Linear Elastic Waves : Cambridge Texts in Applied Mathematics - John G. Harris

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Linear Elastic Waves

By: John G. Harris

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Hardcover | 25 October 2001

At a Glance

Hardcover
180 Pages

Dimensions(cm)
16.1 x 23.7 x 1.8

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Wave propagation and scattering are among the most fundamental processes that we use to comprehend the world around us. While these processes are often very complex, one way to begin to understand them is to study wave propagation in the linear approximation. This is a book describing such propagation using, as a context, the equations of elasticity. Two unifying themes are used. The first is that an understanding of plane wave interactions is fundamental to understanding more complex wave interactions. The second is that waves are best understood in an asymptotic approximation where they are free of the complications of their excitation and are governed primarily by their propagation environments. The topics covered include reflection, refraction, the propagation of interfacial waves, integral representations, radiation and diffraction, and propagation in closed and open waveguides. Linear Elastic Waves is an advanced level textbook directed at applied mathematicians, seismologists, and engineers.

Industry Reviews

'Students of seismology have their choice of many excellent texts to help them in this regard. Linear Elastic Waves is an excellent sequel to them.' Justin Revenaugh, University of California '... the present volume is an excellent textbook for a deeper understanding of waves in linear elasticity.' Zentralblatt MATH '... it is with small wonder that we find a whole host of books devoted to the foundations and applications of wave theory ... the advanced researcher, the post-doctoral students, and all wave enthusiasts will profit from reading this book, whose elegance of presentation holds some fascination for the insider.' Waves In Random Media 'I think it is an excellent text and would recommend it to anyone wishing to learn basic linear wave theory or elastic waves in particular.' R. S. Mackay, Contemporary Physics ' ... the advanced researcher, the post-doctoral student, and all wave enthusiasts will profit from reading this book'. Institute of Physics Publishing, Waves in Random Media 'The book is very well written ... The reviewer would highly recommend this book to researchers and advanced students in applied mathematics, engineering, physics and geology.' Journal of Sound and Vibration

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You Can Find This Book In

Non-Fiction Science Physics Classical Mathematics Wave Mechanics including Vibration & Acoustics Mathematics Applied Mathematics Medicine Medicine in General Engineering & Technology Technology in General Maths for Engineers

Earth Sciences, Geography, Environment, Planning Earth Sciences Geology & The Lithosphere Mechanical Engineering & Materials Mechanical Engineering Science in General Maths for Scientists

Preface	p. xiii
Simple Wave Solutions	p. 1
Model Equations	p. 1
One-Dimensional Models	p. 3
Two-Dimensional Models	p. 4
Displacement Potentials	p. 5
Energy Relations	p. 5
The Fourier and Laplace Transforms	p. 6
A Wave Is Not a Vibration	p. 11
Dispersive Propagation	p. 13
An Isolated Interaction	p. 13
Periodic Structures	p. 15
References	p. 18
Kinematical Descriptions of Waves	p. 20
Time-Dependent Plane Waves	p. 20
Time-Harmonic Plane Waves	p. 22
Plane-Wave or Angular-Spectrum Representations	p. 24
A Gaussian Beam	p. 24
An Angular-Spectrum Representation of a Spherical Wave	p. 26
An Angular-Spectrum Representation of a Cylindrical Wave	p. 28
Asymptotic Ray Expansion	p. 28
Compressional Wave	p. 29
Shear Wave	p. 33
Spherical and Cylindrical Waves	p. 34
References	p. 35
Reflection, Refraction, and Interfacial Waves	p. 37
Reflection of a Compressional Plane Wave	p. 37
Phase Matching	p. 39
Reflection Coefficients	p. 40
Reflection and Refraction	p. 41
Critical Refraction and Interfacial Waves	p. 44
The Rayleigh Wave	p. 48
The Time-Harmonic Wave	p. 49
Transient Wave	p. 50
The Rayleigh Function	p. 51
Branch Cuts	p. 52
References	p. 55
Green's Tensor and Integral Representations	p. 56
Introduction	p. 56
Reciprocity	p. 57
Green's Tensor	p. 58
Notes	p. 61
Principle of Limiting Absorption	p. 62
Integral Representation: A Source Problem	p. 64
Notes	p. 65
Integral Representation: A Scattering Problem	p. 65
Notes	p. 66
Uniqueness in an Unbounded Region	p. 68
No Edges	p. 68
Edge Conditions	p. 69
An Inner Expansion	p. 71
Scattering from an Elastic Inclusion in a Fluid	p. 72
References	p. 76
Tradiation and Diffraction	p. 77
Antiplane Radiation into a Half-Space	p. 77
The Transforms	p. 78
Inversion	p. 79
Buried Harmonic Line of Compression I	p. 82
Asymptotic Approximation of Integrals	p. 86
Watson's Lemma	p. 87
Method of Steepest Descents	p. 90
Stationary Phase Approximation	p. 94
Buried Harmonic Line of Compression II	p. 96
The Complex Plane	p. 96
The Scattered Compressional Wave	p. 98
The Scattered Shear Wave	p. 99
Diffraction of an Antiplane Shear Wave at an Edge	p. 101
Formulation	p. 102
Wiener-Hopf Solution	p. 104
Description of the Scattered Wavefield	p. 108
Matched Asymptotic Expansion Study	p. 112
The Fresnel Integral	p. 116
References	p. 119
Guided Waves and Dispersion	p. 121
Harmonic Waves in a Closed Waveguide	p. 121
Partial Waves and the Transverse Resonance Principle	p. 123
Dispersion Relation: A Closed Waveguide	p. 124
Harmonic Waves in an Open Waveguide	p. 128
Partial Wave Analysis	p. 129
Dispersion Relation: An Open Waveguide	p. 131
Excitation of a Closed Waveguide	p. 134
Harmonic Excitation	p. 134
Transient Excitation	p. 135
Harmonically Excited Waves in an Open Waveguide	p. 139
The Wavefield in the Layer	p. 140
The Wavefield in the Half-Space	p. 145
Leaky Waves	p. 146
A Laterally Inhomogeneous, Closed Waveguide	p. 146
Dispersion and Group Velocity	p. 150
Causes of Dispersion	p. 150
The Propagation of Information	p. 151
The Propagation of Angular Frequencies	p. 153
References	p. 157
Index	p. 159
Table of Contents provided by Syndetics. All Rights Reserved.

Linear Elastic Waves

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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