Springer Series on Waye PhenOHiena 7 Springer Series on Wa"e Phenomena Editors: L.M. Brekhovskikh L.B. Felsen H.A. Haus Managing Editor: H. K. V. Lotsch Volume 1 Mechanics of Continua and Wave Dynamics By L. Brekhovskikh, V. Goncharov Volume 2 Rayleigh-Wave Theory and Application Editors: E.A. Ash, E.G.S. Paige Volume 3 Electromagnetic Surface Excitations Editors: R.F. Wallis, G.I. Stegeman Volume 4 Asymptotic Methods in Shortwave Diffraction Theory By V. M. Babic, V. S. Buldyrev Volume 5 Geometrical Theory of Diffraction By V.A. Borovikov, B.E. Kinber Volume 6 Geometrical Optics of Inhomogeneous Media By Yu. A. Kravtsov, Yu.1. Orlov Volume 7 Recent Developments in Surface Acoustic Waves Editors: D.F. Parker, G.A. Maugin D. F. Parker G. A. Maugin (Eds.) Recent Developments in Surface Acoustic Waves Proceedings of European Mechanics Colloquium 226, University of Nottingham, U. K., September 2-5,1987 With 139 Figures Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Dr. David F. Parker University of Nottingham. Department of Theoretical Mechanics, Nottingham, NG7 2RD, U. K. Professor Gerard A. Maugin Laboratoire de Modelisation en Mecanique, Universite Pierre et Marie Curie, 4 Place lussieu, F-75252 Paris Cedex 05, France Series Editors: Professor Leonie M. Brekhovskikh, Academician P. P. Shirsov Institute of Oceanology, Academy of Sciences USSR, SU-117218 Moscow, USSR Professor Leopold B. Felsen, Ph.D. Polytechnic University, Route 110, Farmingdale, NY 11735, USA Professor Hermann A. Haus Department of Electrical Engineering & Computer Sciences, MIT, Cambridge, MA 02139, USA Managing Editor: Helmut K. V. Lotsch Springer-Verlag, TiergartenstraBe 17, D-6900 Heidelberg, Fed. Rep. of Germany ISBN- 13: 978-3-642-83510-0 e-ISBN-13: 978-3-642-83508-7 DOl: 10.1007/978-3-642-83508-7 Library of Congress Cataloging-in-Publication Data. European Mechanics Colloquium (226th : 1987 : University of Nottingham) Recent developments in surface acoustic waves: proceedings of European Mechanics Colloquium 226. University of Nottingham. U.K., September 2-5, 1987 1 editors, D.F. Parker and G. A. Maugin. - (Springer series on wave phenomena ; 7) Includes index. 1. Acoustic surface waves Congresses. I. Parker. D.F. (David F.), 1940-. II. Maugin, G.A. (Gerard A.), 1944-. III. Title. IV. Series. QCI76.8.A3E97 1987 530.4'I-dc 19 88-16049 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9,1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1988 Softcoverreprint of the hardcover 1st edition 1988 The use of registered names, trademarks, etc. in this publication does not imply, even in the absence ofaspecific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. 2154/3150-543210 Preface The topic of surface waves lies at the interface between a number of disci plines - physics, theoretical and applied mechanics, electroacoustics, ap plied mathematics, surface science and seismology. This volume, based on papers delivered at European Mechanics Colloquium 226, reflects this diversity in approach and background, while showing strong links between phenomena arising from different fields. The emphasis is on recent de velopments such as nonlinear and other nonclassical effects,which have great importance for both pure science and for applications such as signal processing, nondestructive evaluation and seismic studies. In recent years there has been considerable progress in the mathe matical treatment of nonlinear effects, of viscoelastic and of more novel constitutive effects which modify the predictions of linear elastic and piezo electric theory for surface acoustic wave (SAW) propagation. A number of these themes serve to group the contents of this volume. Part I contains recent advances in the rigorous mathematical treatment of nonlinearity, together with a paper giving experimental results showing the need for further theoretical development. Part II