139,99 €
Mehr erfahren.
- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- 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 1 presents the different modes of propagation of elastic waves in increasingly complex media and structures. It first studies the propagation in an unlimited solid where only the material properties are taken into account. It then analyzes reflection and transmission phenomena at an interface with a fluid or a second solid. It explains the search for propagation modes on a free surface or at the interface between two media. Finally, it proposes a study of the dispersive propagation of elastic waves guided by a plate or a cylinder. 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: 437
Veröffentlichungsjahr: 2022
Ähnliche
Table of Contents
Cover
Title Page
Copyright
Preface
List of Main Symbols
1 Propagation in an Unbounded Solid
1.1. Reviewing the mechanics of continuous media
1.2. Isotropic solid
1.3. Anisotropic solid
1.4. Piezoelectric solid
1.5. Viscoelastic media
2 Reflection and Transmission at an Interface
2.1. Boundary conditions
2.2. Direction and polarization of reflected and transmitted waves
2.3. Isotropic solid: transverse horizontal wave
2.4. Isotropic media: longitudinal and transverse vertical waves
2.5. Anisotropic medium: diffraction matrix
3 Surface Waves and Interface Waves
3.1. Surface waves
3.2. Interface waves
3.3. Bleustein–Gulyaev wave
4 Guided Elastic Waves
4.1. Waveguide, group velocity
4.2. Transverse horizontal waves
4.3. Lamb waves
4.4. Cylindrical guides
Appendix 1 Differential Operators in Cylindrical and Spherical Coordinates
Appendix 2 Symmetry and Tensors
Appendix 3 Transport of Energy
References
Index
End User License Agreement
List of Tables
Chapter 1
Table 1.1. Values of Lamé constants, Young’s modulus, Poisson’s ratio and mass d...
Table 1.2. Bulk wave velocities for various isotropic materials. The media that ...
Table 1.3. Remarkable values for the Poisson’s ratio ν, the bulk modulus K and t...
Table 1.4. Relations between the various elastic constants and the Poisson’s rat...
Table 1.5. Components of the stiffness tensor CIJ for crystals, according to the...
Table 1.6.
Mass density (in kg.m
−3
) and stiffness constants (in GPa) for some an...
Table 1.7. Components of the elastic, piezoelectric and dielectric tensors: | an...
Table 1.8.
Piezoelectric constants (C/m
2
) and dielectric constants (
10
−11
F/m) o...
Chapter 3
Table 3.1. Characteristics of Rayleigh waves for different piezoelectric materia...
Chapter 4
Table 4.1. Cut-off frequency and mechanical displacement of higher order Lamb mo...
Table 4.2. Critical values of the velocity ratio VL/VT, of Poisson’s ratio ν and...
Table 4.3. Characteristic velocities of elastic waves propagating in an isotropi...
Guide
Cover
Table of Contents
Title Page
Copyright
Preface
List of Main Symbols
Begin Reading
Appendix 1 Differential Operators in Cylindrical and Spherical Coordinates
Appendix 2 Symmetry and Tensors
Appendix 3 Transport of Energy
References
Index
End User License Agreement
Pages
v
iii
iv
ix
x
xi
xii
xiii
xiv
xv
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
58
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
104
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
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
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
287
288
289
290
291
292
293
295
296
297
299
300
301
302
303
304
305
306
Series EditorsPierre-Noël Favennec† and Frédérique de Fornel
Elastic Waves in Solids 1
Propagation
Daniel RoyerTony Valier-Brasier
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 Ltd27-37 St George’s RoadLondon SW19 4EUUKwww.iste.co.uk
John Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USAwww.wiley.com
© ISTE Ltd 2022
The rights of Daniel Royer and Tony Valier-Brasier 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: 2021951482
British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-78630-814-6
Preface
This book follows two books co-authored with Eugène Dieulesaint devoted to Elastic Waves in Solids; the first book is subtitled Free and Guided Propagation, and the second, Generation, Acousto-optic Interaction, Applications.
This book is also divided into two volumes. It is designed for students who are pursuing their masters in physics, mechanics or geophysics, as well as for other graduate students, PhD students, engineers, researchers and professors. The objective is to analyze the propagation, interactions and generation of elastic waves in a large variety of solid media and structures. Wherever possible, a common formalism has been used that is applicable to both bulk and surface waves, as well as to guided waves.
