Monograph Series in

UNDERWATER ACOUSTICS

Sponsored by Office of Naval Research

Editorial Board: Ralph R. Goodman, Ph.D., ChairHomer P. Bucker, Ph.D.Ira Dyer, Ph.D.Jeffrey A. Simmen, Ph.D.

Monograph Series in

UNDERWATER ACOUSTICS

In 2001 the Office of Naval Research began a program to publish a selected mono-graph series in the field of underwater acoustics. The series publishes in-depthreviews and analysis on the state of understanding of the physics of sound in se-lected areas of research.

The monograph series covers the most important topics in underwater sound in anin-depth, critical, scholarly, and comprehensive fashion. It is intended to provideresearchers with an understanding of the physics of underwater sound, based onboth theory and experiment. The discussion of important unanswered questions isencouraged. Topics of particular importance in the field are low-frequency soundin the deep ocean, shallow-water acoustics, and ambient noise.

Sponsored by:

Office of Naval ResearchOne Liberty Center875 North Randolph Street, Suite 1425Arlington, VA 22203-1995E-mail: onrpao@onr.navy.mil

Series Editors:

Ralph R. Goodman, Ph.D. Homer P. Bucker, Ph.D.Research Professor 808 Moana DriveUSM Department of Marine Science San Diego, CA 921061020 Balch Blvd E-mail: bucker@nosc.milStennis Space Center, MS 39529E-mail: ralph.goodman@usm.edu

Ira Dyer, Ph.D. Jeffrey A. Simmen, Ph.D.Weber Shaughness Professor Applied Physics Laboratory

of Ocean Engineering, Emeritus University of WashingtonMassachusetts Institute of Technology 1013 NE 40th StreetCambridge, MA 02139 Seattle, WA 98105-6698

E-mail: simmen@apl.washington.edu

Charles H. ShermanJohn L. Butler

Transducers and Arraysfor Underwater Sound

With 388 Illustrations

ABC

Charles H. Sherman John L. ButlerPrincipal Scientist Chief ScientistImage Acoustics, Inc. Image Acoustics, Inc.97 Elm Street 97 Elm StreetCohasset, MA 02025 Cohasset, MA 02025

Library of Congress Control Number: 2006921991

ISBN-10: 0-387-32940-4 e-ISBN 0-387-33139-5ISBN-13: 978-0387-32940-6

Printed on acid-free paper.

c© 2007 Springer Science+Business Media, LLCAll rights reserved. This work may not be translated or copied in whole or in part without the writtenpermission of the publisher (Springer Science+Business Media, LLC, 233 Springer Street, New York,NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Usein connection with any form of information storage and retrieval, electronic adaptation, computersoftware, or by similar or dissimilar methodology now known or hereafter developed is forbidden.The use in this publication of trade names, trademarks, service marks, and similar terms, even if theyare not identified as such, is not to be taken as an expression of opinion as to whether or not they aresubject to proprietary rights.

9 8 7 6 5 4 3 2 1

springer.com

To Elizabeth and Nancy

Series Preface

The efficacy of sound to penetrate the seas made acoustic systems in the past cen-tury the leading tools for sensing objects in and measuring properties of the seas.For over sixty years The United States Office of Naval Research (ONR) has beena major sponsor of undersea research and development at universities, nationallaboratories, and industrial organizations. Appropriately ONR is the sponsor ofthis monograph series.

The intent of the series is to summarize recent accomplishments in, and tooutline perspectives for, underwater acoustics in specific fields of research. Thegeneral field has escalated in importance and spread broadly with richness anddepth of understanding. It has also, quite naturally, become more specialized. Thegoal of this series is to present monographs that critically review both past andrecent accomplishments in order to address the shortcomings in present under-standing. In this way, these works will bridge the gaps in understanding amongthe specialists and favorably color the direction of new research and development.Each monograph is intended to be a stand-alone advanced contribution to the field.We trust that the reader will also find that each is a critical introduction to relatedspecialized topics of interest as well.

ONR has sponsored the series through grants to the authors. Authors areselected by ONR based on the quality and relevance of each proposal and theauthor’s experience in the field. The Editorial Board, selected by ONR, has, attimes, provided independent views to ONR in this process. Its sole official role,however, is to judge the manuscripts before publication and to assist each authorat his request through the process with suggestions and broad encouragement.

Ralph R. Goodman, Ph.D.Ira Dyer, Ph.D.

Homer P. Bucker, Ph.D.Jeffrey A. Simmen, Ph.D.

vii

Preface

We have written this book as part of the underwater acoustics monograph seriesinitiated by the Office of Naval Research (ONR), Department of the Navy of theUnited States. The ONR objective for this series is publication of in-depth reviewsand analyses of the state of understanding of the physics of sound in selectedareas of undersea research. This monograph presents the theory and practice ofunderwater electroacoustic transducers and arrays as developed during the lasthalf of the twentieth century and into the initial part of the twenty-first century.

We have attempted to present a comprehensive coverage of the subject of trans-ducers and arrays for underwater sound starting with a brief historical review anda survey of some of the many modern applications. Descriptions of the six majortypes of electroacoustic transducers are presented in a unified way that facilitatestheir comparison and explains why some types are better suited than others forproducing and receiving sound in the water. The characteristics of transducersused as both projectors and hydrophones, and the methods available for predict-ing and measuring transducer performance, are presented in detail. The reasonsfor combining large numbers of transducers in arrays are explained, and the spe-cial problems that must be considered in such arrays are analyzed. The nonlinearmechanisms that exist in all transducers are described, and analyses of some oftheir most important effects are given. Many different acoustical quantities playessential roles in the design and performance of electroacoustic transducers andarrays, and the methods for determining these quantities are presented. Analyt-ical modeling and understanding is emphasized throughout the book, but it isalso made clear that numerical modeling is now an essential part of transducerand array design. Non-electroacoustic types of transducers that are used in certainunderwater applications, such as explosive sources, spark sources, hydroacousticsources, and optical hydrophones, are not included in this book.

The monograph is organized in a manner that brings the reader quickly to themain body of results on current transducers and arrays in the first six chapterswith a minimum of background material. The most important basic concepts ofelectroacoustic transduction are introduced in Chapter 1, after a brief historicalreview and a survey of some of the many applications of transducers and ar-rays. Chapter 2 describes and compares the six major types of electroacoustic

ix

x Preface

transducers, presents additional transducer concepts and characteristics, and intro-duces the equivalent circuit method of transducer analysis. Chapters 3 through 6contain the main body of results on modern transducers and arrays. Chapters 3and 4 cover transducers as projectors, which produce sound, and as hydrophones,which receive sound, including many details of specific transducer designs as theyare used in current applications. Chapters 5 and 6 explain the benefits of combin-ing large numbers of transducers in arrays that often contain more than a thousandindividual transducers. These large arrays are necessary in many sonar applica-tions, but they introduce other problems that are also discussed and analyzed.

