E-Book Overview
John G. Harris intended to explain in this book the special techniques required to model the radiation and diffraction of elastic and surface waves. He sadly died before he could fulfil this ambition, but his plan has been brought to fruition by a team of his distinguished collaborators. The book begins with the basic underlying equations for wave motion and then builds upon this foundation by solving a number of fundamental scattering problems. The remaining chapters provide a thorough introduction to modern techniques that have proven essential to understanding radiation and diffraction at high frequencies. Graduate students, researchers and professionals in applied mathematics, physics and engineering will find that the chapters increase in complexity, beginning with plane-wave propagation and spectral analyses. Other topics include elastic wave theory, the Wiener-Hopf technique, the effects of viscosity on acoustic diffraction, and the phenomenon of channelling of wave energy along guided structures.
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This page intentionally left blank Elastic Waves at High Frequencies Techniques for Radiation and Diffraction of Elastic and Surface Waves Elastic Waves at High Frequencies Techniques for Radiation and Diffraction of Elastic and Surface Waves JOHN G. HARRIS Late, University of Illinois at Urbana–Champaign Edited and Prepared for Publication by GARETH I. BLOCK Flemington, NJ RICHARD V. CRASTER University of Alberta ANTHONY M. J. DAVIS University of California, San Diego PAUL A. MARTIN Colorado School of Mines ANDREW N. NORRIS Rutgers University CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Dubai, Tokyo 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/9780521875301 © J. G. Harris 2010 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2010 ISBN-13 978-0-511-78982-3 eBook (NetLibrary) ISBN-13 978-0-521-87530-1 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Do not go gentle into that good night, Old age should burn and rave at close of day; Rage, rage against the dying of the light. Though wise men at their end know dark is right, Because their words had forked no lightning they Do not go gentle into that good night. Do not go gentle into that good night By Dylan Thomas, from THE POEMS OF DYLAN c THOMAS, copyright 1952 by Dylan Thomas. Reprinted by permission of New Directions Publishing Corp. and J. M. Dent & Sons Ltd. Contents Foreword page ix 1 Linear elastic waves 1.1 Model equations 1.2 Continuity and boundary conditions 1.3 Flux of energy 1.4 The Fourier and Laplace transforms 1.5 A wave is not a vibration 1.6 Dispersive propagation 1.7 General references 1 1 6 6 9 12 15 20 2 Canonical acoustic-wave problems 2.1 Radiation from a piston in an infinite baffle 2.2 Diffraction of an acoustic plane wave by an edge 2.3 Summary 23 23 40 50 3 Canonical elastic-wave problems 3.1 The scattering of a spherical wave from a fluid–solid interface 3.2 Rayleigh–Lamb modes and Rayleigh surface waves 52 4 Radiation and impedance 4.1 Reciprocity 4.2 Gr