deals with anisotropic elasticity, showing that even the linear theory presents many possible behaviours, which are still not fully categorized. Parts III and V concern two themes which emerged strongly from the papers presented. The first is the analysis of waves travelling across rough or corrugated surfaces. The papers show that these (in practice unavoid able) irregularities can produce a variety of effects such as wave slowing, stop bands and retroreflection. The second theme is the interest in waves on composites, particularly periodically layered laminates. As shown in the survey which opens Part V, application is not just to waves in struc tural composites but also to phenomena on the microscopic scale of su perlattices. The accompanying papers emphasize the need for approxima tions. They well represent the two main approaches, either simplification of the modal analysis within the layers of a composite, or else idealization to "strictly inextensible" materials. In Part IV, a number of electromechanical interaction processes are described. These couplings are basic to the design of all SAW devices such as are used in signal processing. One paper discusses current proce dures for transducer design, while others describe a number of features of V piezoelectric waves and of surface waves in materials with more novel in teraction mechanisms. The final part, Part VI, includes analysis of waves guided along cylindrical cavities, surface waves used both in flaw detection (material evaluation) and in instruments for evaluating rheological prop erties of a surrounding fluid. It also includes treatment of surface waves in viscoelastic and thermoelastic materials. It is hoped that the reader will find, in this collection, an up-to-date account of theoretical methods for analysis of surface waves, treatment of a number of novel SAW phenomena and suggestions for future research. For this the editors have to thank the many authors for their enthusiasm at the Colloquium and their readiness to prepare written accounts. We wish to put on record our gratitude to the European Research Office of the U.S. Army for financial support and encouragement in running the Colloquium. Also, we wish to thank the University of Nottingham for providing a wide range of help and facilities, and in particular Florence Boot Hall for providing a pleasant ambience for the meeting. Nottingham, Paris, February 1988 D.F.Parker G.A.Maugin VI Contents Part I Nonlinear Surface Acoustic Waves and Applications State-of-the-Art Elastic SAW Convolvers By H.P. Grassl, L. Reindl, and H.-W. Worz (With 9 Figures) 2 Multiple Scale Techniques Applie'd to Nonlinear Elastic and Piezoelectric Surface Waves By G.E. Tupholme .................................. 14 Nonlinear Evolution of Piezoelectric SAWs By E.A. David and D.F. Parker (With 4 Figures) ............ 21 Nonlinear Piezoelectric Surface Acoustic Waves Using the Multiple Scales Technique By A.P. Harvey, R.E. Craine, and S. Syngellakis (With 1 Figure) 30 Linear and Nonlinear Surface Waves on Magnetostrictive Crystals in a Bias Magnetic Field By Abo-EI-Nour Abd-Alla and G.A. Maugin (With 2 Figures) 36 Nonlinear Mode Coupling Between Rayleigh and Love Waves on an Isotropic Layered Half-Space By N. Kalyanasundaram .............................. 47 Finite Amplitude Love Waves on an Incompressible Elastic Layered Half Space By M. Teymur (With 1 Figure) ......................... 54 Nonlinear Surface Acoustic Waves and Their Associated Surface Acoustic Solitons By A.A. Maradudin ................................. 62 Experiments on Nonlinear Effects in Ground-Surface Vibration By P.P. Dimitriu (With 6 Figures) ....................... 72 VII Part II Surface Waves on Anisotropic Substrates Aspects of the Behaviour of Surface Waves in Transversely Isotropic Elastic Media By P. Chadwick (With 3 Figures) ....................... 