Transducers and arrays for underwater sound second edition

Preface to Second EditionThis second edition presents the theory and practice of underwater sound acoustic transducers and arrays as developed during the last half of the twentiethcentur

Modern Acoustics and Signal Processing

Modern Acoustics and Signal Processing

Editor-in-Chief

William M Hartmann, East Lansing, USA

Editorial Board

Yoichi Ando, Kobe, Japan

Whitlow W.L Au, Kane’ohe, USA

Arthur B Baggeroer, Cambridge, USA

Neville H Fletcher, Canberra, Australia

Christopher R Fuller, Blacksburg, USA

William A Kuperman, La Jolla, USA

Joanne L Miller, Boston, USA

Alexandra I Tolstoy, McLean, USA

More information about this series at http://www.springer.com/series/3754

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of America and Springer dedicated to encouraging the publication of important newbooks in acoustics Published titles are intended to reflect the full range of research

in acoustics ASA Press books can include all types of books published by Springerand may appear in any appropriate Springer book series

Editorial Board

James Cottingham (Chair), Coe College

Diana Deutsch, University of California, San Diego

Timothy F Duda, Woods Hole Oceanographic Institution

Robin Glosemeyer Petrone, Threshold Acoustics

Mark F Hamilton, University of Texas at Austin

William M Hartmann, Michigan State University

James F Lynch, Woods Hole Oceanographic Institution

Philip L Marston, Washington State University

Arthur N Popper, University of Maryland

Martin Siderius, Portland State University

Andrea M Simmons, Brown University

Ning Xiang, Rensselaer Polytechnic Institute

William Yost, Arizona State University

John L Butler • Charles H Sherman

Transducers and Arrays for Underwater Sound Second Edition

Chief Scientist

Image Acoustics, Inc

Cohasset, MA, USA

Image Acoustics, Inc

Cohasset, MA, USA

Modern Acoustics and Signal Processing

DOI 10.1007/978-3-319-39044-4

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to increase and diffuse the knowledge of acoustics and promote its practicalapplications The ASA is recognized as the world’s premier international scientificsociety in acoustics, and counts among its more than 7,000 members, professionals

in the fields of bioacoustics, engineering, architecture, speech, music, phy, signal processing, sound and vibration, and noise control

oceanogra-Since its first meeting in 1929, The Acoustical Society of America has enjoyed ahealthy growth in membership and in stature The present membership of approx-imately 7,500 includes leaders in acoustics in the United States of America andother countries The Society has attracted members from various fields related tosound including engineering, physics, oceanography, life sciences, noise and noisecontrol, architectural acoustics; psychological and physiological acoustics; appliedacoustics; music and musical instruments; speech communication; ultrasonics,radiation, and scattering; mechanical vibrations and shock; underwater sound;aeroacoustics; macrosonics; acoustical signal processing; bioacoustics; and manymore topics

To assure adequate attention to these separate fields and to new ones that maydevelop, the Society establishes technical committees and technical groups chargedwith keeping abreast of developments and needs of the membership in theirspecialized fields This diversity and the opportunity it provides for interchange

of knowledge and points of view has become one of the strengths of the Society.The Society’s publishing program has historically included the Journal of theAcoustical Society of America, the magazine Acoustics Today, a newsletter, andvarious books authored by its members across the many topical areas of acoustics

In addition, ASA members are involved in the development of acoustical standardsconcerned with terminology, measurement procedures, and criteria for determiningthe effects of noise and vibration

In the popular mind, the term “acoustics” refers to the properties of a room or otherenvironment—the acoustics of a room are good or the acoustics are bad But asunderstood in the professional acoustical societies of the world, such as the highlyinfluential Acoustical Society of America, the concept of acoustics is much broader.

Of course, it is concerned with the acoustical properties of concert halls, rooms, offices, and factories—a topic generally known as architectural acoustics,but it is also concerned with vibrations and waves too high or too low to be audible.Acousticians employ ultrasound in probing the properties of materials, or inmedicine for imaging, diagnosis, therapy, and surgery Acoustics includesinfrasound—the wind-driven motions of skyscrapers, the vibrations of the earth,and the macroscopic dynamics of the sun

class-Acoustics studies the interaction of waves with structures, from the detection ofsubmarines in the sea to the buffeting of spacecraft The scope of acoustics rangesfrom the electronic recording of rock and roll and the control of noise in ourenvironments to the inhomogeneous distribution of matter in the cosmos

Acoustics extends to the production and reception of speech and to the songs ofhumans and animals It is in music, from the generation of sounds by musicalinstruments to the emotional response of listeners Along this path, acousticsencounters the complex processing in the auditory nervous system, its anatomy,genetics, and physiology—perception and behavior of living things

Acoustics is a practical science, andmodern acoustics is so tightly coupled todigital signal processing that the two fields have become inseparable Signalprocessing is not only an indispensable tool for synthesis and analysis but it alsoinforms many of our most fundamental models about how acoustical communica-tion systems work

