 113
Acoustic material signature	p. 116
Summary	p. 119
Acoustic diffraction in viscous fluids	p. 121
Theory	p. 121
Diffraction by a half-plane	p. 123
Scattering of a spherical wave at a plane interface	p. 127
Diffraction by an elastic sphere	p. 130
Near-cut-off behavior in waveguides	p. 133
Shear horizontal and acoustic waveguides	p. 133
Elastic waveguides	p. 136
Long waves	p. 138
Asymptotic expansions	p. 147
Some special functions	p. 154
References	p. 157
Index	p. 163
Table of Contents provided by Ingram. All Rights Reserved.

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Elastic Waves at High Frequencies: Techniques for Radiation and Diffraction of Elastic and Surface Waves

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