John G. Harris intended to explain in this book the special techniques required to model the radiation and diffraction of elastic and surface waves. He sadly 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 Wiener-Hopf technique, the effects of viscosity on acoustic diffraction, and the phenomenon of channelling of wave energy along guided structures.
Author(s): Harris J.G.
Series: Cambridge Monographs on Mechanics
Publisher: CUP
Year: 2008
Language: English
Pages: 183
Tags: Механика;Механика жидкостей и газов;
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Foreword......Page 11
1.1 Model equations......Page 19
1.3 Flux of energy......Page 24
1.4 The Fourier and Laplace transforms......Page 27
1.5 A wave is not a vibration......Page 30
1.6 Dispersive propagation......Page 33
1.7 General references......Page 38
2.1 Radiation from a piston in an infinite baffle......Page 41
2.2 Diffraction of an acoustic plane wave by an edge......Page 58
2.3 Summary......Page 68
3.1 The scattering of a spherical wave from a fluid–solid interface......Page 70
3.2 Rayleigh–Lamb modes and Rayleigh surface waves......Page 80
4.1 Reciprocity......Page 89
4.2 Green's tensor......Page 90
4.3 Reciprocity revisited......Page 96
4.4 Force on a particle from an elastic wave......Page 97
5.1 Formulation......Page 99
5.2 A hypersingular integral equation......Page 102
5.3 Low-frequency scattering......Page 104
5.5 Flat cracks as a special case......Page 106
5.6 Flat cracks: direct approach......Page 107
5.7 Flat cracks: how to compute [u]......Page 109
5.8 Curved cracks......Page 111
6 Scanned acoustic imaging......Page 114
6.1 Scanned, reflection acoustic microscope......Page 115
6.3 Converging spherical wave......Page 117
6.4 Focused acoustic beam......Page 119
6.5 Scattered focused beam......Page 121
6.6 An electromechanical reciprocity relation......Page 127
6.7 Measurement model......Page 131
6.8 Acoustic material signature......Page 134
6.9 Summary......Page 137
7.1 Theory......Page 139
7.2 Diffraction by a half-plane......Page 141
7.3 Scattering of a spherical wave at a plane interface......Page 145
7.4 Diffraction by an elastic sphere......Page 148
8.1 Shear horizontal and acoustic waveguides......Page 151
8.2 Elastic waveguides......Page 154
8.3 Long waves......Page 156
Appendix A Asymptotic expansions......Page 165
Appendix B Some special functions......Page 172
References......Page 175
Index......Page 181