The remaining six chapters, 7 through 12, support the earlier chapters and carrythe discussion of concepts and methods into much more detail for those who seeka deeper understanding of transducer operation. Chapter 7 describes all the princi-pal methods of transducer modeling, analysis, and design, including an introduc-tion to the finite element method. Chapter 8 gives further discussion of the mostimportant transducer characteristics. Chapter 9 describes the principal nonlinearmechanisms that occur in all the transducer types and presents methods of analyz-ing important nonlinear effects such as harmonic distortion. Chapter 10 presentsthe basic acoustics necessary for determining those acoustical quantities, such asdirectivity patterns and radiation impedance, that are essential to transducer andarray analysis and design. It also includes useful results for such quantities inseveral typical cases. Chapter 11 extends the discussion of acoustical quantitiesby introducing more advanced methods of analysis that can be applied to morecomplicated cases including a brief introduction to numerical methods. Chapter12 is a summary of the major methods of measurement used for the evaluationof transducer and array performance. The book ends with an extensive Appen-dix containing several types of specific information that can be used in transduceranalysis and design and with a Glossary of Terms.

We have attempted to make this monograph suitable for beginners to learnfrom— and for practitioners in the transducer field to learn more from. In addition,those concerned in any way with undersea research may find useful guidance re-garding applications of transducers and arrays. Although some parts of this bookmay be useful to undergraduates, it is written on a graduate level for engineers andscientists in the fields of electrical engineering, mechanical engineering, physics,ocean engineering, and acoustical engineering. The book uses SI (MKS) unitsin general, but English units are also occasionally used to clarify the relationshipto practical devices.

C.H. Sherman and J.L. ButlerCohasset, Massachusetts

July 2006.

Acknowledgements

This monograph is based on the experience of the authors in both governmentand industrial organizations. Our careers have been devoted mainly to the manyneeds of the United States Navy for underwater sound transducers and arrays,and we are grateful to ONR and other organizations in government and industryfor support through all those years. We are also grateful to our early teachersin the fields of transducers and acoustics: Dr. R.S. Woollett, E.J. Parsinnen, andH. Sussman of the Navy Underwater Sound Laboratory (now Naval UnderseaWarfare Center, NUWC), Dr. W.J. Remillard, Northeastern University, Dr. R.T.Beyer, Brown University, Dr. T.J. Mapes, NUWC, G.W. Renner, HazeltineCorporation (now Ultra Electronics), B. McTaggart, NUWC, Frank Massa, MassaProducts Corporation, and Stan Ehrlich, Raytheon Company.

We are also grateful to the many other people who have contributed in spe-cific ways to this book: To Jan F. Lindberg of ONR and NUWC for encouragingus to take on this task and advising us as it progressed. To Dr. J.A. Simmen andDr. D. Todoroff of ONR for initiating and overseeing this monograph series. To theBoard of Editors appointed by ONR, Drs. R.R. Goodman, I. Dyer, H.P. Bucker,and J.A. Simmen, for their discussions and suggestions. To A.L. Butler ofImage Acoustics for preparation of the numerous illustrations and graphs. ToDr. W. Thompson, Jr. of Pennsylvania State University and W.J. Marshall ofRaytheon Company for their review of the book as the work progressed; their sug-gestions and comments were very helpful and encouraging. To Dr. M.B. Moffettfor help with the section on parametric arrays and for information on piezoelec-tric materials, D.T. Porter for reviewing Chapter 10 and Dr. R.C. Elswick forreviewing parts of Chapter 6. Discussions with the following colleagues were alsovery helpful at various points: S.C. Butler and Drs. H.H. Schloemer, S.H. Ko,W.A. Strawderman, R.T. Richards, A.E. Clark, and J.E. Boisvert.

We are especially grateful to our wives, Elizabeth Bugbee Sherman and NancyClark Butler, for their understanding and assistance.

xi

Contents

Series Preface viiPreface ixAcknowledgements xiChapter 1: Introduction 1

1.1 Brief History of Underwater Sound Transducers . . . . . . . . 21.2 Underwater Transducer Applications . . . . . . . . . . . . . . . . . 91.3 General Description of Linear

Electroacoustic Transduction . . . . . . . . . . . . . . . . . . . . . . . . 181.4 Transducer Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . 23

1.4.1 Electromechanical Coupling Coefficient . . . . . . . . 231.4.2 Transducer Responses, Directivity Index and

Source Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251.5 Transducer Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Chapter 2: Electroacoustic Transduction 312.1 Piezoelectric Transducers . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.1.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322.1.2 The 33-Mode Longitudinal Vibrator . . . . . . . . . . . 372.1.3 The 31-Mode Longitudinal Vibrator . . . . . . . . . . . 40

2.2 Electrostrictive Transducers . . . . . . . . . . . . . . . . . . . . . . . . . 422.3 Magnetostrictive Transducers . . . . . . . . . . . . . . . . . . . . . . . 452.4 Electrostatic Transducers . . . . . . . . . . . . . . . . . . . . . . . . . . . 482.5 Variable Reluctance Transducers . . . . . . . . . . . . . . . . . . . . . 512.6 Moving Coil Transducers . . . . . . . . . . . . . . . . . . . . . . . . . . . 532.7 Comparison of Transduction Mechanisms . . . . . . . . . . . . . 552.8 Equivalent Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

2.8.1 Equivalent Circuit Basics . . . . . . . . . . . . . . . . . . . . 582.8.2 Circuit Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . 602.8.3 Circuit Q and Bandwidth . . . . . . . . . . . . . . . . . . . . . 612.8.4 Power Factor and Tuning . . . . . . . . . . . . . . . . . . . . . 632.8.5 Power Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 672.8.6 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

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xiv Contents

2.8.7 Hydrophone Circuit and Noise . . . . . . . . . . . . . . . . 712.8.8 Extended Equivalent Circuits . . . . . . . . . . . . . . . . . 73

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Chapter 3: Transducers as Projectors 76

3.1 Principles of Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 783.2 Ring and Spherical Transducers . . . . . . . . . . . . . . . . . . . . . 81