Elastic waves are vibrations that propagate in any medium: gaseous, liquid or solid. The term “elastic” is used to describe the mechanical behavior of the propagation medium. When the frequency of these waves is in the audible range (approximately between 20 Hz and 20 kHz), they are commonly called “acoustic waves” or “sound waves”; they are called infrasound or ultrasonic waves if their frequency is below or above this range. The term “acoustics” is often broadly used for anything related to matter waves, regardless of their frequency. Given the earlier specifications, this is not the most appropriate term; however, it has the advantage of defining a discipline, such as mechanics, optics, thermodynamics, and so on. Acoustics is often considered as the oldest of the physical sciences. A brief review of the historical evolution of this field and a summary of the applications of elastic waves are used to explain the contents of this book.
It was known since Poisson’s memoir, published in 1829, that longitudinal or transverse matter waves can propagate in the bulk of an isotropic, elastic solid. At the end of the 19th century, on the earliest seismic recordings, P wave trains (arriving first) and S (or secondary) wave trains were identified with the arrivals of bulk longitudinal waves (the fastest) and bulk transverse waves. A third, late echo was attributed to surface waves, discovered in 1885 by Lord Rayleigh. In the early 20th century, seismic waves were used to study the interior of the Earth and to determine its structure. Therefore, it is not surprising that most elastic waves were discovered by geophysicists and carry their names: Lamb, Love, Stoneley and Scholte waves.
Until 1915 and the research carried out by Paul Langevin and Constantin Chilowsky, earthquakes were the only means for generating these elastic waves, and this phenomenon was hard to reproduce and was quite destructive. However, experiments carried out at the École Supérieure de Physique et de Chimie Industrielles (ESPCI) in Paris, then in the Seine, and finally in Toulon demonstrated that the piezoelectric effect (discovered in 1880 by Pierre and Jacques Curie) could generate ultrasound waves in water and detect the echo reflected by a target. For many decades, quartz was the only piezoelectric crystal used. Given its exceptional mechanical properties and thermal stability, it began to be used in the emerging field of telecommunications to stabilize and filter the frequency of broadcasting transmitters and receivers. The usage of quartz resonators spread after K.S. Van Dyke and D.W. Dye independently developed an equivalent circuit of a piezoelectric resonator.
Following intense research carried out after the Second World War, new piezoelectric materials were developed. These included notably lead zirconate titanate (PZT) ceramics, which could be made piezoelectric by applying an electric field. These materials, whose electromechanical coupling coefficient is much higher than that of quartz, greatly facilitated the generation and detection of elastic waves of frequency lower than 10 MHz. As they could be used to create sensitive transducers of large dimensions and of varied shapes, these ceramics constitute the active elements of transmitters and receivers in sonars and of medical and metallurgical ultrasonic equipment.
In 1965, R.M. White and F.W. Voltmer implemented the idea of generating and detecting surface acoustic waves using two comb-shaped electrodes deposited on a piezoelectric material. The exploitation of this technique led to a series of spectacular applications of Rayleigh waves. These surface acoustic wave filters, which are very compact, can be mass-produced owing to microelectronic technologies and operate in a wide range of frequencies (50 MHz–5 GHz). They have invaded the consumer electronics market, in products such as televisions and mobile phones. The continuous improvement in their performances required the elaboration of new piezoelectric crystals of large dimensions, as well as a finer and finer analysis of the propagation, interaction and generation of surface waves.
From the 1990s onward, we have witnessed a large-scale development of elastic waves in varied domains, such as medical imaging and therapy, non-destructive evaluation of materials, sensors of physical or biological quantities, acoustic detection and localization systems for submarines applications, and for locating and exploring oil fields. These advances have different origins, sometimes involving a combination of factors: the elaboration of composite materials and thin piezoelectric layers, the refinement of high-performance instruments (acoustic microscopes, multi-element transducers), innovative methods (time-reversal acoustics), as well as progress in computer sciences, whether for simulations or running processes. Given the scope of our current text, it is not possible to fully describe these applications, which evolve so fast.
