IUTAM Symposium on Diffraction and Scattering in Fluid Mechanics and Elasticity: Proceeding of the IUTAM Symposium held in Manchester, United Kingdom, 16–20 July 2000 PDF
Preview IUTAM Symposium on Diffraction and Scattering in Fluid Mechanics and Elasticity: Proceeding of the IUTAM Symposium held in Manchester, United Kingdom, 16–20 July 2000
IUTAM SYMPOSIUM ON DIFFRACTION AND SCATTERING IN FLUID MECHANICS AND ELASTICITY FLUID MECHANICS AND ITS APPLICATIONS Volume 68 Series Editor: R. MOREAU MADYLAM Ecole Nationale Superieure d'Hydraulique de Grenoble Boite Postale 95 38402 Saint Martin d'Heres Cedex, France Aims and Scope ofthe Series The purpose of this series is to focus on subjects in which fluid mechanics plays a funda - mental role . As well as the more traditional applications of aeronautics, hydraulics, heat and mass transfer etc., books will be published dealing with topics which are currently in a state of rapid development, such as turbulence, suspensions and multiphase fluids, super and hy- personic flows and numerical modelling techniques. It is a widely held view that it is the interdisciplinary subjects that will receive intense scientific attention, bringing them to the forefront of technological advancement. Fluids have the ability to transport matter and its properties as well as transmit force, therefore fluid mechanics is a subject that is particulary open to cross fertilisation with other scien- ces and disciplines of engineering. The subject of fluid mechanics will be highly relevant in domains such as chemical, metallurgical, biological and ecological engineering. This series is particularly open to such new multidisciplinary domains. The median level of presentation is the first year graduate student. Some texts are mono- graphs defining the current state of a field; others are accessible to final year undergradu- ates; but essentially the emphasis is on readability and clarity. IUTAM Symposium on Diffraction and Scattering in Fluid Mechanics and Elasticity Proceedings of the IUTAM Symposium held in Manchester, United Kingdom, 16-20 July 2000 Edited by 1. DAVID ABRAHAMS University ofManchester, Manchester, United Kingdom PAUL A. MARTIN Colorado School ofMines , Golden, Colorado , U.S.A. and MICHAEL J. SIMON University ofManchester, Manchester, United Kingdom Springer-Science+Business Media, B.V. A c.l.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-90-481-6010-5 ISBN 978-94-017-0087-0 (eBook) DOI 10.1007/978-94-017-0087-0 Printed on acid-free paper All Rights Reserved © 2002 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2002. Softcover reprint of the hardcover I st edition 2002 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Contents Preface ix Symposium Photograph xi Introduction xiii Part I Free surface and other geophysical waves 1 The scattering of Rossby waves by ocean ridges 3 I. D. Abrahams, G. W . Owen , A . J. Willmott 2 Wave diffraction through a gap in a breakwater of non-z ero thicknes s 13 N. R. T. B iggs, D. Porter 3 Nonlinear effec t s in wave scattering a nd ge nerat ion 23 R . H. J. Grimsha w 4 Reflection by slotted thick barriers under oblique wav e a ttack: 35 a numerical st ud y M. K anoria, B . N. Mandai 5 The finite dock problem 45 C. M. Linton 6 Long periodic waves on a beach 53 A. Sh errn en eu, M. Sh ermen eva 7 Wav es trapped under a moving pressure distribution 61 J.-M. Vand en-Broeck v vi IUTAM SYMPOSIUM ON DIFFRACTION AND SCATTERING Part II Energy trapping and propagation 8 Localised oscillations near submerged obstacles 71 M. McIver 9 Approximations to embedded trapped modes in wave guides 79 P. McIver 10 Trapped modes about tube bundles in waveguides 87 R. Porter, D. V. Evans 11 Phononic band structures for arrays of circular cavities in an 95 elastic medium V. V. Zalipaev, A. B. Movchan, C. G. Poulton, R . C. McPhedran Part III Propagation through inhomogeneous media 12 The split-operator technique in acoustical physics 107 D. Bosquetti, J. Stinchez-Dehesa 13 A unified model for the properties of composite materials 115 P. R. Brazier-Smith 14 Acoustic modelling of signature reduction materials for 123 underwater applications F. H. Kerr, A . M. Baird 15 Acoustic wave phase conjugation in active media 133 A. Merlen , S. Ben-Khelil, V. Preobrazhensky, P. Pernod 16 Wave passage through a string having multielement inclusions 141 with partial interior dynamics A . D. Sergeyev, D. A . Sergeyev Part IV Diffraction and propagation of acoustic waves 17 Diffraction coefficients for a circular impedance cone 151 Y. A . Antipov Contents vii 18 On the acoustics of a thick shear layer 159 L. M. B. C. Campos , M. H. Kobayashi 19 The wavenumber surface in blade-vortex interaction 169 C. J. Chapman 20 Diffraction of creeping waves by conical points 179 V. P. Smyshlyaev, V. M. Babich, D. B. Dementiev, B . A . Samokish 21 Effects of temperature gradient on the propagation of an acoustic 189 solitary wave in an air-filled tube N. Sugimoto, K. Tsujimoto 22 Scattering by blunt and sharp convex obstacles in two dimensions 199 R. H. Tew Part V Scattering by cracks 23 Diffraction coefficients for tilted