UNDERWATER ACOUSTICS. Monograph Series in. Sponsored by Office of Naval Research

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1 Monograph Series in UNDERWATER ACOUSTICS Sponsored by Office of Naval Research Editorial Board: Ralph R. Goodman, Ph.D., Chair Homer P. Bucker, Ph.D. Ira Dyer, Ph.D. Jeffrey A. Simmen, Ph.D.

2 Monograph Series in UNDERWATER ACOUSTICS In 2001 the Office of Naval Research began a program to publish a selected monograph series in the field of underwater acoustics. The series publishes in-depth reviews and analysis on the state of understanding of the physics of sound in selected areas of research. The monograph series covers the most important topics in underwater sound in an in-depth, critical, scholarly, and comprehensive fashion. It is intended to provide researchers with an understanding of the physics of underwater sound, based on both theory and experiment. The discussion of important unanswered questions is encouraged. Topics of particular importance in the field are low-frequency sound in the deep ocean, shallow-water acoustics, and ambient noise. Sponsored by: Office of Naval Research One Liberty Center 875 North Randolph Street, Suite 1425 Arlington, VA onrpao@onr.navy.mil Series Editors: Ralph R. Goodman, Ph.D. Homer P. Bucker, Ph.D. Research Professor 808 Moana Drive USM Department of Marine Science San Diego, CA Balch Blvd bucker@nosc.mil Stennis Space Center, MS 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 Washington Massachusetts Institute of Technology 1013 NE 40th Street Cambridge, MA Seattle, WA simmen@apl.washington.edu

3 Charles H. Sherman John L. Butler Transducers and Arrays for Underwater Sound

4 Charles H. Sherman John L. Butler Principal Scientist Chief Scientist Image Acoustics, Inc. Image Acoustics, Inc. 97 Elm Street 97 Elm Street Cohasset, MA Cohasset, MA ISBN: e-isbn: DOI: / Library of Congress Control Number: Springer Science+Business Media New York 2007, Corrected at 3rd printing 2013 This work is subject to copyright. All rights are reserved by the Publisher, 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 any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (

5 To Elizabeth and Nancy

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7 Series Preface The efficacy of sound to penetrate the seas made acoustic systems in the past century 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 been a major sponsor of undersea research and development at universities, national laboratories, and industrial organizations. Appropriately ONR is the sponsor of this monograph series. The intent of the series is to summarize recent accomplishments in, and to outline perspectives for, underwater acoustics in specific fields of research. The general field has escalated in importance and spread broadly with richness and depth of understanding. It has also, quite naturally, become more specialized. The goal of this series is to present monographs that critically review both past and recent accomplishments in order to address the shortcomings in present understanding. In this way, these works will bridge the gaps in understanding among the 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 related specialized topics of interest as well. ONR has sponsored the series through grants to the authors. Authors are selected by ONR based on the quality and relevance of each proposal and the author s experience in the field. The Editorial Board, selected by ONR, has, at times, provided independent views to ONR in this process. Its sole official role, however, is to judge the manuscripts before publication and to assist each author at 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

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9 Preface We have written this book as part of the underwater acoustics monograph series initiated by the Office of Naval Research (ONR), Department of the Navy of the United States. The ONR objective for this series is publication of in-depth reviews and analyses of the state of understanding of the physics of sound in selected areas of undersea research. This monograph presents the theory and practice of underwater electroacoustic transducers and arrays as developed during the last half 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 transducers and arrays for underwater sound starting with a brief historical review and a survey of some of the many modern applications. Descriptions of the six major types of electroacoustic transducers are presented in a unified way that facilitates their comparison and explains why some types are better suited than others for producing and receiving sound in the water. The characteristics of transducers used as both projectors and hydrophones, and the methods available for predicting and measuring transducer performance, are presented in detail. The reasons for combining large numbers of transducers in arrays are explained, and the special problems that must be considered in such arrays are analyzed. The nonlinear mechanisms that exist in all transducers are described, and analyses of some of their most important effects are given. Many different acoustical quantities play essential roles in the design and performance of electroacoustic transducers and arrays, and the methods for determining these quantities are presented. Analytical modeling and understanding is emphasized throughout the book, but it is also made clear that numerical modeling is now an essential part of transducer and array design. Non-electroacoustic types of transducers that are used in certain underwater applications, such as explosive sources, spark sources, hydroacoustic sources, and optical hydrophones, are not included in this book. The monograph is organized in a manner that brings the reader quickly to the main body of results on current transducers and arrays in the first six chapters with a minimum of background material. The most important basic concepts of electroacoustic transduction are introduced in Chapter 1, after a brief historical review and a survey of some of the many applications of transducers and arrays. Chapter 2 describes and compares the six major types of electroacoustic ix

