Reciprocity in elastodynamics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York , Port Melbourne ; Madrid ; Cape Town
Cambridge University Press
2003
|
| Ausgabe: | first published |
| Schriftenreihe: | Cambridge monographs on mechanics
|
| Schlagworte: | |
| Online-Zugang: | Publisher description Table of contents Inhaltsverzeichnis |
| Beschreibung: | x, 255 Seiten Diagramme |
| ISBN: | 052181734X 9780521817349 |
Internformat
MARC
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| 100 | 1 | |a Achenbach, Jan D. |4 aut | |
| 245 | 1 | 0 | |a Reciprocity in elastodynamics |c J.D. Achenbach |
| 250 | |a first published | ||
| 264 | 1 | |a Cambridge ; New York , Port Melbourne ; Madrid ; Cape Town |b Cambridge University Press |c 2003 | |
| 300 | |a x, 255 Seiten |b Diagramme | ||
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| 490 | 0 | |a Cambridge monographs on mechanics | |
| 650 | 7 | |a Elasticidade |2 larpcal | |
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| 650 | 7 | |a Mecânica ondulatória |2 larpcal | |
| 650 | 7 | |a Solide élastique |2 rasuqam | |
| 650 | 7 | |a Théorème de réciprocité |2 rasuqam | |
| 650 | 7 | |a Élasticité |2 rasuqam | |
| 650 | 7 | |a Élastodynamique |2 rasuqam | |
| 650 | 4 | |a Elastic solids | |
| 650 | 4 | |a Elasticity | |
| 650 | 4 | |a Reciprocity theorems | |
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| 650 | 0 | 7 | |a Reziprozitätsgesetz |0 (DE-588)4177972-1 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804130141270441984 |
|---|---|
| adam_text | Contents
Preface page ix
1 Introduction 1
1.1 Reciprocity 1
1.2 Static reciprocity for an elastic body subjected to concentrated
loads 4
1.3 Static reciprocity for distributed body forces and surface loads 5
1.4 The wave equation in one dimension 6
1.5 Use of a virtual wave in reciprocity considerations 7
1.6 Synopsis 9
2 Some elastodynamic theory 13
2.1 Introduction 13
2.2 Linear elastodynamics 14
2.3 One dimensional problems 20
2.4 Two dimensional problems 21
2.5 Linearly viscoelastic solid 23
2.6 Acoustic medium 25
2.7 Governing equations for linear elasticity in cylindrical
coordinates 28
3 Wave motion in an unbounded elastic solid 30
3.1 Introduction 30
3.2 Plane waves 31
3.3 Flux of energy in plane time harmonic waves 33
3.4 Reflection of time harmonic plane waves at a free surface 35
3.5 Energy partition 40
3.6 Solving the wave equation for polar symmetry 40
3.7 The Helmholtz decomposition 42
3.8 Displacement potentials 44
3.9 Wave motion generated by a point load 45
v
vi Contents
3.10 Expressions for the far field 50
3.11 Wave motion generated by a line load 52
4 Reciprocity in acoustics 55
4.1 Introduction 55
4.2 Reciprocity in the frequency domain 57
4.3 Reciprocity in the Laplace transform domain 58
4.4 Reciprocity in the presence of a compact inhomogeneity 60
4.5 Direct reciprocity for the wave equation 61
4.6 Other reciprocity theorems 62
4.7 Reciprocity between source solutions 64
4.8 Distribution of sources 65
4.9 Inverse problem for scattering by a compact
inhomogeneity 65
5 Reciprocity in one dimensional elastodynamics 70
5.1 Introduction 70
5.2 Reciprocity for the Bernoulli Euler beam 71
5.3 Waves in a Bernoulli Euler beam due to a time harmonic
force 73
5.4 Forced vibrations of a simply supported beam 74
5.5 Reciprocity for wave motion in one dimensional strain 77
5.6 The effect of an interface 79
5.7 Use of reciprocity to determine the reflection coefficient 81
5.8 Reciprocity of two one dimensional solutions for
concentrated forces 82
5.9 An inverse problem 84
5.10 Comparison of Born approximation with exact solution 85
6 Reciprocity in two and three dimensional elastodynamics 90
6.1 Introduction 90
6.2 Reciprocity theorems 91
6.3 Reciprocity in the time domain 92
6.4 Reciprocity in a two material body 94
6.5 Reciprocity theorems for linearly viscoelastic solids 94
6.6 Anti plane line load in an unbounded elastic solid 95
6.7 Anti plane surface waves 99
6.8 The wave equation with polar symmetry 104
6.9 Reciprocity for waves reflected from a free surface 105
6.10 Reciprocity for fields generated by point loads in a bounded
body 107
6.11 Reciprocity for point loads in an unbounded body 108
6.12 Distribution of body forces 109
Contents vii
6.13 Domain integral equation for scattering by an inclusion 110
6.14 Examples from the technical literature 112
7 Wave motion guided by a carrier wave 116
7.1 Introduction 116
7.2 Guided wave motion 117
7.3 Rayleigh surface waves 119
7.4 Carrier waves 122
7.5 Equivoluminal waves in an elastic layer 124
7.6 Lamb waves 127
8 Computation of surface waves by reciprocity considerations 132
8.1 Introduction 132
8.2 Surface waves generated by a line load 132
8.3 Surface waves generated by a sub surface
point load 135
8.4 Application of elastodynamic reciprocity in cylindrical
coordinates 138
8.5 Surface wave motion generated by a vertical force P 141
8.6 Check of calculated surface wave amplitude 142
