Ray methods for waves in elastic solids: with applications to scattering by cracks
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston, Mass. [u.a.]
Pitman
1982
|
| Ausgabe: | 1. publication |
| Schriftenreihe: | Monographs and Studies in Mathematics
14 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 251 Seiten graph. Darst. |
| ISBN: | 0273084534 |
Internformat
MARC
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| 100 | 1 | |a Achenbach, Jan D. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Ray methods for waves in elastic solids |b with applications to scattering by cracks |c Jan D. Achenbach, A. K. Gautesen, H. MacMaken |
| 250 | |a 1. publication | ||
| 264 | 1 | |a Boston, Mass. [u.a.] |b Pitman |c 1982 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface ix
Introduction 1
0.1 Ray theory 1
0.2 Scattering of waves 2
0.3 Edge diffraction 3
0.4 Waves in elastic solids 6
0.5 Applications to quantitative non destructive evaluation 9
References 9
1 Wave propagation in elastic solids 11
1.1 Introduction 11
1.2 Linearized elasticity 12
1.3 Displacement potentials 16
1.4 Steady state time harmonic solutions 18
1.5 Plane waves 19
1.6 Wave motions generated by a point load 22
1.7 Basic singular solution for two dimensional problems 27
1.8 The centre of pressure 29
References 31
2 Integral relations and energy considerations 33
2.1 Introduction 33
2.2 Reciprocal identity for time harmonic motions 34
2.3 Integral representation 34
2.4 Integral equations 38
2.5 Balance of rates of energies 39
2.6 Energy transfer 40
2.7 The scattered power theorem 42
2.8 Reciprocity relations 43
References 46
V
vi CONTENTS
3 Waves in a half space 47 !
3.1 Introduction 47
3.2 Reflection of plane waves at the surface of a half space 48
3.3 Energy partition and reciprocity relations 51
3.4 Surface waves 53
3.5 Rayleigh surface waves 55 !
3.6 Surface wave excitation 56
3.7 Point load in an elastic half space 63 !
Appendix 3.A: Method of steepest descent 73
References 75 f
4 Elastodynamic ray theory 76
4.1 Introduction 76
4.2 Asymptotic solutions 77
4.3 Geometry of wavefronts and rays 79
4.4 Solutions to the zeroth order transport equations 84
4.5 Energy transfer 87
4.6 Two dimensional geometry 88
4.7 Ray theory analysis of reflection 89
4.8 Two dimensional problems 96
4.9 Examples 98
References 108
5 Diffraction of a plane wave by the edge of a semi infinite crack 109
5.1 Introduction 109
5.2 Some notation 110
5.3 Method of solution 112
5.4 Formal solution for the scattered field 119
5.5 Asymptotic analysis of diffracted body waves 126
5.6 Uniform corrections 128
5.7 Diffraction of a surface wave by the edge of a semi infinite
crack 133
5.8 Reciprocity relations 138
Appendix 5.A: The Wiener—Hopf technique 138
Appendix 5.B: Decomposition of K(|) 141
Appendix 5.C: Diffraction coefficients 143
References 148
,¦
6 Scattering by cracks in elastic solids 149
6.1 Introduction 149
6.2 Two scattering of plane waves by a slit 150
6.3 Method of solution of dual integral equations 153
6.4 Numerical analysis and results 158
CONTENTS vii
6.5 Scattered fields 164
6.6 Normal incidence of a longitudinal wave on a circular
crack 165
References 169
7 Geometrical theory of diffraction 171
7.1 Introduction 171
7.2 The canonical problem for edge diffraction of scalar waves 172
7.3 Geometrical theory of diffraction 175
7.4 Geometrical theory of diffraction for waves in elastic solids 180
7.5 Ray analysis 186
7.6 Uniform asymptotic theory 191
7.7 Two dimensional scattering of a plane wave by a crack 193
7.8 Normal incidence of an L wave on a circular crack 201
Appendix 7.A: Fresnel type integrals 208
References 210
8 Uniform COD theory 211
8.1 Introduction 211
8.2 Fourier integrals for the crack opening displacement 213
8.3 COD generated by TH waves on the crack faces 216