10 x Preface transducers, presents additional transducer concepts and characteristics, and introduces the equivalent circuit method of transducer analysis. Chapters 3 through 6 contain the main body of results on modern transducers and arrays. Chapters 3 and 4 cover transducers as projectors, which produce sound, and as hydrophones, which receive sound, including many details of specific transducer designs as they are used in current applications. Chapters 5 and 6 explain the benefits of combining large numbers of transducers in arrays that often contain more than a thousand individual transducers. These large arrays are necessary in many sonar applications, but they introduce other problems that are also discussed and analyzed. The remaining six chapters, 7 through 12, support the earlier chapters and carry the discussion of concepts and methods into much more detail for those who seek a deeper understanding of transducer operation. Chapter 7 describes all the principal methods of transducer modeling, analysis, and design, including an introduction to the finite element method. Chapter 8 gives further discussion of the most important transducer characteristics. Chapter 9 describes the principal nonlinear mechanisms that occur in all the transducer types and presents methods of analyzing important nonlinear effects such as harmonic distortion. Chapter 10 presents the basic acoustics necessary for determining those acoustical quantities, such as directivity patterns and radiation impedance, that are essential to transducer and array analysis and design. It also includes useful results for such quantities in several typical cases. Chapter 11 extends the discussion of acoustical quantities by introducing more advanced methods of analysis that can be applied to more complicated cases including a brief introduction to numerical methods. Chapter 12 is a summary of the major methods of measurement used for the evaluation of transducer and array performance. The book ends with an extensive Appendix containing several types of specific information that can be used in transducer analysis and design and with a Glossary of Terms. We have attempted to make this monograph suitable for beginners to learn from 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 regarding applications of transducers and arrays. Although some parts of this book may be useful to undergraduates, it is written on a graduate level for engineers and scientists in the fields of electrical engineering, mechanical engineering, physics, ocean engineering, and acoustical engineering. The book uses SI (MKS) units in general, but English units are also occasionally used to clarify the relationship to practical devices. C.H. Sherman and J.L. Butler Cohasset, Massachusetts July 2006.

11 Acknowledgements This monograph is based on the experience of the authors in both government and industrial organizations. Our careers have been devoted mainly to the many needs of the United States Navy for underwater sound transducers and arrays, and we are grateful to ONR and other organizations in government and industry for support through all those years. We are also grateful to our early teachers in the fields of transducers and acoustics: Dr. R.S. Woollett, E.J. Parsinnen, and H. Sussman of the Navy Underwater Sound Laboratory (now Naval Undersea Warfare Center, NUWC), Dr. W.J. Remillard, Northeastern University, Dr. R.T. Beyer, Brown University, Dr. T.J. Mapes, NUWC, G.W. Renner, Hazeltine Corporation (now Ultra Electronics), B. McTaggart, NUWC, Frank Massa, Massa Products Corporation, and Stan Ehrlich, Raytheon Company. We are also grateful to the many other people who have contributed in specific ways to this book: To Jan F. Lindberg of ONR and NUWC for encouraging us to take on this task and advising us as it progressed. To Dr. J.A. Simmen and Dr. D. Todoroff of ONR for initiating and overseeing this monograph series. To the Board 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 of Image Acoustics for preparation of the numerous illustrations and graphs. To Dr. W. Thompson, Jr. of Pennsylvania State University and W.J. Marshall of Raytheon Company for their review of the book as the work progressed; their suggestions and comments were very helpful and encouraging. To Dr. M.B. Moffett for help with the section on parametric arrays and for information on piezoelectric materials, D.T. Porter for reviewing Chapter 10 and Dr. R.C. Elswick for reviewing parts of Chapter 6. Discussions with the following colleagues were also very 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 Nancy Clark Butler, for their understanding and assistance. xi