3.2.1 Piezoelectric 31-Mode Ring . . . . . . . . . . . . . . . . . . 813.2.2 Piezoelectric 33-Mode Ring . . . . . . . . . . . . . . . . . . 863.2.3 The Spherical Transducer . . . . . . . . . . . . . . . . . . . . 883.2.4 The Magnetostrictive Ring . . . . . . . . . . . . . . . . . . . 903.2.5 Free Flooded Rings . . . . . . . . . . . . . . . . . . . . . . . . . 913.2.6 Multimode Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

3.3 Piston Transducers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 983.3.1 The Tonpilz Projector . . . . . . . . . . . . . . . . . . . . . . . 983.3.2 The Hybrid Transducer . . . . . . . . . . . . . . . . . . . . . . 106

3.4 Transmission Line Transducers . . . . . . . . . . . . . . . . . . . . . . 1103.4.1 Sandwich Transducers . . . . . . . . . . . . . . . . . . . . . . . 1113.4.2 Wideband Transmission Line Transducers . . . . . . 1153.4.3 Large Plate Transducers . . . . . . . . . . . . . . . . . . . . . . 1203.4.4 Composite Transducers . . . . . . . . . . . . . . . . . . . . . . 122

3.5 Flextensional Transducers . . . . . . . . . . . . . . . . . . . . . . . . . . 1263.5.1 The Class IV and VII

Flextensional Transducers . . . . . . . . . . . . . . . . . . . . 1273.5.2 The Class I Barrel Stave Flextensional . . . . . . . . . 1313.5.3 The Class V and VI

Flextensional Transducers . . . . . . . . . . . . . . . . . . . . 1323.5.4 The Astroid and X-spring

Flextensional Transducers . . . . . . . . . . . . . . . . . . . . 1333.6 Flexural Transducers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

3.6.1 Bender Bar Transducer . . . . . . . . . . . . . . . . . . . . . . 1373.6.2 Bender Disc Transducer . . . . . . . . . . . . . . . . . . . . . . 1403.6.3 The Slotted Cylinder Transducer . . . . . . . . . . . . . . 1423.6.4 The Bender Mode X-spring Transducer . . . . . . . . . 145

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146Chapter 4: Transducers as Hydrophones 152

4.1 Principles of Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1534.1.1 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1544.1.2 Figure of Merit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1564.1.3 Simplified Equivalent Circuit . . . . . . . . . . . . . . . . . 1574.1.4 Other Sensitivity Considerations . . . . . . . . . . . . . . 159

4.2 Cylindrical and Spherical Hydrophones . . . . . . . . . . . . . . . 1624.2.1 Performance with Shielded Ends . . . . . . . . . . . . . . 1624.2.2 Spherical Hydrophones . . . . . . . . . . . . . . . . . . . . . . 1654.2.3 Performance with End Caps . . . . . . . . . . . . . . . . . . 166

Contents xv

4.3 Planar Hydrophones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1684.3.1 Tonpilz Hydrophones . . . . . . . . . . . . . . . . . . . . . . . . 1694.3.2 The 1-3 Composite Hydrophone . . . . . . . . . . . . . . . 1704.3.3 Flexible Hydrophones . . . . . . . . . . . . . . . . . . . . . . . 173

4.4 Bender Hydrophones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1744.5 Vector Hydrophones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

4.5.1 Dipole Vector Sensors, Baffles, and Images . . . . . 1774.5.2 Pressure Gradient Vector Sensor . . . . . . . . . . . . . . . 1824.5.3 Velocity Vector Sensor . . . . . . . . . . . . . . . . . . . . . . . 1834.5.4 Accelerometer Sensitivity . . . . . . . . . . . . . . . . . . . . 1844.5.5 Multimode Vector Sensor . . . . . . . . . . . . . . . . . . . . 1874.5.6 Summed Scalar and Vector Sensors . . . . . . . . . . . . 1894.5.7 Intensity Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

4.6 The Plane Wave Diffraction Constant . . . . . . . . . . . . . . . . . 1954.7 Hydrophone Thermal Noise . . . . . . . . . . . . . . . . . . . . . . . . . 199

4.7.1 Directivity and Noise . . . . . . . . . . . . . . . . . . . . . . . . 2004.7.2 Low Frequency Hydrophone Noise . . . . . . . . . . . . 2024.7.3 A More General Description

of Hydrophone Noise . . . . . . . . . . . . . . . . . . . . . . . . 2024.7.4 A Comprehensive Hydrophone Noise Model . . . . 2054.7.5 Vector Sensor Internal Noise . . . . . . . . . . . . . . . . . . 2064.7.6 Vector Sensor Susceptibility to Local Noise . . . . . 208

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209Chapter 5: Projector Arrays 213

5.1 Array Directivity Functions . . . . . . . . . . . . . . . . . . . . . . . . . 2175.1.1 The Product Theorem . . . . . . . . . . . . . . . . . . . . . . . 2175.1.2 Line, Rectangular, and Circular Arrays . . . . . . . . . 2185.1.3 Grating Lobes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2215.1.4 Beam Steering and Shaping . . . . . . . . . . . . . . . . . . 2235.1.5 Effects of Random Variations . . . . . . . . . . . . . . . . . 229

5.2 Mutual Radiation Impedance and the Array Equations . . . 2305.2.1 Solving the Array Equations . . . . . . . . . . . . . . . . . . 2305.2.2 Velocity Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2345.2.3 Negative Radiation Resistance . . . . . . . . . . . . . . . . 235

5.3 Calculation of Mutual Radiation Impedance . . . . . . . . . . . 2365.3.1 Planar Arrays of Piston Transducers . . . . . . . . . . . 2365.3.2 Non-Planar Arrays, Nonuniform Velocities . . . . . . 241

5.4 Arrays of Non-FVD Transducers . . . . . . . . . . . . . . . . . . . . . 2445.4.1 Modal Analysis of Radiation Impedance . . . . . . . . 2445.4.2 Modal Analysis of Arrays . . . . . . . . . . . . . . . . . . . . 245

5.5 Volume Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2495.6 Near Field of a Projector Array . . . . . . . . . . . . . . . . . . . . . . 2515.7 The Nonlinear Parametric Array . . . . . . . . . . . . . . . . . . . . . 253References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259

xvi Contents

Chapter 6: Hydrophone Arrays 2626.1 Hydrophone Array Directional and

Wavevector Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2646.1.1 Directivity Functions . . . . . . . . . . . . . . . . . . . . . . . . 2646.1.2 Beam Steering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2676.1.3 Shading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2696.1.4 Wavevector Response of Arrays . . . . . . . . . . . . . . . 274