9 Reciprocity considerations for an elastic layer 145
9.1 Introduction 145
9.2 Two dimensional horizontally polarized
transverse waves 146
9.3 Equivoluminal wave modes 148
9.4 Lamb waves in plane strain 149
9.5 Lamb waves in polar coordinates 152
10 Forced motion of an elastic layer 157
10.1 Introduction 157
10.2 Elastic layer subjected to a time harmonic anti plane line
load 159
10.3 Response to a line load normal to the plate faces 162
10.4 Response to a point load parallel to the
plate faces 164
10.5 Summary of solutions 168
10.6 Comparison with plane stress solution 170
10.7 Comparison with plate theory for the normal point load
problem 172
11 Integral representations and integral equations 175
11.1 Introduction 175
11.2 Radiation of anti plane shear waves from a cavity 176
11.3 Integral representation in three dimensions 181
viii Contents
11.4 Integral equation 185
11.5 Scattering by a crack 188
11.6 Reciprocity relations 191
11.7 Kirchhoff approximation for scattering by a crack 194
11.8 Reciprocity considerations for a diffraction problem 196
12 Scattering in waveguides and bounded bodies 199
12.1 Introduction 199
12.2 Interaction of an incident wave with a defect in a layer 200
12.3 Thin film on an inhomogeneous substrate 208
12.4 Scattering by a disbond 210
12.5 Interaction of a Rayleigh surface wave with a crack 212
12.6 Scattering matrix 214
12.7 Transducer response to scattering by a flaw 216
13 Reciprocity for coupled acousto elastic systems 220
13.1 Introduction 220
13.2 Reciprocity for configurationally coupled systems 221
13.3 Reciprocity between source solutions 223
13.4 Scattering by a flaw in a submerged solid body 223
13.5 Reciprocity for free field sources and sources located
on rigid baffles 225
13.6 Interaction of sound and structural vibrations 228
13.7 Reciprocity for free field sources and sources located on
elastic baffles 231
14 Reciprocity for piezoelectric systems 233
14.1 Introduction 233
14.2 Piezoelectricity 234
14.3 Governing equations 235
14.4 Reciprocity theorem for a piezoelectric solid 236
14.5 Application to scattering by a flaw 238
14.6 Reflection by the bottom surface of an elastic layer 241
14.7 Reflection and transmission by a fatigue crack 243
References 247
Index of cited names 251
Subject index 253
|
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| indexdate | 2024-07-09T19:16:19Z |
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| isbn | 052181734X 9780521817349 |
| language | English |
| lccn | 2003055420 |
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| spelling | Achenbach, Jan D. aut Reciprocity in elastodynamics J.D. Achenbach first published Cambridge ; New York , Port Melbourne ; Madrid ; Cape Town Cambridge University Press 2003 x, 255 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Cambridge monographs on mechanics Elasticidade larpcal Mecânica clássica larpcal Mecânica ondulatória larpcal Solide élastique rasuqam Théorème de réciprocité rasuqam Élasticité rasuqam Élastodynamique rasuqam Elastic solids Elasticity Reciprocity theorems Elastodynamik (DE-588)4151692-8 gnd rswk-swf Reziprozitätsgesetz (DE-588)4177972-1 gnd rswk-swf Elastodynamik (DE-588)4151692-8 s Reziprozitätsgesetz (DE-588)4177972-1 s DE-604 http://www.loc.gov/catdir/description/cam032/2003055420.html Publisher description http://www.loc.gov/catdir/toc/cam032/2003055420.html Table of contents HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010427436&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Achenbach, Jan D. Reciprocity in elastodynamics Elasticidade larpcal Mecânica clássica larpcal Mecânica ondulatória larpcal Solide élastique rasuqam Théorème de réciprocité rasuqam Élasticité rasuqam Élastodynamique rasuqam Elastic solids Elasticity Reciprocity theorems Elastodynamik (DE-588)4151692-8 gnd Reziprozitätsgesetz (DE-588)4177972-1 gnd |
| subject_GND | (DE-588)4151692-8 (DE-588)4177972-1 |
| title | Reciprocity in elastodynamics |
| title_auth | Reciprocity in elastodynamics |
| title_exact_search | Reciprocity in elastodynamics |
| title_full | Reciprocity in elastodynamics J.D. Achenbach |
| title_fullStr | Reciprocity in elastodynamics J.D. Achenbach |
| title_full_unstemmed | Reciprocity in elastodynamics J.D. Achenbach |
| title_short | Reciprocity in elastodynamics |
| title_sort | reciprocity in elastodynamics |
| topic | Elasticidade larpcal Mecânica clássica larpcal Mecânica ondulatória larpcal Solide élastique rasuqam Théorème de réciprocité rasuqam Élasticité rasuqam Élastodynamique rasuqam Elastic solids Elasticity Reciprocity theorems Elastodynamik (DE-588)4151692-8 gnd Reziprozitätsgesetz (DE-588)4177972-1 gnd |
| topic_facet | Elasticidade Mecânica clássica Mecânica ondulatória Solide élastique Théorème de réciprocité Élasticité Élastodynamique Elastic solids Elasticity Reciprocity theorems Elastodynamik Reziprozitätsgesetz |
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