Introduction to wave propagation in nonlinear fluids and solids

535 Pages·1998·23.836 MB·English

by  D S Drumheller

Waves occur widely in nature and have innumerable commercial uses. Pressure waves are
responsible for the sound of speech, bow waves created by meteors can virtually ignite the
earth's atmosphere, ultrasonic waves are used for medical imaging, and shock waves are
used for the synthesis of new materials.
Although much has been written about these linear and nonlinear waves, most books
approach the topic at an advanced level. This book provides a thorough, modern introduction
to the subject.
Beginning with fundamental concepts of motion, the book goes on to discuss linear
and nonlinear mechanical waves, thermodynamics, and constitutive models. In contrast to
many classic works, which were limited to nonlinear waves in gases, this text also includes
liquids and solids as integral parts of the subject. Among the important areas of research
and application that will benefit from this text are impact analysis, shock wave research,
explosive detonation, nonlinear acoustics, and hypersonic aerodynamics.
Students at an advanced undergraduate/graduate level will find this text a clear and
comprehensive introduction to the study of wave phenomena, and it will also be a valuable
professional reference for engineers and applied physicists.

Introduction to Wave Propagation in Nonlinear Fluids and Solids

Introduction to Wave
Propagation in Nonlinear
Fluids and Solids
D. S. DRUMHELLER
Sandia National Laboratories
CAMBRIDGE
UNIVERSITY PRESS
CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo
Cambridge University Press
The Edinburgh Building, Cambridge CB2 8RU, UK
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridge.org/9780521583138
© D. S. Drumheller 1998
This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without the written
permission of Cambridge University Press.
First published 1998
A catalogue record for this publication is available from the British Library
Library of Congress Cataloguing in Publication data
Drumheller, D. S.
Introduction to wave propagation in nonlinear fluids and solids /
D. S. Drumheller.
p. cm.
Includes bibliographical references (p. - ) and index.
ISBN 0-521-58313-6 (hardback). - ISBN 0-521-58746-8 (paperback)
1. Wave motion. Theory of. 2. Nonlinear waves. I. Title.
QA927.D77 1998
531'.1133-dc21 97-3266
CIP
ISBN 978-0-521-58313-8 hardback
ISBN 978-0-521-58746-4 paperback
Transferred to digital printing 2007
To
Phylis,
my love, my friend,
who gave me MeLinda and Paul
one Monday morning

Contents
Preface Xlll
Nomenclature xvii
Chapter 0 Introduction 1
0.1 Shock-Tube Experiment 2
0.2 Flyer-Plate Experiment 4
0.3 Plan of the Book 6
Chapter 1 Fundamentals 9
1.1 Index]dotation 9
.1.1 Cartesian Coordinates and Vectors 9
L.1.2 Products of Vectors 11
L.1.3 Areas and Volumes 14
[.1.4 Evaluation of a Determinant 15
[.1.5 Direction of a Vector 16
1[.1.6 Change of Coordinates 17
1[.1.7 Rotations about a Coordinate Axis 19
11.1.8 Orientation Lemma 21
]1.1.9 Transformations for Coordinate Rotations 22
][.1.10 Exercises 24
1.2 Motion 28
]L.2.1 Motion and Inverse Motion 29
]L.2.2 Material and Spatial Descriptions 29
]L.2.3 Displacement, Velocity, and Acceleration 30
L.2.4 Pure Translation and Rotation of a Body 32
L.2.5 Exercises 34
1.3 (3ne-Dimensional Motion 36
1.4 1Deformation 37
;L.4.1 Deformation Gradient Tensor 37
;L.4.2 Strain Tensor 40
42
L.4.3 Longitudinal Strain
43
L.4.4 Shear Strain
44
1.4.5 Volume Strain
46
1.4.6 Deviatoric Strain
47
1.4.7 Velocity Gradient, Deformation Rate, and Spin
48
1.4.8 Exercises
49
1.5 One-Dimensional Deformation
vn
viii Contents
1.5.1 Triaxial Deformation 50
1.5.2 Exercises 57
1.6 Stress 59
1.6.1 Body Force 59
1.6.2 Traction 61
1.6.3 Cauchy Stress 62
1.6.4 Pressure and Deviatoric Stress 66
1.6.5 Exercises 66
1.7 One-Dimensional Stress 67
1.7.1 Spherical Stress 69
1.7.2 Triaxial Stress 70
1.7.3 Exercises 73
1.8 Laws of Motion 73
1.8.1 Simplified Notation: One-Dimensional Motion 74
1.8.2 Conservation of Mass: One-Dimensional Motion 75
1.8.3 Balance of Linear Momentum: One-Dimensional Motion 79
1.8.4 Transport Theorm: Three-Dimensional Motion 82
1.8.5 Conservation of Mass: Three-Dimensional Motion 83
1.8.6 Balance of Linear Momentum: Three-Dimensional Motion 84
1.8.7 Balance of Angular Momentum: Three-Dimensional Motion 84
1.8.8 Exercises 85
Chapter 2 Mechanical Waves 87
2.1 Elastic Material 87
2.1.1 Linear-Elastic Material 88
2.1.2 Isotropic, Linear-Elastic Material 89
2.1.3 Nonlinear-Elastic Material 92
2.1.4 AdiabaticGas 98
2.1.5 Exercises 98
2.2 One-Dimensional Nonlinear-Elastic Equations 99
2.2.1 Material Description 99
2.2.2 Spatial Description 100
2.3 Wave Equations 100
2.3.1 Material Description 101
2.3.2 The x-t Diagram 102
2.3.3 D' Alembert Solution 105
2.3.4 Superposition of Linear Waves 108
2.3.5 Initial- and Boundary-Value Problems 109
2.3.6 Transverse Waves 114
2.3.7 Exercises 117
2.4 Method of Characteristics 119
2.4.1 Riemann Invariants 119
2.4.2 Simple Wave 120
2.4.3 The T-v Diagram 122
2.4.4 Initial-Value Problems 123
2.4.5 Boundary-Value Problems 124