80 A New Method for Surface Impedance and Surface Wave Calculations By S.A. Gundersen and J. Lothe (With 3 Figures) ........... 91 Part III Surface Waves on Rough Surfaces Surface Acoustic Waves on Rough Surfaces By A.A. Maradudin (With 12 Figures) ................... 100 Rayleigh Waves Along a Corrugated Surface By A. Bostrom (With 3 Figures) ........................ 129 Localization Effects in the Scattering of Acoustic Waves from a Random Stress-free Grating Surface By A.R. McGurn and A.A. Maradudin (With 3 Figures) ....... 135 A Comparison of Some Methods for Corrugated Waveguides By S.-E. Sandstrom (With 1 Figure) ..................... 143 Love Waves in a Slab with Rough Boundaries By A. Wirgin (With 2 Figures) ......................... 145 Part IV Surface Waves on Electromagnetic Bodies Shear Horizontal Surface Acoustic Waves on Solids By G.A. Maugin (With 6 Figures) ....................... 158 Calculation of Interdigital Transducer Interaction with SAWs and BAWs By F. Seifert, A.R. Baghai-Wadji, K.C. Wagner, and G. Kovacs (With 7 Figures) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 173 Bleustein-Gulyaev Surface Waves of Arbitrary Form By W. Larecki ...................................... 185 A Dynamic Problem for a Piezoelectric Medium By J.P. Nowacki and C. Trimarco ....................... 193 Electromechanical Surface Waves in Layered Elastic Dielectrics with Polarization Gradient By K. Majorkowska-Knap and J. Lenz (With 5 Figures) ....... 201 VIII Surface Waves in a Semiconductor with Relaxation of Charge Carrier Field By B. Maruszewski (With 3 Figures) ..................... 211 Part V Surface Waves on Composites Acoustic Properties of Periodic Layers By G.W. Farnell (With 20 Figures) ...................... 218 Surface Waves on a Laminated Half-Space By W.A. Green (With 1 Figure) ........................ 236 Surface and Interface Waves in a Sandwich Plate with Interface Soft Layers By S.K. Datta, A.H. Shah, T. Chakraborty, and R.L. Bratton (With 5 Figures) .................................... 243 Rayleigh Waves in Materials Reinforced by Two Families of Fibres By D.l. Milosavljevic (With 1 Figure) .................... 251 Dispersion of Harmonic Waves in Elastic and Viscoelastic Periodic Composite Materials By Y. Chevalier (With 4 Figures) ....................... 260 Part VI Waves on Curved and Fluid-Loaded Surfaces, in Viscoelasticity and in Thermoelasticity Mathematical and Computational Aspects of the Determination of Elastic Surface Waves Along Cylindrical Cavities of General Cross Section By A. Bamberger, P. Joly, and M. Kern (With 2 Figures) ...... 270 Low Frequency Propagation of Elastic Waves in a Fluid-Filled Borehole By A. Bamberger, P. Joly, M. Kern, L. Nicoletis, and J. Quiblier (With 4 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 282 Surface Vibration of a Semi-infinite Viscoelastic Medium By P.M. O'Leary (With 4 Figures) . . . . . . . . . . . . . . . . . . . . . .. 291 Surface Waves on an Isotropic Viscoelastic Half-Space: The Method of Generalized Rays By P. Borejko and F. Ziegler (With 9 Figures) .............. 299 Acoustical Scattering by a Shallow Surface-Breaking Crack in an Elastic Solid Under Light Fluid Loading By R.H. Tew, J.R. Ockendon, and G.A.D. Briggs (With 6 Figures) 309 IX Determination of the Rheological Parameters of Viscoelastic Liquids Using Shear Surface Waves By P. KielczyIiski and W. Pajewksi ...................... 317 The Influence of Off-Centre Defects on SAW Characteristics By J. Kapelewski and W. Przybylski ..................... 322 On the Propagation of Surface Waves By T.P. Ivanov (With 6 Figures) ........................ 328 Surface Waves in Thermoelasticity with Relaxation Times By R. Wojnar (With 1 Figure) ......................... 335 Surface Waves in a Nonlocal Elastic Medium By C. Rymarz (With 5 Figures) ........................ 342 Index of Contributors . . . . . 351 x