6.2 Array Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2766.3 Sources and Properties of Noise in Arrays . . . . . . . . . . . . . 279

6.3.1 Ambient Sea Noise . . . . . . . . . . . . . . . . . . . . . . . . . . 2796.3.2 Structural Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2836.3.3 Flow Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284

6.4 Reduction of Array Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . 2856.4.1 Reduction of Ambient Noise . . . . . . . . . . . . . . . . . . 2856.4.2 Reduction of Structural Noise . . . . . . . . . . . . . . . . . 2896.4.3 Reduction of Flow Noise . . . . . . . . . . . . . . . . . . . . . 2946.4.4 Summary of Noise Reduction . . . . . . . . . . . . . . . . . 297

6.5 Arrays of Vector Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . 3006.5.1 Directionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3016.5.2 Unbaffled Vector Sensor Arrays in

Ambient Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3036.5.3 Hull-Mounted Vector Sensor Arrays in

Structural Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317

Chapter 7: Transducer Models 3207.1 Lumped Parameter Models and Equivalent Circuits . . . . . 321

7.1.1 Mechanical Single Degree-of-Freedom LumpedEquivalent Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . 321

7.1.2 Mechanical Lumped Equivalent Circuits forHigher Degrees of Freedom . . . . . . . . . . . . . . . . . . 324

7.1.3 Piezoelectric Ceramic Lumped-ParameterEquivalent Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . 327

7.1.4 Magnetostrictive Lumped-ParameterEquivalent Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . 332

7.1.5 Eddy Currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3367.2 Distributed Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338

7.2.1 Distributed Mechanical Model . . . . . . . . . . . . . . . . 3397.2.2 Matrix Representation . . . . . . . . . . . . . . . . . . . . . . . 3437.2.3 Piezoelectric Distributed-Parameter

Equivalent Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . 3467.2.3.1 Segmented 33 Bar . . . . . . . . . . . . . . . . . . . 3467.2.3.2 Un-segmented 31 Bar . . . . . . . . . . . . . . . . 3507.2.3.3 Length Expander Bar . . . . . . . . . . . . . . . . . 3517.2.3.4 Thickness-Mode Plate . . . . . . . . . . . . . . . . 3537.2.3.5 Magnetostrictive Rod . . . . . . . . . . . . . . . . . 354

Contents xvii

7.3 Matrix Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3557.3.1 Three-Port Matrix Model . . . . . . . . . . . . . . . . . . . . . 3557.3.2 Two-Port ABCD Matrix Model . . . . . . . . . . . . . . . 358

7.4 Finite Element Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3607.4.1 A Simple FEM Example . . . . . . . . . . . . . . . . . . . . . 3607.4.2 FEM Matrix Representation . . . . . . . . . . . . . . . . . . 3617.4.3 Inclusion of a Piezoelectric Finite Element . . . . . . 3647.4.4 Application of FEM without Water Loading . . . . . 3657.4.5 Application of FEM with Water Loading . . . . . . . 3687.4.6 Water Loading of Large Arrays . . . . . . . . . . . . . . . 3717.4.7 Magnetostrictive FEM . . . . . . . . . . . . . . . . . . . . . . . 372

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373Chapter 8: Transducer Characteristics 376

8.1 Resonance Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3768.2 The Mechanical Quality Factor . . . . . . . . . . . . . . . . . . . . . . 379

8.2.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3798.2.2 Effect of the Mass of the Bar . . . . . . . . . . . . . . . . . . 3818.2.3 The Effect of Frequency-Dependent Resistance . . 383

8.3 Characteristic Mechanical Impedance . . . . . . . . . . . . . . . . . 3848.4 Electromechanical Coupling Coefficient . . . . . . . . . . . . . . 386

8.4.1 Energy Definitions of Coupling andOther Interpretations . . . . . . . . . . . . . . . . . . . . . . . . 3868.4.1.1 Mason’s Energy Definition . . . . . . . . . . . . 3868.4.1.2 The Mutual Energy Definition . . . . . . . . . 3898.4.1.3 Other Features of the

Coupling Coefficient . . . . . . . . . . . . . . . . . 3908.4.2 The Effect of Inactive Components on the

Coupling Coefficient . . . . . . . . . . . . . . . . . . . . . . . . 3918.4.3 The Effect of Dynamic Conditions on the

Coupling Coefficient . . . . . . . . . . . . . . . . . . . . . . . . 396References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400

Chapter 9: Nonlinear Mechanisms and Their Effects 4029.1 Nonlinear Mechanisms in

Lumped-Parameter Transducers . . . . . . . . . . . . . . . . . . . . . 4039.1.1 Piezoelectric Transducers . . . . . . . . . . . . . . . . . . . . 4039.1.2 Electrostrictive Transducers . . . . . . . . . . . . . . . . . . 4089.1.3 Magnetostrictive Transducers . . . . . . . . . . . . . . . . . 4099.1.4 Electrostatic and Variable

Reluctance Transducers . . . . . . . . . . . . . . . . . . . . . . 4129.1.5 Moving Coil Transducers . . . . . . . . . . . . . . . . . . . . 4139.1.6 Other Nonlinear Mechanisms . . . . . . . . . . . . . . . . . 415

9.2 Analysis of Nonlinear Effects . . . . . . . . . . . . . . . . . . . . . . . 4159.2.1 Harmonic Distortion–Direct Drive

Perturbation Analysis . . . . . . . . . . . . . . . . . . . . . . . . 4169.2.2 Harmonic Distortion for Indirect Drive . . . . . . . . . 424

xviii Contents

9.2.3 Instability in Electrostatic andVariable-Reluctance Transducers . . . . . . . . . . . . . . 425

9.3 Nonlinear Analysis of Distributed-Parameter Transducers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428

9.4 Nonlinear Effects on the ElectromechanicalCoupling Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435Chapter 10: Acoustic Radiation from Transducers 438

10.1 The Acoustic Radiation Problem . . . . . . . . . . . . . . . . . . . . . 43810.2 Far-Field Acoustic Radiation . . . . . . . . . . . . . . . . . . . . . . . . 445

10.2.1 Line Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44510.2.2 Flat Sources in a Plane . . . . . . . . . . . . . . . . . . . . . . . 44710.2.3 Spherical and Cylindrical Sources . . . . . . . . . . . . . 454

10.3 Near-Field Acoustic Radiation . . . . . . . . . . . . . . . . . . . . . . . 45510.3.1 Field on the Axis of a Circular Piston . . . . . . . . . . 45510.3.2 The Effect of the Near Field on Cavitation . . . . . . 45610.3.3 Near Field of Circular Sources . . . . . . . . . . . . . . . . 459

