Linear Elastic Waves

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Overview

"Wave propagation and scattering are among the most fundamental processes that we use to comprehend the world around us. Whereas 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, 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.
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Editorial Reviews

From The Critics
This advanced level textbook for applied mathematicians, engineers, and seismologists delves into the ubiquitous natural processes of wave propagation and scattering. In applying equations of elasticity—model equations and Fourier and Laplace transforms, Harris (theoretical and applied mechanics, U. of Illinois at Urbana- Champaign) posits that understanding plane wave interactions underlies fathoming more complex interactions, and that waves are best understood in the linear approximation where they are governed primarily by their propagation environments. Topics covered include reflection, refraction, propagation of interfacial waves, integral representations, radiation and refraction, and propagation in closed and open waveguides. Chapters include problems to work. Annotation c. Book News, Inc., Portland, OR (booknews.com)
From the Publisher
"Abstract concepts are carefully explained and supported with a wealth of examples and illustrations and a wonderful collection of problems, a few of which are elementary enough for any beginner." CHOICE

"This is a book to be read with pad and pencil in hand. Although the text is clear, the author lets the mathematics do most of the speaking." EOS

"Abstract concepts are carefully explained and supported with a wealth of examples and illustrations and a wonderful collection of problems, a few of which are elementary enough for any beginner." CHOICE

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Product Details

Table of Contents

Preface
1 Simple Wave Solutions 1
1.1 Model Equations 1
1.2 The Fourier and Laplace Transforms 6
1.3 A Wave Is Not a Vibration 11
1.4 Dispersive Propagation 13
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
2.4 Asymptotic Ray Expansion 28
3 Reflection, Refraction, and Interfacial Waves 37
3.1 Reflection of a Compressional Plane Wave 37
3.2 Reflection and Refraction 41
3.3 Critical Refraction and Interfacial Waves 44
3.4 The Rayleigh Wave 48
4 Green's Tensor and Integral Representations 56
4.1 Introduction 56
4.2 Reciprocity 57
4.3 Green's Tensor 58
4.4 Principle of Limiting Absorption 62
4.5 Integral Representation: A Source Problem 64
4.6 Integral Representation: A Scattering Problem 65
4.7 Uniqueness in an Unbounded Region 68
4.8 Scattering from an Elastic Inclusion in a Fluid 72
5 Radiation and Diffraction 77
5.1 Antiplane Radiation into a Half-Space 77
5.2 Buried Harmonic Line of Compression I 82
5.3 Asymptotic Approximation of Integrals 86
5.4 Buried Harmonic Line of Compression II 96
5.5 Diffraction of an Antiplane Shear Wave at an Edge 101
5.6 Matched Asymptotic Expansion Study 112
6 Guided Waves and Dispersion 121
6.1 Harmonic Waves in a Closed Waveguide 121
6.2 Harmonic Waves in an Open Waveguide 128
6.3 Excitation of a Closed Waveguide 134
6.4 Harmonically Excited Waves in an Open Waveguide 139
6.5 A Laterally Inhomogeneous, Closed Waveguide 146
6.6 Dispersion and Group Velocity 150
References 157
Index 159
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