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13 Contents Series Preface vii Preface ix Acknowledgements xi Chapter 1: Introduction Brief History of Underwater Sound Transducers Underwater Transducer Applications General Description of Linear Electroacoustic Transduction Transducer Characteristics Electromechanical Coupling Coefficient Transducer Responses, Directivity Index and Source Level Transducer Arrays References Chapter 2: Electroacoustic Transduction Piezoelectric Transducers General The 33-Mode Longitudinal Vibrator The 31-Mode Longitudinal Vibrator Electrostrictive Transducers Magnetostrictive Transducers Electrostatic Transducers Variable Reluctance Transducers Moving Coil Transducers Comparison of Transduction Mechanisms Equivalent Circuits Equivalent Circuit Basics Circuit Resonance Circuit Q and Bandwidth PowerFactorandTuning Power Limits Efficiency xiii

14 xiv Contents Hydrophone Circuit and Noise Extended Equivalent Circuits References Chapter 3: Transducers as Projectors Principles of Operation Ring and Spherical Transducers Piezoelectric 31-Mode Ring Piezoelectric 33-Mode Ring The Spherical Transducer The Magnetostrictive Ring Free Flooded Rings Multimode Rings Piston Transducers TheTonpilzProjector The Hybrid Transducer Transmission Line Transducers Sandwich Transducers Wideband Transmission Line Transducers Large Plate Transducers Composite Transducers Flextensional Transducers The Class IV and VII Flextensional Transducers The Class I Barrel Stave Flextensional The Class V and VI Flextensional Transducers The Astroid and X-spring Flextensional Transducers Flexural Transducers Bender Bar Transducer Bender Disc Transducer The Slotted Cylinder Transducer The Bender Mode X-spring Transducer References Chapter 4: Transducers as Hydrophones Principles of Operation Sensitivity FigureofMerit Simplified Equivalent Circuit Other Sensitivity Considerations Cylindrical and Spherical Hydrophones Performance with Shielded Ends Spherical Hydrophones Performance with End Caps

15 Contents xv 4.3 Planar Hydrophones Tonpilz Hydrophones The 1-3 Composite Hydrophone Flexible Hydrophones Bender Hydrophones Vector Hydrophones Dipole Vector Sensors, Baffles, and Images Pressure Gradient Vector Sensor Velocity Vector Sensor Accelerometer Sensitivity Multimode Vector Sensor Summed Scalar and Vector Sensors Intensity Sensors ThePlaneWaveDiffractionConstant Hydrophone Thermal Noise DirectivityandNoise Low Frequency Hydrophone Noise A More General Description of Hydrophone Noise A Comprehensive Hydrophone Noise Model Vector Sensor Internal Noise Vector Sensor Susceptibility to Local Noise References Chapter 5: Projector Arrays Array Directivity Functions The Product Theorem Line, Rectangular, and Circular Arrays Grating Lobes Beam Steering and Shaping Effects of Random Variations Mutual Radiation Impedance and the Array Equations Solving the Array Equations VelocityControl Negative Radiation Resistance Calculation of Mutual Radiation Impedance Planar Arrays of Piston Transducers Non-Planar Arrays, Nonuniform Velocities Arrays of Non-FVD Transducers Modal Analysis of Radiation Impedance Modal Analysis of Arrays VolumeArrays Near Field of a Projector Array The Nonlinear Parametric Array References

16 xvi Contents Chapter 6: Hydrophone Arrays Hydrophone Array Directional and Wavevector Response Directivity Functions Beam Steering Shading Wavevector Response of Arrays ArrayGain Sources and Properties of Noise in Arrays Ambient Sea Noise StructuralNoise FlowNoise Reduction of Array Noise Reduction of Ambient Noise Reduction of Structural Noise Reduction of Flow Noise Summary of Noise Reduction Arrays of Vector Sensors Directionality Unbaffled Vector Sensor Arrays in Ambient Noise Hull-Mounted Vector Sensor Arrays in StructuralNoise References Chapter 7: Transducer Models Lumped Parameter Models and Equivalent Circuits Mechanical Single Degree-of-Freedom Lumped Equivalent Circuits Mechanical Lumped Equivalent Circuits for Higher Degrees of Freedom Piezoelectric Ceramic Lumped-Parameter Equivalent Circuits Magnetostrictive Lumped-Parameter Equivalent Circuits Eddy Currents Distributed Models Distributed Mechanical Model Matrix Representation Piezoelectric Distributed-Parameter Equivalent Circuit Segmented 33 Bar Un-segmented 31 Bar Length Expander Bar Thickness-Mode Plate Magnetostrictive Rod