10.4 Radiation Impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46010.4.1 Spherical Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . 46010.4.2 Circular Sources in a Plane . . . . . . . . . . . . . . . . . . . 463

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465Chapter 11: Advanced Acoustic Radiation Calculations 467

11.1 Mutual Radiation Impedance . . . . . . . . . . . . . . . . . . . . . . . . 46711.1.1 Piston Transducers on a Sphere . . . . . . . . . . . . . . . 46711.1.2 Piston Transducers on a Cylinder . . . . . . . . . . . . . . 47211.1.3 The Hankel Transform . . . . . . . . . . . . . . . . . . . . . . . 47711.1.4 The Hilbert Transform . . . . . . . . . . . . . . . . . . . . . . . 479

11.2 Green’s Theorem and Acoustic Reciprocity . . . . . . . . . . . . 48111.2.1 Green’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . 48111.2.2 Acoustic Reciprocity . . . . . . . . . . . . . . . . . . . . . . . . 48211.2.3 Green’s Function Solutions . . . . . . . . . . . . . . . . . . . 48311.2.4 The Helmholtz Integral Formula . . . . . . . . . . . . . . . 487

11.3 Effects of Acoustic Scattering . . . . . . . . . . . . . . . . . . . . . . . 49011.3.1 The Diffraction Constant . . . . . . . . . . . . . . . . . . . . . 49011.3.2 Scattering from Cylinders . . . . . . . . . . . . . . . . . . . . 493

11.4 Numerical Methods for Acoustic Calculations . . . . . . . . . 49511.4.1 Mixed Boundary Conditions—Collocation . . . . . . 49511.4.2 Boundary Element Methods . . . . . . . . . . . . . . . . . . 498

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501Chapter 12: Transducer Evaluation and Measurement 505

12.1 Electrical Measurement of Transducers in Air . . . . . . . . . . 50512.1.1 Electric Field Transducers . . . . . . . . . . . . . . . . . . . . 50612.1.2 Magnetic Field Transducers . . . . . . . . . . . . . . . . . . 509

12.2 Measurement of Transducers in Water . . . . . . . . . . . . . . . . 51112.3 Measurement of Transducer Efficiency . . . . . . . . . . . . . . . . 516

Contents xix

12.4 Acoustic Responses of Transducers . . . . . . . . . . . . . . . . . . 51712.5 Reciprocity Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52112.6 Tuned Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524

12.6.1 Electric Field Transducers . . . . . . . . . . . . . . . . . . . . 52512.6.2 Magnetic Field Transducers . . . . . . . . . . . . . . . . . . 528

12.7 Near-field Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 53012.7.1 Distance to the Far-field . . . . . . . . . . . . . . . . . . . . . . 53012.7.2 Measurements in Tanks . . . . . . . . . . . . . . . . . . . . . . 53112.7.3 Near- to Far-field Extrapolation—

Small Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53412.7.4 Near- to Far-field Extrapolation—

Large Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53512.7.5 Effect of Transducer Housings . . . . . . . . . . . . . . . . 539

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541The Future 543Appendix 546

A.1 Conversions and Constants . . . . . . . . . . . . . . . . . . . . . . . . . . 546A.2 Transducer Materials Ordered by Impedance, ρc . . . . . . . 547A.3 Time Averages, Power Factor, Complex Intensity . . . . . . . 548A.4 Relationships Between Piezoelectric Coefficients . . . . . . . 550A.5 Small-Signal Properties of Piezoelectric Ceramics . . . . . . 551A.6 Piezoelectric Ceramic Approximate

Frequency Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554A.7 Small Signal Properties of Magnetostrictive Materials . . . 554A.8 Voltage Divider and Thevenin Equivalent Circuit . . . . . . . 555A.9 Magnetic Circuit Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 556A.10 Norton Circuit Transformations . . . . . . . . . . . . . . . . . . . . . . 558A.11 Integral Transform Pairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559A.12 Calibrated Transducers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560A.13 Frequently Used Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . 567A.14 Stress and Field Limits for Piezoelectric Ceramics . . . . . . 570A.15 Comprehensive Hydrophone Noise Model . . . . . . . . . . . . . 571A.16 Cables and Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . 579A.17 Thermal Noise and Radiation Resistance . . . . . . . . . . . . . . 582

Glossary of Terms 587Index 599

1Introduction

The development of underwater electroacoustic transducers expanded rapidly dur-ing the twentieth century, and continues to be a growing field of knowledge,with many significant applications, one that combines mechanics, electricity, mag-netism, solid state physics and acoustics. In the most general sense, a transduceris a process or a device that converts energy from one form to another. Thus anelectroacoustic transducer converts electrical energy to acoustical energy or viceversa. Such processes and devices are very common. For example, a thunderstormis a naturally occurring process in which electrical energy, made visible by thelightning flash, is partially converted to the sound of thunder. On the other hand,the moving coil loudspeaker used in radio, television and other sound systems isa familiar man-made transducer. Loudspeakers are so common that they probablyoutnumber people in developed parts of the world. The familiar designations loud-speaker and microphone for transducers used as sources and receivers of sound inair become projector and hydrophone for sources and receivers in water. The termSONAR (SOund Navigation And Ranging) is used for the process of detecting andlocating objects by receiving the sounds they emit (passive sonar), or by receivingthe echoes reflected from them when they are insonified (see Glossary of Terms)in echo-ranging (active sonar). Every use of sound in the water requires transduc-ers for the generation and reception of the sound, and most of the transducers arebased on electroacoustics. Several non-electroacoustic transducers also find appli-cations in water, (e.g., projectors based on explosions, sparks and hydroacousticsas well as optical hydrophones), but they are not included in this book.

This book presents the theory and practice of underwater electroacoustic trans-ducers at the beginning of the twenty-first century. Chapter 1 begins with a briefhistorical survey of the development of electroacoustics and its many applicationsto underwater sound. It also introduces the basic concepts of electroacoustic trans-duction in a general way applicable to all types of electroacoustic transducers.Chapter 2 describes and compares the six major types of electroacoustic trans-duction mechanisms to show why certain piezoelectric materials now dominatethe field of underwater transducers. Chapter 2 also introduces the transducercharacteristics and analysis methods needed to discuss the specific projector andhydrophone designs presented in Chapters 3 and 4. Chapters 5 and 6 discuss arrays

1

2 1. Introduction

of projectors and hydrophones and the benefits and problems associated with ar-rays. The last half century has seen many improvements in transduction materials,and in the concepts, models and methods of calculation and measurement thatare available for current transducer design and future transducer development. Allthese matters are discussed in more detail in Chapters 7 through 12.

