126,99 €
Mehr erfahren.
- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
Elastic waves are used in fields as diverse as the non-destructive evaluation of materials, medicine, seismology and telecommunications. Elastic Waves in Solids 2 analyzes the radiation, scattering and generation of these waves. It studies the emission of bulk or surface waves from sources localized on the surface of an isotropic or anisotropic solid. It then examines the scattering of a longitudinal or transverse elastic wave by one or more cylindrical or spherical heterogeneities. Finally, it explores the methods and devices used to generate and detect elastic waves, using the piezoelectric effect or the interaction with a laser beam. Accompanying figures illustrate these properties, and the text provides the orders of magnitude of some characteristic parameters. This book is intended for students completing a master's degree in acoustics, mechanics, geophysics or engineering, as well as teachers and researchers in these disciplines.
Sie lesen das E-Book in den Legimi-Apps auf:
Seitenzahl: 288
Veröffentlichungsjahr: 2022
Ähnliche
Table of Contents
Cover
Title Page
Copyright
Preface
List of Main Symbols
1 Radiation of Elastic Waves
1.1. Acoustic radiation in a fluid
1.2. Generation of elastic waves by a surface source
1.3. Radiation of elementary spherical sources
2 Scattering of Elastic Waves
2.1. Acoustic scattering by an immersed cylinder
2.2. Scattering of elastic waves by a cylinder
2.3. Scattering of elastic waves by a spherical particle
2.4. Scattering by a set of particles
3 Generation and Detection
3.1. Piezoelectric transducer for bulk waves
3.2. Piezoelectric transducer for surface waves
3.3. Generation by laser impact
3.4. Optical measurement of mechanical displacements
Appendix 1: Developments in Cylindrical and Spherical Harmonics
A1.1. Cylindrical harmonics
A1.2. Spherical harmonics
Appendix 2: Matrix Representation of a Dioptric System
A2.1. Diffraction matrix
A2.2. Emission, admittance and reception matrices
A2.3. Isotropic solid
References
Index
Wiley End User License Agreement
List of Tables
Chapter 1
Table 1.1. Piston mode: main operating regimes
Chapter 3
Table 3.1. Velocity (V), acoustic impedance (Z), electromechanical coupling coef...
Table 3.2. Characteristics of piezoelectric pseudo-surface acoustic waves
Guide
Cover
Table of Contents
Title Page
Copyright
Preface
List of Main Symbols
Begin Reading
Appendix 1: Developments in Cylindrical and Spherical Harmonics
Appendix 2: Matrix Representation of a Dioptric System
References
Index
End User License Agreement
Pages
v
iii
iv
vii
viii
ix
xi
xii
xiii
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
185
186
187
188
189
190
191
192
193
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
211
212
213
214
215
216
217
218
Series Editors
Pierre-Noël Favennec† and Frédérique de Fornel
Elastic Waves in Solids 2
Radiation, Scattering, Generation
Tony Valier-Brasier
Daniel Royer
First published 2022 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:
ISTE Ltd
27-37 St George’s Road
London SW19 4EU
UK
www.iste.co.uk
John Wiley & Sons, Inc.
111 River Street
Hoboken, NJ 07030
USA
www.wiley.com
© ISTE Ltd 2022
The rights of Tony Valier-Brasier and Daniel Royer to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s), contributor(s) or editor(s) and do not necessarily reflect the views of ISTE Group.
Library of Congress Control Number: 2022931520
British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-78630-815-3
Preface
In Volume 1 (Royer and Valier-Brasier 2022), the propagation of elastic waves was studied in isotropic, anisotropic, piezoelectric or viscoelastic solids. The phenomena of reflection and transmission of bulk waves at one or more interfaces were analyzed in detail. A wide variety of elastic waves propagating on a free surface or at the interface between a solid and a fluid, or between two solids, were presented. Finally, the properties of various types of waves guided in most usual structures (plate, ribbon, cylinder) were established. In addition to these general developments, the objective of this second volume is to analyze the radiation, scattering and generation of elastic waves.
Plane waves are not physically realizable because, in practice, sources are of finite dimensions. Acoustic waves generated by a real device diverge, so that their amplitude decreases with the distance from the transmitter. The understanding of radiation from sources is therefore necessary to predict the acoustic field emitted by the transducers used in imaging and measurement systems. In Chapter 1, we start by studying the acoustic radiation in a fluid emitted by a vibrating surface having the shape of a disc or a spherical cup, respectively, modeling a planar or a focused transducer. Then, we study the radiation emitted by a multi-element antenna such as those used in ultrasound imaging systems. In the second section, we analyze the radiation of elastic waves, in an isotropic or anisotropic solid, by sources located on its surface. The generation of bulk and Rayleigh waves by a linear distribution of normal or tangential impulsive forces, modeling a seismic or a thermoelastic source, is examined. The last section is devoted to the radiation of an elementary spherical source embedded in an isotropic matrix.
