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

183 Pages·2010·0.995 MB·English

by  John G. Harris

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

Elastic Waves at High Frequencies
Techniques for Radiation and Diffraction
of Elastic and Surface Waves
JOHN G. HARRIS
Late, University of Illinois at Urbana–Champaign
Edited and Prepared for Publication by
GARETH I. BLOCK
Flemington, NJ
RICHARD V. CRASTER
University of Alberta
ANTHONY M. J. DAVIS
University of California, San Diego
PAUL A. MARTIN
Colorado School of Mines
ANDREW N. NORRIS
Rutgers University
CAMBRIDGE UNIVERSITY PRESS
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Cambridge University Press
The Edinburgh Building, Cambridge CB2 8RU, UK
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridge.org/9780521875301
© J. G. Harris 2010
This publication is in copyright. Subject to statutory exception and to the
provision of relevant collective licensing agreements, no reproduction of any part
may take place without the written permission of Cambridge University Press.
First published in print format 2010
ISBN-13 978-0-511-78982-3 eBook (NetLibrary)
ISBN-13 978-0-521-87530-1 Hardback
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and does not guarantee that any content on such websites is, or will remain,
accurate or appropriate.
Do not go gentle into that good night,
Old age should burn and rave at close of day;
Rage, rage against the dying of the light.
Though wise men at their end know dark is right,
Because their words had forked no lightning they
Do not go gentle into that good night.
Do not go gentle into that good night
ByDylanThomas,fromTHEPOEMSOFDYLAN
THOMAS,copyright(cid:2)c1952byDylanThomas.
ReprintedbypermissionofNewDirections
PublishingCorp.andJ.M.Dent&SonsLtd.

Contents
Foreword page ix
1 Linear elastic waves 1
1.1 Model equations 1
1.2 Continuity and boundary conditions 6
1.3 Flux of energy 6
1.4 The Fourier and Laplace transforms 9
1.5 A wave is not a vibration 12
1.6 Dispersive propagation 15
1.7 General references 20
2 Canonical acoustic-wave problems 23
2.1 Radiation from a piston in an infinite baffle 23
2.2 Diffraction of an acoustic plane wave by an edge 40
2.3 Summary 50
3 Canonical elastic-wave problems 52
3.1 The scattering of a spherical wave from a fluid–solid
interface 52
3.2 Rayleigh–Lamb modes and Rayleigh surface waves 62
4 Radiation and impedance 71
4.1 Reciprocity 71
4.2 Green’s tensor 72
4.3 Reciprocity revisited 78
4.4 Force on a particle from an elastic wave 79
5 Integral equations for crack scattering 81
5.1 Formulation 81
5.2 A hypersingular integral equation 84
5.3 Low-frequency scattering 86
vii
viii Contents
5.4 Some strategies 88
5.5 Flat cracks as a special case 88
5.6 Flat cracks: direct approach 89
5.7 Flat cracks: how to compute [u] 91
5.8 Curved cracks 93
6 Scanned acoustic imaging 96
6.1 Scanned, reflection acoustic microscope 97
6.2 Fresnel and F number 99
6.3 Converging spherical wave 99
6.4 Focused acoustic beam 101
6.5 Scattered focused beam 103
6.6 An electromechanical reciprocity relation 109
6.7 Measurement model 113
6.8 Acoustic material signature 116
6.9 Summary 119
7 Acoustic diffraction in viscous fluids 121
7.1 Theory 121
7.2 Diffraction by a half-plane 123
7.3 Scattering of a spherical wave at a plane interface 127
7.4 Diffraction by an elastic sphere 130
8 Near-cut-off behavior in waveguides 133
8.1 Shear horizontal and acoustic waveguides 133
8.2 Elastic waveguides 136
8.3 Long waves 138
Appendix A Asymptotic expansions 147
Appendix B Some special functions 154
References 157
Index 163