1.1. Brief History of Underwater Sound Transducers

Electroacoustics began to develop more than 200 years ago with observations ofthe mechanical effects associated with electricity and magnetism, and found animportant place in underwater sound early in the twentieth century. F.V. Hunt hasgiven the most complete historical survey of the development of electroacoustics,including a section entitled Electroacoustics Goes to Sea [1]. (Numbered refer-ences are listed at the end of each chapter.) R.J. Urick’s brief historical introduc-tion concentrates on underwater applications of electroacoustics [2]. R.T. Beyer’srecent history of the past 200 years of acoustics also contains many references tounderwater sound transducers [3]. A few historical items taken from these bookswill be briefly described here. Daniel Colladon and Charles Sturm collaboratedin 1826 on the first direct measurement of the speed of sound in the fresh waterof Lake Geneva in Switzerland [3]. They had no electroacoustic transducer togenerate sound in the water; instead their projector was a mechanoacoustictransducer—the striking of a bell under water. At one point on the lake the bellwas struck simultaneously with a flash of light, while an observer in a boat 13 kmaway measured the time interval between the flash and the arrival of the sound.The observer also had no electroacoustic transducer for detecting the arrival ofthe sound; his hydrophone consisted of his ear placed at one end of a tube withthe other end in the water. Their measured value at a water temperature of 8◦C isgiven by Beyer as 1438 m/s [3], and by Rayleigh as 1435 m/s [4]. A modern valuefor fresh water at 8◦C is 1439 m/s [3, 5]. This is remarkable accuracy for a firstmeasurement and for a propagation time of less than 10 seconds.

Interest in telegraphy in the latter part of the eighteenth and the first part ofthe nineteenth centuries provided the first practical impetus for the developmentof electrical transducers. Acoustics was not involved at first; a mechanical inputcausing an electrical signal could be visually observed at the other end of thetelegraph wires as another mechanical effect, (e.g., the motion of a needle). Thedevices used at each end of the system were electromechanical or magnetome-chanical transducers. Electroacoustic transducers were introduced into telegraphyby Joseph Henry in 1830 using a moving armature transducer (now often calledvariable reluctance transducer) in which the transmitted signal was observed bythe sound of the armature striking its stops. These developments led to the inven-tion of the telephone, primarily by Alexander Graham Bell in 1876, using movingarmature electroacoustic transducers on both ends of the line.

James Joule is usually credited with the discovery of magnetostriction based onhis quantitative experiments between 1842 and 1847 including measurement of

Brief History of Underwater Sound Transducers 3

FIGURE 1.1. Early simple underwater signaling system using hammer, rod and piston,courtesy Raytheon Company [27].

the change in length of an iron bar when it is magnetized, although various mani-festations of magnetostriction had been observed earlier by others [1]. In 1880,piezoelectricity was discovered in quartz and other crystals by Jacques and PierreCurie [1]. The discoveries of magnetostriction and piezoelectricity would even-tually have tremendous importance for underwater sound, since materials withsuch properties are now used in most underwater transducers. Magnetostrictiveand piezoelectric materials change dimensions when placed in magnetic or elec-tric fields, respectively, and have other properties that make them very suitable forradiating or receiving sound in water. Interest in the mechanical effects of elec-tric and magnetic fields was also closely associated with the development duringthe nineteenth century of a theoretical understanding of electricity, magnetism andelectromagnetism.

The first application of underwater sound to navigation was made by the Sub-marine Signal Company (later a division of the Raytheon Company) early in thetwentieth century. It required the crew of a ship to measure the time interval be-tween hearing the arrival of an underwater sound and an airborne sound. A bellstriking underwater was the source of sound in the water while the simultaneousblast of a foghorn at the same location provided the sound in air. Early shipboardacoustic devices included mechanical means for generating sound, as illustratedin Fig. 1.1 and binaural means for determining the direction of sound as shown inFig. 1.2.

L.F. Richardson filed patent applications with the British Patent Office for echoranging with both airborne and underwater sound in 1912, soon after the Titaniccollided with an iceberg. He apparently did not implement these ideas, probably

4 1. Introduction

FIGURE 1.2. Early binaural detection and localization air tube underwater sensor, courtesyRaytheon Company [27].

because suitable transducers were not available. However, R.A. Fessenden, aCanadian working in the United States, soon filled that need by developing a newtype of moving coil transducer (see Fig. 1.3) which, by 1914, was successfullyused for signaling between submarines and for echo ranging.

On 27 April, 1914 an iceberg was detected at a distance of nearly two miles byunderwater echo ranging using Fessenden’s transducers. These “Fessenden Oscil-lators” operating at 500 and 1000 Hz were installed on United States submarinesduring World War I. This was probably the first practical application of underwaterelectroacoustic transducers [27, 28].

Before the start of World War I it was understood that electromagnetic waveswere absorbed in a short distance in water, except for extremely low frequenciesand also for blue-green light. Thus sound waves were the only means availablefor practical signaling through the water. For the first time a significant submarinemenace existed [6], and many underwater echo ranging experiments were initiated.In France Paul Langevin and others started work early in 1915 using an electro-static transducer as a projector and a waterproofed carbon microphone as a hydro-phone. Although some success was achieved in receiving echoes from targets atshort range, numerous problems made it clear that improved transducers werenecessary. When the French results were communicated to the British, a groupunder R. W. Boyle (the Allied Submarine Detection Investigation Committee,ASDIC) began similar experiments in 1916. While both sides realized that use

Brief History of Underwater Sound Transducers 5

FIGURE 1.3. Fessenden low frequency moving coil linear induction motor transducer,Courtesy Raytheon Company [27]. See Fay [27], Stewart and Lindsay [28] and paper byFay in Groves [29] for description of operation and response.

of the piezoelectric effect in quartz had the potential for improved transducers, itwas Langevin who demonstrated the value of piezoelectricity as soon as he foundsuitable samples of quartz. Improved results were obtained first by replacing thecarbon hydrophone with a quartz hydrophone, and again in early 1917 when quartztransducers were used for both projector and hydrophone. After further improve-ments in the design of the quartz transducers, echoes were heard from a submarinein early 1918. The major design improvement consisted of making a resonator bysandwiching the quartz between steel plates (see Fig. 1.4), an approach still usedin modern transducers.