Phenomena related to the scattering of elastic waves by various targets are developed in Chapter 2. The scattering theory accounts for different phenomena observed in Volume 1 (refraction, transmission, absorption) in a global way. The scattered waves propagate away from the target, possibly in preferred directions, even if the medium is isotropic. As in other areas of physics, scattering phenomena are characterized by a cross-section, which can be calculated in the case of cylindrical or spherical scatterers. In the first section, the target is a cylinder immersed in a perfect fluid; the incident wave is therefore longitudinal. The two examples studied explain some phenomena, such as the shadow behind a rigid cylinder in the geometric regime, or the existence of circumferential waves propagating around an elastic cylinder in the resonant regime. The second section is devoted to the scattering of elastic waves by a cylinder buried in a solid matrix, and the third section is devoted to the scattering by a sphere. In the case of a sphere, strong monopolar and dipolar resonances are highlighted. The multiple scattering by a set of particles is discussed at the end of this chapter, with the determination of the effective wave number of coherent waves propagating in heterogeneous media. For small concentration of particles, this effective wave number is close to that of the host medium and contains information on the scattering by a single particle.
In Chapter 3, we investigate the generation and detection of bulk and surface elastic waves. The most efficient and widespread technique for generating and detecting free bulk waves in a solid or a liquid, and also elastic guided waves in a plate or a cylinder, is to exploit the inverse and direct piezoelectric effects. The operating principle and the structure of transducers are described according to the frequency range. Their performances and their domain of application are specified. The properties of active materials commonly used (polarized piezoceramic or piezocomposite, piezoelectric polymer or single crystal) are given. In the second section, we analyze the generation and detection of surface acoustic waves, directly on a piezoelectric substrate, by transducers composed of two comb-shaped electrodes. Several models are developed to explain how these interdigital transducers operate. Their impulse and frequency responses, and their efficiency, are evaluated. The last two sections are devoted to optical methods, first the excitation of elastic waves by photothermal effects and second the detection of mechanical displacements by laser interferometry. The spatiotemporal characteristics of transmitted bulk and Rayleigh waves are given. These laser-based ultrasonic techniques present some advantages: they do not require any mechanical contact with the propagation medium; they can reach very high frequency domains and very small wavelengths. Therefore, they can be used for material evaluation at a large distance or with a high spatial resolution.
The authors would like to thank for their assistance in the preparation of this book:
– Claire Prada, Director of Research at the CNRS, at the Institute Langevin Ondes et Images;
– Jean-Marc Conoir, Director of Research at the CNRS, at the Institute Jean le Rond d’Alembert.
Tony VALIER-BRASIER
Daniel ROYER
February 2022
List of Main Symbols
a,b
: amplitude of the waves.
c
ijkl
(
C
I J
): stiffnesses (Voigt notation).
D
: directivity factor.
: electric induction (displacement) vector.
E
: Young modulus.
: electric field vector.
e
k
(e
p
)
: kinetic (potential) energy per unit volume.
e
ijk
(εij)
: piezoelectric (dielectric) constants.
: force density per unit mass.
H(t)
: Heaviside step function.
I
: acoustic intensity.
: Poynting vector.
K
: bulk modulus.
: wave vector (number).
K
M
: electromechanical coupling coefficient (mode M).
: unit vector normal to a surface.
: unit vector of the propagation direction.
P
: transported power.
p
a
: acoustic pressure.
p(p
0
)
thermodynamic pressure (at rest).
: polarization vectors.
P
s
(p
s
)
: power supplied by the source (per unit volume).
r(t)
: amplitude reflection (transmission) coefficients.
R(T): intensity reflection (transmission) coefficients.
s: entropy per unit volume.
: phase slowness vector.
T
absolute temperature.
: mechanical traction, stress vector.
U
: internal energy per unit volume.
: mechanical displacement vector.
: particle velocity vector.
: energy velocity vector.
V(V
g
)
: phase (group) velocity.
V
L
(V
T
)
: velocity of longitudinal (transverse) bulk waves.
W(w)
: work (per unit volume).
: position vector.
X, Y, Z
: crystallographic axes.
Z
e
(Y)
: electrical impedance (admittance).
: acoustic (mechanical) impedance.
α
: attenuation coefficient.
: elastic (piezoelectric) Christoffel tensor.
δ
ij
: Kronecker’s symbol.
δ(t)
: Dirac function.
: linearized strain tensor (piezoelectric solid).
η
: viscosity coefficient.
θ
i, r, t
: angle of incidence, reflection, transmission.
Θ: dilatation.
κ
: bulk wave velocity ratio (VT /VL).
λ, μ
: Lamé constants.
v
: Poisson’s ratio.
ρ
: mass density.
ρ
e
(σ
e
)
: electric charge density per unit volume (area).
σ(σ
d
)
: effective (differential) scattering cross-section.
: Cauchy stress tensor.
: scalar (vector) potential.
Φ: electric potential.
χ
: decay factor.
ω
: angular frequency.