Our objective is to provide the reader with the theoretical bases required to understand these developments, to explore them in detail and to elaborate on other advances. In order to move away from abstraction, the phenomena are illustrated by many figures corresponding to commonly used structures and materials. Furthermore, the text regularly specifies the order of magnitude of physical parameters.
The first volume is divided into four chapters and three appendices. Chapter 1 deals with the propagation of elastic waves in an unbounded solid. In the absence of any boundary, the only problem is to establish the equations for the propagation of a mechanical disturbance and to solve them. However, in order to do this, the constitutive laws for the solid must be known. This solid may be isotropic, anisotropic, piezoelectric, purely elastic or viscoelastic. Chapter 2 focuses on the phenomena of reflection and transmission between two semi-infinite media separated by a planar interface. The propagation equations in each medium must be supplemented by limiting conditions that ensure the connection of the physical quantities on the boundary. Several examples are treated: solid–vacuum interfaces, solid-perfect fluid and isotropic solid-anisotropic crystal. For each configuration, the analysis shows modes that exist in the absence of any incident waves; these surface and interface waves are studied in Chapter 3. A very important example is that of the semi-infinite solid, along whose surface a pure or generalized Rayleigh wave is always propagated, regardless of the material. Other waves appear at the interface between a solid and a fluid (Scholte waves), while the conditions for existence are very restrictive at the interface between two solids (Stoneley waves). When the solid is limited by several parallel planes, the successive reflections of the bulk elastic waves give rise to guided waves. The properties of these guided waves are analyzed in Chapter 4. The simplest are transverse horizontal waves, discovered by Love, which are partly propagated in a layer and partly in its substrate. Given their practical importance, the Lamb waves, with two components, progressing in a plate are treated in detail both in the case of isotropic and anisotropic solids. The propagation of these plate modes is dispersive, like that of guided waves in cylinders, studied at the end of this chapter.
The second volume investigates the properties of acoustic fields emitted by various sources of finite dimensions, the interaction of elastic waves with cylindrical and spherical targets immersed in a fluid or buried in a solid, the means of generating and detecting the waves studied in the first volume.
The authors wish to extend their gratitude to Claire Prada, Director of Research at CNRS, institut Langevin Ondes et Images, for her help during the writing of this first volume.
October 2021
List of Main Symbols
a, b : amplitude of the waves.
cijkl (CIJ) : stiffnesses (Voigt notation).
D : directivity factor.
D : electric induction (displacement) vector.
E : Young modulus.
E : electric field vector.
ec (ep) : kinetic (potential) energy per unit volume.
eijk (εij) : piezoelectric (dielectric) constants.
F : force density per unit mass.
H(t) : Heaviside step function.
I : acoustic intensity.
J : Poynting vector.
K : bulk modulus.
k (k) : wave vector (number).
KM : electromechanical coupling coefficient (mode M).
l : unit vector normal to a surface.
n : unit vector of the propagation direction.
P : transported power.
pa : acoustic pressure.
p (p0) : thermodynamic pressure (at rest).
p , q : polarization vectors.
Ps (ps) : 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.
s : phase slowness vector.
T : absolute temperature.
T : mechanical traction, stress vector.
u : mechanical displacement vector.
U : internal energy per unit volume.
v : particle velocity vector.
Ve : energy velocity vector.
V (Vg) : phase (group) velocity.
VL (VT) : velocity of longitudinal (transverse) bulk waves.
W (w) : work (per unit volume).
x : position vector.
X, Y, Z : crystallographic axes.
Ze (Y) : electrical impedance (admittance).
acoustic (mechanical) impedance.
α : attenuation coefficient.
: elastic (piezoelectric) Christoffel tensor.
δij : Kronecker’s symbol.
δ(t) : Dirac function.
: linearized strain tensor (piezoelectric solid).
η : viscosity coefficient.
θi,r,t : angle of incidence, reflection, transmission.
Θ : dilatation.
κ : bulk wave velocity ratio (VT/VL).
λ, μ : Lamé constants.
ν : Poisson’s ratio.
ρ : mass density.
ρe (σe) : electric charge density per unit volume (area).
σ (σd) : effective (differential) scattering cross-section.
σ : Cauchy stress tensor.
ϕ (ψ) : scalar (vector) potential.
Φ : electric potential.
χ : decay factor.
ω : angular frequency.