6 1. Introduction

FIGURE 1.4. British Patent 145,691, July 28, 1921 of P. Langevin invention showing steel(g)-quarts(a)-steel(g’) sandwich transducer.

These successes greatly improved the outlook for effective echo ranging onsubmarines, and the efforts increased in France, Great Britain, the United Statesand also in Germany. Boyle’s group developed equipment, referred to as “ASDICgear”, for installation on some ships of the British fleet. In the United States anecho ranging program was initiated at the Naval Experimental Station at New Lon-don, Connecticut with supporting research, especially in piezoelectric materials,from several other laboratories. Although none of this work progressed rapidlyenough to have a significant role in World War I, it did provide the basis for con-tinued research in echo ranging that would soon be needed in World War II.

Between the World Wars, depth sounding by ships underway was developedcommercially, and the search for effective echo ranging on submarines was con-tinued in the United States primarily at the Naval Research Laboratory under H.C.Hayes. One of the main problems was the lack of transducers powerful enough toachieve the necessary ranges. It was found that magnetostrictive transducers couldproduce greater acoustic power, while their ruggedness made them very suitablefor underwater use. However, both electrical and magnetic losses in magnetostric-tive materials resulted in lower efficiency compared to piezoelectric transducers.Other transducer concepts were also explored including one that used the exten-sional motion of magnetostriction to drive a radiating surface in flexure (called aflextensional transducer; see Fig. 1.5).

After World War I Rochelle salt, which was known to have a stronger piezo-electric effect than quartz, also became available in the form of synthetic crystalsto provide another possibility for improved transducers. Synthetic Rochelle saltwas probably the first example of what would become the most important typeof innovation in the field of electroacoustic transducers, new man-made materialswith improved electromechanical properties.

Early in World War II these accomplishments in transducers, combined withadvances in electronics and better understanding of the propagation of sound in

Brief History of Underwater Sound Transducers 7

FIGURE 1.5. An experimental flextensional transducer built at NRL in May, 1929 for in-airoperation with magnified shell motion driven by three magnetostrictive tubes [7].

the ocean, provided the basis for development of sonar systems with useful butlimited capability. The potential for significant improvement was clear, and, withGerman submarines causing serious damage to shipping off the east coast of theUnited States, the need was great [6]. The work had already started in 1941 withColumbia University’s Division of War Research at New London, Harvard Uni-versity’s Underwater Sound Laboratory (HUSL) in Cambridge, and the Universityof California’s Division of War Research in San Diego. Their work, some of whichis illustrated in Figs. 1.6 and 1.7, resulted in many American ships being equippedwith echo ranging and passive listening systems.

Other types of equipment employing transducers and underwater sound werealso developed such as acoustic homing torpedoes, acoustic mines and sonobuoys.A large amount of practical experience was accumulated from the use of all thisequipment, and it provided a firm basis for many new developments during andafter the war [7].

At the end of World War II the Columbia work at New London continued underthe direction of the Naval Research Laboratory [8]. The New London facility wascalled the Navy Underwater Sound Laboratory with John M. Ide as Technical Di-rector and J. Warren Horton as Chief Consultant. Later in 1945 the sonar projectsat the Harvard Underwater Sound Laboratory, and about half the personnel, wentto New London to join the Navy Underwater Sound Laboratory, while the Harvardordnance projects, and the remaining personnel, went to a new Ordnance ResearchLaboratory at Pennsylvania State University. In 1946 the Navy Underwater SoundLaboratory came under the direction of the Bureau of Ships, in 1970 it became partof the Naval Underwater Systems Center (NUSC), and in 1992, part of the NavalUndersea Warfare Center (NUWC) with headquarters in Newport, Rhode Island.Research and development in sonar transducers and arrays continued throughoutthese organizational changes and continues now at NUWC. During the same pe-riod research on transducers and arrays was also conducted at the Naval Research

8 1. Introduction

b

S h

y

L + 12y

G

N

g

2

W

FIGURE 1.6. Tapered, laminated magnetostrictive transducer stack polarized by permanentmagnet in the tail slot. These transducers were used in early cylindrical array scanningsystems [7].

Laboratory in Washington, D C and Orlando, Florida (the Orlando facilities arenow located at NUWC), at the Navy Electronics Laboratory in San Diego, Cali-fornia and in many university and industrial laboratories. Most of this research hasbeen, and continues to be, supported by the Office of Naval Research.

World War II, and the Cold War that followed, strongly motivated the searchfor new man-made transduction materials which led to ammonium dihydrogenphosphate (ADP), lithium sulfate and other crystals in the early 1940’s. Then in1944 piezoelectricity was discovered by A.R. von Hippel in permanently polarizedbarium titanate ceramics [9], and in 1954 even stronger piezoelectricity was foundin polarized lead zirconate titanate ceramics [10]. The discovery of these materialsinitiated the modern era of piezoelectric transducers in time to play an importantrole in once again meeting the threat of submarines off the east coast of the UnitedStates, this time Soviet submarines armed with long range nuclear missiles.

At the end of the twentieth century lead zirconate titanate (PZT) compoundsare still being used in most underwater sound transducers. However, other similarmaterials are being developed, such as lead magnesium niobate (PMN) and singlecrystals of related compounds, and the magnetostrictive materials Terfenol-D andGalfenol, which have the potential for improvement over PZT in some applica-tions. Piezoelectric ceramics and ceramic-elastomer composites can be made in agreat variety of shapes and sizes with many variations of composition that provide

Underwater Transducer Applications 9

Lobe SuppressedReceiver

Half-cylinder ofSteel for Strength

Impedance Matchedor "Rho-C" RubberWindow

Isolationmember

CylindricalTransmitter80 Degree

FIGURE 1.7. Early sonar array system with cylindrical transmitter for wide beam patternand planar array for narrow beam receiving. A baffle between the two minimizes the soundfed from transmitter to receiver [7].

specific properties of interest. The characteristics of these materials have led tothe development and manufacture of innovative, relatively inexpensive transducerdesigns that would have been unimaginable in the early days of electroacoustics.

1.2. Underwater Transducer Applications

The useful spectrum of underwater sound extends from about 1 Hz to over 1 MHzwith most applications in large (but sometimes shallow) bodies of water. For ex-ample, acoustic communication over thousands of kilometers is possible in theoceans, but frequencies below about 100 Hz are required because the absorptionof sound increases rapidly as the frequency increases [2]. On the other hand, depthsounding in water as shallow as 1 meter is important for small boats, but it re-quires short pulses of sound at a few hundred kHz to separate the echo from thetransmission. High resolution, short-range active sonar has used frequencies upto 1.5 MHz. Applications over this wide frequency range require many differenttransducer designs.