surface-breaking cracks 209 V. M. Babich, V. A . Borovikov , L. Ju. Fradkin, D. Gridin, V. Kamotski, V. P. Smyshlyaev 24 Domain sensitivity analysis of the elas t ic far-field patterns 217 M. Bochniak, F. Cakoni 25 Factorisation of a cert ain Wien er-Hopf matrix arising in 227 diffraction theory P. A. Lewis 26 Theory of crack front waves 235 1. R . Willis, A . B. Movchan Part VI Fluid structural wave interaction 27 Formation of an unknown discr ete spectrum in a general spectrum 253 A . K. Abramian 28 A new class of point models in diffraction by thin elastic plates 261 I. V. Andronov viii IUTAM SYMPOSIUM ON DIFFRACTION AND SCATTERING 29 A 2-D model of the interaction between a pressure wave and a 269 submerged sandwich panel S. Kadyrov 30 On the propagation and scattering of fluid-structural waves in a 279 three-dimensional duct bounded by thin elastic walls J. B. Lawrie, 1. D. Abrahams 31 Ultrasonic backscattering enhancements for truncated objects in 289 water: quantitative models, tests and special cases P. L. Marston, F. J. Blonigen, B. T. Hefner, K. Gipson, S. F. Morse Part VII Elastic Wave Propagation 32 Kiss singularities of Green's functions of non-strictly 295 hyperbolic equations V. A . Borovikov, D. Gridin 33 Deflection of a partially clamped elastic plate 303 I. D. Abrahams, A . M. J. Davis 34 Seismic wave dynamics in regular and singular points of the ray 313 A . A. Duchkov, S. V. Goldin 35 Propagation in curved waveguides 321 J. G. Harris 36 Eigensolutions for Rayleigh wave analysis 329 A. V. Kaptsov, S. V. Kuznetsov 37 Waves in wood 337 P. A. Martin, J. R . Berger 38 Boundary integral methods for elastic layered media 345 M. Stojek, A . T. Peplow, 1. Karasalo Index 353 Preface These Conference Proceedings are intended to sum marise t he latest developments in diffraction a nd scat ter ing t heory as reported a t the IU- TAM Symposium on Diffract ion and S cattering in Fluid M echanics and Elasticity held in Manchester , England on 16-20 July 2000. This in- formal m eeting was organised to di scuss m athematical advances, both from the theoretical a nd more a pp lied points of view. However , it s pri- m ary goal was to brin g together groups of researchers working in di s- parate a pp licat ion a re as , but who nevertheless share com mon models, phenomenologi cal features a r ising in such problems, a nd com m on m ath- em a t ica l tools . To this end, we were delighted to have four Plenary Speakers, Professo rs Allan Pierce, Ed Kerschen, Roger Grimshaw a nd John Willis FRS, who are undisputed leaders in the four thematic ar- eas of ou r meeting (these a re respectively acoustics , aeroacoustics , water or other free surfac e waves , elast ici ty ) . These Proceedings shou ld offer a n exc ellent vehicle for continuing the di alogue between these gro ups of researchers . The participants were invi ted because of their ex pertise a nd recent cont r ibu t ions to this field . Collectively, there wer e around 90 cont r ib- utors to the Symposium from some 13 countries loca ted a ll a round the world . These included 45 speakers, 35 co-authors a n d about 10 other delegates . Individual s came from many of the m ajor international cen- tres of excellence in the field of scattering theory. I would like to thank my colleagues on the local Organising Commit- tee , a nd members of the Scient ific Committee , for their enormous help and advice on a ll aspects of this meeting. We a re also most grateful to the sponsors of this event, namely lUTAM, the Leverhulme Trust , the London M athematical So ciety, a nd M anch ester and K eele Universities . Their financia l ass istance a llowed us to supp or t a good number of stu- dents, research assistant s and staff from former Soviet Union countries . Finally I offer sincere thanks to Mr Andrew Looms, Learning and Tech- nology Officer a t Keele University, for the crea t ion and maintenance of our excelle nt Symposium Web site. ix x I UTA M S YMPOSIUM ON DIFFRACTION AND S CATTERING Organising Committee Chair: I D Abrahams, University of Manchester , Manchest er , UK Treasurer: M J Simon , University of Manchester , Manchest er , UK C J Chapman, Keele University, Keele, Staffordshire, UK P A Martin , Colorado School of Mines , Golden CO , USA G Wilks, Keele University, Keele, Staffordshire, UK A J Willmott, Keele University, Keele, Staffords hire, UK International Scientific Committee M A Hayes, University College, Du blin , Ireland V M Babich, Steklov Mathematical Insti tu te, St Pet ersburg, Russia A Bost rom, Chalmers University of Technology, Gotebo rg, Sweden D V Eva ns, Univers ity of Bristol, Bristol, UK R H J Gr imshaw, Loughborough University, Loughborough , UK E J Kerschen, University of Arizona, Tucson AZ, USA A N Norris , Rutgers University, Piscataway NJ , USA Sponsorship T he organisers extend their thanks to the following for sponsorship of this IUTAM Symposium : The International Union of Theoretical and Applied M echanics The Leverhulme Trust The London Mathematical Society The University of Manch ester Keele University DAVID A BRAHAMS
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