17 Contents xvii 7.3 Matrix Models Three-Port Matrix Model Two-Port ABCD Matrix Model Finite Element Models A Simple FEM Example FEM Matrix Representation Inclusion of a Piezoelectric Finite Element Application of FEM without Water Loading Application of FEM with Water Loading Water Loading of Large Arrays Magnetostrictive FEM References Chapter 8: Transducer Characteristics Resonance Frequency The Mechanical Quality Factor Definitions EffectoftheMassoftheBar The Effect of Frequency-Dependent Resistance Characteristic Mechanical Impedance Electromechanical Coupling Coefficient Energy Definitions of Coupling and OtherInterpretations Mason s Energy Definition The Mutual Energy Definition Other Features of the Coupling Coefficient The Effect of Inactive Components on the Coupling Coefficient The Effect of Dynamic Conditions on the Coupling Coefficient References Chapter 9: Nonlinear Mechanisms and Their Effects Nonlinear Mechanisms in Lumped-Parameter Transducers Piezoelectric Transducers Electrostrictive Transducers Magnetostrictive Transducers Electrostatic and Variable Reluctance Transducers Moving Coil Transducers Other Nonlinear Mechanisms Analysis of Nonlinear Effects Harmonic Distortion Direct Drive Perturbation Analysis Harmonic Distortion for Indirect Drive

18 xviii Contents Instability in Electrostatic and Variable-Reluctance Transducers Nonlinear Analysis of Distributed- Parameter Transducers Nonlinear Effects on the Electromechanical Coupling Coefficient References Chapter 10: Acoustic Radiation from Transducers The Acoustic Radiation Problem Far-Field Acoustic Radiation Line Sources Flat Sources in a Plane Spherical and Cylindrical Sources Near-Field Acoustic Radiation Field on the Axis of a Circular Piston The Effect of the Near Field on Cavitation Near Field of Circular Sources Radiation Impedance Spherical Sources Circular Sources in a Plane References Chapter 11: Advanced Acoustic Radiation Calculations Mutual Radiation Impedance Piston Transducers on a Sphere Piston Transducers on a Cylinder The Hankel Transform TheHilbertTransform Green s Theorem and Acoustic Reciprocity Green s Theorem Acoustic Reciprocity Green s Function Solutions TheHelmholtzIntegralFormula Effects of Acoustic Scattering TheDiffractionConstant Scattering from Cylinders Numerical Methods for Acoustic Calculations Mixed Boundary Conditions Collocation Boundary Element Methods References Chapter 12: Transducer Evaluation and Measurement Electrical Measurement of Transducers in Air Electric Field Transducers Magnetic Field Transducers Measurement of Transducers in Water Measurement of Transducer Efficiency

19 Contents xix 12.4 Acoustic Responses of Transducers Reciprocity Calibration Tuned Responses Electric Field Transducers Magnetic Field Transducers Near-field Measurements Distance to the Far-field Measurements in Tanks Near- to Far-field Extrapolation Small Sources Near- to Far-field Extrapolation Large Sources Effect of Transducer Housings References The Future 543 Appendix 546 A.1 ConversionsandConstants A.2 Transducer Materials Ordered by Impedance, ρc A.3 Time Averages, Power Factor, Complex Intensity A.4 Relationships Between Piezoelectric Coefficients A.5 Small-Signal Properties of Piezoelectric Ceramics A.6 Piezoelectric Ceramic Approximate Frequency Constants A.7 Small Signal Properties of Magnetostrictive Materials A.8 VoltageDividerandTheveninEquivalentCircuit A.9 Magnetic Circuit Analysis A.10NortonCircuitTransformations A.11IntegralTransformPairs A.12 Calibrated Transducers A.13 Frequently Used Formulas A.14 Stress and Field Limits for Piezoelectric Ceramics A.15 Comprehensive Hydrophone Noise Model A.16 Cables and Transformers A.17 Thermal Noise and Radiation Resistance Glossary of Terms 587 Index 599