Naval applications of underwater sound require a large number and varietyof transducers. Acoustic communication between two submerged submarines re-quires a projector to transmit sound and a hydrophone to receive sound on eachsubmarine; echo ranging requires a projector and a hydrophone usually on thesame ship; passive listening requires only a hydrophone. However, hydrophonesand projectors are often used in large groups of up to 1000 or more transducersclosely packed in planar, cylindrical, or spherical arrays mounted on naval ships.

Other naval applications include acoustic mines activated by the voltage froma hydrophone sensitive to the low frequency sound radiated by a moving ship.Special projectors and hydrophones are required for acoustic communication

10 1. Introduction

between submerged submarines or from a surface ship to a submarine. Torpedoeswith active acoustic homing systems require high-frequency directional arrays,while those with passive homing require lower-frequency capability to detectship-radiated noise. Submarines are usually equipped with other specializedhydrophones to monitor their self noise or to augment the major sonar systems.Sonobuoys are expendable hydrophone/radio transmitter combinations droppedinto the water from an aircraft. The radio floats on the surface, with the tetheredhydrophone at a suitable depth for detecting submarines. Some types of sonobuoyslisten passively, while others echo range, but both types radio information back tothe aircraft. Urick [2] discusses most of these naval applications.

As sonar technology matured it began to have significant commercial applica-tions such as depth sounding, a form of active sonar in which echoes are receivedfrom the bottom. Accurate knowledge of the water depth under the boat is impor-tant not only to navies but to all mariners from those aboard the largest ships tothose on small recreational boats. And sonar can do more than find the water depthat the point where the ship is located. It can be extended to provide detailed bottommapping, and with good bottom maps navigation by depth sounding is feasible.Bottom maps now exist for much, but not all, of Earth’s 140 million square milesof ocean. In a similar way sounding on the lower surface of ice is critical for sub-marines navigating under the Arctic ice cap. Bottom mapping techniques can bereadily extended to exploration and search for sunken objects that vary from shipand aircraft wreckage to ancient treasure. Active sonar has commercial impor-tance in the fishing industry where systems have been developed specifically forlocating schools of fish. Underwater transducers can even be used to kill mosquitolarva by irradiating them with ultrasonic energy [11].

Bottom mapping with sonar is an important part of oceanography, and it canbe extended to sub-bottom mapping and determination of bottom characteristics.For example, the bottom of Peconic Bay, Long Island, New York has been studiedby sonar in an attempt to determine the reasons for the decrease in the scalloppopulation [12]. Acoustic propagation measurements can be used for modelingocean basins using echo sounding and tomographic techniques.

Underwater sound is useful in ocean engineering in many ways. The preciselocation of specific points or objects is often crucial when drilling for oil andgas deep in the ocean or laying underwater cables or pipelines. A combinationof underwater and seismic acoustics is needed for finding deposits of oil or gasunder the oceans. Networked underwater communication systems involving manyacoustic modems, each with a projector and a hydrophone, are important for navaloperations and other underwater projects.

Several research projects make use of underwater sound to gather data relatedto a wide variety of topics. The Acoustic Thermometry of Ocean Climate project(ATOC) measures the acoustic travel time over ocean paths thousands of kilo-meters long to determine whether the average sound speed is increasing as timepasses. Since an increasing sound speed in ocean waters means an increasing av-erage temperature over a large portion of the earth, it may be one of the best mea-sures of global warming. This project requires very low frequency projectors and

Underwater Transducer Applications 11

hydrophones as well as very careful signal processing [13]. The Sound Surveil-lance System has been used to study the behavior of sperm whales by detectingthe “clicks” which they emit, and to detect earthquakes and volcanic eruptionsunder the sea [14]. In what may become the ultimate version of the sonobuoyconcept, plans have been made to land acoustic sensors on Jupiter’s moon Europasometime around the year 2020. Cracks which are thought to occur naturally inthe ice that covers the surface of Europa generate sound in the ice and in the oceanthat may lie beneath the ice. The sounds received by the acoustic sensors may beinterpretable in terms of the ice thickness and the depth and temperature of theunderlying ocean. Such information may give clues about the possible existenceof extraterrestrial life [15]. Underwater sound may even play a role in the field ofparticle physics if physicists succeed in showing that hydrophone arrays are capa-ble of detecting the sounds caused by high energy neutrinos passing through theocean [16].

All these applications of underwater sound require large numbers of trans-ducers, with a great variety of special characteristics for use over a wide rangeof frequency, power, size, weight, and water depth. The problems raised bythe variety of applications and the numerous possibilities for solutions continueto make underwater sound transducer research and development a challengingsubject. Figs. 1.8 through 1.12 illustrate several more recent underwater sound

FIGURE 1.8. Low frequency cylindrical hydrophone with isolation mounting system,courtesy Massa Products [30].

12 1. Introduction

Nodal plate Stress bolt

TailCeramic

Head

FIGURE 1.9. Sketch of a Tonpilz transducer with nodal plate mounting system.

Head mass

Collar Tuning ring Tail mass Bias barNut

Transformer

Cableassembly

Retainer ringCaseCeramic stack

Molded rubber

FIGURE 1.10. Sketch of a high power low frequency Tonpilz transducer with head and tailmounting system and steel housing case.

transducers, Fig. 1.13 shows an early low frequency array, Figs. 1.14 through 1.16illustrate more current arrays, Figs. 1.17 and 1.18 show flextensional transduc-ers and Figs. 1.19 through 1.21 illustrate transducers that use the new materials,Terfenol - D and single crystal PMN-PT.

Underwater Transducer Applications 13

FIGURE 1.11. Photograph of a low frequency high power Tonpilz transducer showingrubber molded piston, fiberglass wrapped drive stack of six piezoelectric ceramic rings, tailmass, transformer and housing.

FIGURE 1.12. Photograph of cut away housing and cross sectional sketch of a mid fre-quency Tonpilz transducer showing detail of compression bolt as well as molded rubberencapsulation housing and water tight “pig tail” connector, courtesy of Massa Products[30].

14 1. Introduction

FIGURE 1.13. Photograph of large array of very low frequency magnetic variable reluc-tance dipole “shaker box” transducers ready for deep submergance testing, courtesy ofMassa Products [30].

FIGURE 1.14. Cylindrical scanning array of Tonpilz transducers.