Linear elastic waves:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2001
|
| Edition: | 1. publ. |
| Series: | Cambridge texts in applied mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 162 S. graph. Darst. |
| ISBN: | 0521643686 052164383X |
Staff View
MARC
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| 245 | 1 | 0 | |a Linear elastic waves |c John G. Harris |
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Record in the Search Index
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| adam_text | Contents
Preface page xiii
1 Simple Wave Solutions 1
1.1 Model Equations 1
1.1.1 One Dimensional Models 3
1.1.2 Two Dimensional Models 4
1.1.3 Displacement Potentials 5
1.1.4 Energy Relations 5
1.2 The Fourier and Laplace Transforms 6
1.3 A Wave Is Not a Vibration 11
1.4 Dispersive Propagation 13
1.4.1 An Isolated Interaction 13
1.4.2 Periodic Structures 15
References 18
2 Kinematical Descriptions of Waves 20
2.1 Time Dependent Plane Waves 20
2.2 Time Harmonic Plane Waves 22
2.3 Plane Wave or Angular Spectrum Representations 24
2.3.1 A Gaussian Beam 24
2.3.2 An Angular Spectrum Representation of a
Spherical Wave 26
2.3.3 An Angular Spectrum Representation of a
Cylindrical Wave 28
2.4 Asymptotic Ray Expansion 28
2.4.1 Compressional Wave 29
2.4.2 Shear Wave 33
ix
x Contents
Appendix: Spherical and Cylindrical Waves 34
References 35
3 Reflection, Refraction, and Interfacial Waves 37
3.1 Reflection of a Compressional Plane Wave 37
3.1.1 Phase Matching 39
3.1.2 Reflection Coefficients 40
3.2 Reflection and Refraction 41
3.3 Critical Refraction and Interfacial Waves 44
3.4 The Rayleigh Wave 48
3.4.1 The Time Harmonic Wave 49
3.4.2 Transient Wave 50
3.4.3 The Rayleigh Function 51
3.4.4 Branch Cuts 52
References 55
4 Green s Tensor and Integral Representations 56
4.1 Introduction 56
4.2 Reciprocity 57
4.3 Green s Tensor 58
4.3.1 Notes 61
4.4 Principle of Limiting Absorption 62
4.5 Integral Representation: A Source Problem 64
4.5.1 Notes 65
4.6 Integral Representation: A Scattering Problem 65
4.6.1 Notes 66
4.7 Uniqueness in an Unbounded Region 68
4.7.1 No Edges 68
4.7.2 Edge Conditions 69
4.7.3 An Inner Expansion 71
4.8 Scattering from an Elastic Inclusion in a Fluid 72
References 76
5 Radiation and Diffraction 77
5.1 Antiplane Radiation into a Half Space 77
5.1.1 The Transforms 78
5.1.2 Inversion 79
5.2 Buried Harmonic Line of Compression I 82
5.3 Asymptotic Approximation of Integrals 86
Contents xi
5.3.1 Watson s Lemma 87
5.3.2 Method of Steepest Descents 90
5.3.3 Stationary Phase Approximation 94
5.4 Buried Harmonic Line of Compression II 96
5.4.1 The Complex Plane 96
5.4.2 The Scattered Compressional Wave 98
5.4.3 The Scattered Shear Wave 99
5.5 Diffraction of an Antiplane Shear Wave at an Edge 101
5.5.1 Formulation 102
5.5.2 Wiener Hopf Solution 104
5.5.3 Description of the Scattered Wavefield 108
5.6 Matched Asymptotic Expansion Study 112
Appendix: The Fresnel Integral 116
References 119
6 Guided Waves and Dispersion 121
6.1 Harmonic Waves in a Closed Waveguide 121
6.1.1 Partial Waves and the Transverse Resonance Principle 123
6.1.2 Dispersion Relation: A Closed Waveguide 124
6.2 Harmonic Waves in an Open Waveguide 128
6.2.1 Partial Wave Analysis 129
6.2.2 Dispersion Relation: An Open Waveguide 131
6.3 Excitation of a Closed Waveguide 134
6.3.1 Harmonic Excitation 134
6.3.2 Transient Excitation 135
6.4 Harmonically Excited Waves in an Open Waveguide 139
6.4.1 The Wavefield in the Layer 140
6.4.2 The Wavefield in the Half Space 145
6.4.3 Leaky Waves 146
6.5 A Laterally Inhomogeneous, Closed Waveguide 146
6.6 Dispersion and Group Velocity 150
6.6.1 Causes of Dispersion 150
6.6.2 The Propagation of Information 151
6.6.3 The Propagation of Angular Frequencies 153
References 157
Index 159
|
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| id | DE-604.BV013918520 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:54:23Z |
| institution | BVB |
| isbn | 0521643686 052164383X |
| language | English |
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| physical | XV, 162 S. graph. Darst. |
| publishDate | 2001 |
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| publishDateSort | 2001 |
| publisher | Cambridge Univ. Press |
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| series2 | Cambridge texts in applied mathematics |
| spelling | Harris, John G. Verfasser aut Linear elastic waves John G. Harris 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2001 XV, 162 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge texts in applied mathematics Wellenausbreitung - Lineare Elastizitätstheorie Elastische Welle (DE-588)4151684-9 gnd rswk-swf Elastische Welle (DE-588)4151684-9 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009523105&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Harris, John G. Linear elastic waves Wellenausbreitung - Lineare Elastizitätstheorie Elastische Welle (DE-588)4151684-9 gnd |
| subject_GND | (DE-588)4151684-9 |
| title | Linear elastic waves |
| title_auth | Linear elastic waves |
| title_exact_search | Linear elastic waves |
| title_full | Linear elastic waves John G. Harris |
| title_fullStr | Linear elastic waves John G. Harris |
| title_full_unstemmed | Linear elastic waves John G. Harris |
| title_short | Linear elastic waves |
| title_sort | linear elastic waves |
| topic | Wellenausbreitung - Lineare Elastizitätstheorie Elastische Welle (DE-588)4151684-9 gnd |
| topic_facet | Wellenausbreitung - Lineare Elastizitätstheorie Elastische Welle |
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