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

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  • Edition: Revised
  • Format: Hardcover
  • Copyright: 2010-09-06
  • Publisher: Cambridge University Press
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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.

Table of Contents

Forewordp. ix
Linear elastic wavesp. 1
Model equationsp. 1
Continuity and boundary conditionsp. 6
Flux of energyp. 6
The Fourier and Laplace transformsp. 9
A wave is not a vibrationp. 12
Dispersive propagationp. 15
General referencesp. 20
Canonical acoustic-wave problemsp. 23
Radiation from a piston in an infinite bafflep. 23
Diffraction of an acoustic plane wave by an edgep. 40
Summaryp. 50
Canonical elastic-wave problemsp. 52
The scattering of a spherical wave from a fluid-solid interfacep. 52
Rayleigh-Lamb modes and Rayleigh surface wavesp. 62
Radiation and impedancep. 71
Reciprocityp. 71
Green's tensorp. 72
Reciprocity revisitedp. 78
Force on a particle from an elastic wavep. 79
Integral equations for crack scatteringp. 81
Formulationp. 81
A hypersingular integral equationp. 84
Low-frequency scatteringp. 86
Some strategiesp. 88
Flat cracks as a special casep. 88
Flat cracks: direct approachp. 89
Flat cracks: how to compute [u]p. 91
Curved cracksp. 93
Scanned acoustic imagingp. 96
Scanned, reflection acoustic microscopep. 97
Fresnel and F numberp. 99
Converging spherical wavep. 99
Focused acoustic beamp. 101
Scattered focused beamp. 103
An electromechanical reciprocity relationp. 109
Measurement modelp. 113
Acoustic material signaturep. 116
Summaryp. 119
Acoustic diffraction in viscous fluidsp. 121
Theoryp. 121
Diffraction by a half-planep. 123
Scattering of a spherical wave at a plane interfacep. 127
Diffraction by an elastic spherep. 130
Near-cut-off behavior in waveguidesp. 133
Shear horizontal and acoustic waveguidesp. 133
Elastic waveguidesp. 136
Long wavesp. 138
Asymptotic expansionsp. 147
Some special functionsp. 154
Referencesp. 157
Indexp. 163
Table of Contents provided by Ingram. All Rights Reserved.

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