8.4 COD generated by in plane waves on the crack faces 222
8.5 Two dimensional scattering of a plane wave by a crack 226
8.6 Some notes on the construction of the COD 231
8.7 Curved wavefronts and curved crack edges 234
8.8 Normal incidence of an L wave on a circular crack 237
8.9 Kirchhoff approximation 241
Appendix 8.A: Evaluation of Au£ for /3 = L or 0 =
TV 244
References 246
Index 247
|
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| author | Achenbach, Jan D. Gautesen, A. K. MacMaken, H. |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T15:40:12Z |
| institution | BVB |
| isbn | 0273084534 |
| language | English |
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| physical | XI, 251 Seiten graph. Darst. |
| publishDate | 1982 |
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| series | Monographs and Studies in Mathematics |
| series2 | Monographs and Studies in Mathematics |
| spelling | Achenbach, Jan D. Verfasser aut Ray methods for waves in elastic solids with applications to scattering by cracks Jan D. Achenbach, A. K. Gautesen, H. MacMaken 1. publication Boston, Mass. [u.a.] Pitman 1982 XI, 251 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs and Studies in Mathematics 14 Elastic waves Diffraction Elastizität (DE-588)4014159-7 gnd rswk-swf Festkörper (DE-588)4016918-2 gnd rswk-swf Beugung (DE-588)4145094-2 gnd rswk-swf Elastische Welle (DE-588)4151684-9 gnd rswk-swf Wellenausbreitung (DE-588)4121912-0 gnd rswk-swf Festkörper (DE-588)4016918-2 s Elastische Welle (DE-588)4151684-9 s Beugung (DE-588)4145094-2 s DE-604 Wellenausbreitung (DE-588)4121912-0 s Elastizität (DE-588)4014159-7 s Gautesen, A. K. Verfasser aut MacMaken, H. Verfasser aut Monographs and Studies in Mathematics 14 (DE-604)BV000004171 14 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001370868&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Achenbach, Jan D. Gautesen, A. K. MacMaken, H. Ray methods for waves in elastic solids with applications to scattering by cracks Monographs and Studies in Mathematics Elastic waves Diffraction Elastizität (DE-588)4014159-7 gnd Festkörper (DE-588)4016918-2 gnd Beugung (DE-588)4145094-2 gnd Elastische Welle (DE-588)4151684-9 gnd Wellenausbreitung (DE-588)4121912-0 gnd |
| subject_GND | (DE-588)4014159-7 (DE-588)4016918-2 (DE-588)4145094-2 (DE-588)4151684-9 (DE-588)4121912-0 |
| title | Ray methods for waves in elastic solids with applications to scattering by cracks |
| title_auth | Ray methods for waves in elastic solids with applications to scattering by cracks |
| title_exact_search | Ray methods for waves in elastic solids with applications to scattering by cracks |
| title_full | Ray methods for waves in elastic solids with applications to scattering by cracks Jan D. Achenbach, A. K. Gautesen, H. MacMaken |
| title_fullStr | Ray methods for waves in elastic solids with applications to scattering by cracks Jan D. Achenbach, A. K. Gautesen, H. MacMaken |
| title_full_unstemmed | Ray methods for waves in elastic solids with applications to scattering by cracks Jan D. Achenbach, A. K. Gautesen, H. MacMaken |
| title_short | Ray methods for waves in elastic solids |
| title_sort | ray methods for waves in elastic solids with applications to scattering by cracks |
| title_sub | with applications to scattering by cracks |
| topic | Elastic waves Diffraction Elastizität (DE-588)4014159-7 gnd Festkörper (DE-588)4016918-2 gnd Beugung (DE-588)4145094-2 gnd Elastische Welle (DE-588)4151684-9 gnd Wellenausbreitung (DE-588)4121912-0 gnd |
| topic_facet | Elastic waves Diffraction Elastizität Festkörper Beugung Elastische Welle Wellenausbreitung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001370868&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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