Given the importance of acoustics to modern science, industry, and humanwelfare Springer presents this series of scientific literature, entitled Modern Acous-tics and Signal Processing This series of monographs and reference books isintended to cover all areas of today’s acoustics as an interdisciplinary field Weexpect that scientists, engineers, and graduate students will find the books in thisseries useful in their research, teaching, and studies

William M Hartmann

To Nancy

Preface to Second Edition

This second edition presents the theory and practice of underwater sound acoustic transducers and arrays as developed during the last half of the twentiethcentury and into the initial part of the twenty-first century This second edition hasbeen reorganized into a form suitable for students as well as engineers or scientistswho use or design transducers and arrays and includes new design concepts,analysis, and data

electro-Comprehensive coverage is presented on the subject of transducers and arraysfor underwater sound The most important basic concepts of electroacoustic trans-duction are introduced in Chap.1, after a brief historical review and a survey ofsome of the many applications of transducers and arrays Chapter2describes andcompares the six major types of electroacoustic transducers, presents additionaltransducer concepts and characteristics, and introduces the equivalent circuitmethod of transducer analysis Chapter 3 describes the principal methods oftransducer modeling, analysis, and design, including an introduction to the finiteelement method Chapter4 gives further discussion of the most important trans-ducer characteristics

Chapters5 8contain the main body of results on modern transducers and arrays.Chapters5and6cover transducers as projectors, which produce sound, and trans-ducers as hydrophones, which receive sound, including many details of specifictransducer designs as they are used in current applications as well as new designs.Chapters7and8explain the benefits of combining large numbers of transducers inarrays that often contain hundreds of individual transducers These large arrays arenecessary in many sonar applications, but they introduce other problems that arealso discussed and analyzed Chapter 9 is a summary of the major methods ofmeasurement used for the evaluation of transducer and array performance.Chapter 10 presents the basic acoustics concepts and analysis necessary fordetermining those acoustical quantities, such as directivity patterns and radiationimpedance, which are essential to transducer and array analysis and design It alsoincludes useful results for such quantities in several typical cases Chapter 11extends the discussion of acoustical quantities by introducing more advanced

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methods of analysis that can be applied to more complicated cases including a briefintroduction to numerical methods Chapter12 describes the principal nonlinearmechanisms that occur in all the transducer types and presents methods of analyz-ing important nonlinear effects such as harmonic distortion The book ends with anextensive Appendix containing several types of specific information that can beused in transducer analysis and design along with a Glossary of Terms andSolutions for the Odd-Numbered Exercises given in the 12 chapters of the book.Instructors who have adopted the text in their courses can contact the publisher forSolutions to the Even-Numbered Exercises.

This second edition has been structured to be more suitable for students andteachers as well as practitioners Although some parts of this book may be useful toundergraduates, it is written on a graduate level for engineers, scientists, andstudents in the fields of electrical engineering, mechanical engineering, physics,ocean engineering, and acoustical engineering The book uses SI (MKS) units ingeneral, but English units are also occasionally used to clarify the relationship topractical devices

March 2016

Preface to First Edition

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 selected areas

of undersea research This monograph presents the theory and practice of water sound electroacoustic transducers and arrays as developed during the last half

under-of the twentieth century and into the initial part under-of the twenty-first century

We have attempted a comprehensive coverage of the subject of transducers andarrays for underwater sound starting with a brief historical review and a survey ofsome of the many modern applications Descriptions of the six major types ofelectroacoustic transducers are presented in a unified way that facilitates theircomparison and explains why some types are better suited than others for producingand receiving sound in the water The characteristics of transducers used as bothprojectors and hydrophones, and the methods available for predicting and measur-ing transducer performance, are presented in detail The reasons for combininglarge numbers of transducers in arrays are explained, and the special problems thatmust be considered in such arrays are analyzed The nonlinear mechanisms thatexist in all transducers are described, and analyses of some of their most importanteffects are given Many different acoustical quantities play essential roles in thedesign and performance of electroacoustic transducers and arrays, and the methodsfor determining these quantities are presented Analytical modeling and under-standing are emphasized throughout the book, but it is also made clear thatnumerical modeling is now an essential part of transducer and array design.Non-electroacoustic types of transducers that are used in certain underwater appli-cations, such as explosive sources, spark sources, hydroacoustic sources, andoptical 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 chapters with aminimum of background material The most important basic concepts of electro-acoustic transduction are introduced in Chap.1, after a brief historical review and a

xi

survey of some of the many applications of transducers and arrays Chapter 2describes and compares the six major types of electroacoustic transducers, presentsadditional transducer concepts and characteristics, and introduces the equivalentcircuit method of transducer analysis Chapters3 6contain the main body of results

on modern transducers and arrays Chapters3and4cover transducers as projectors,which produce sound, and as hydrophones, which receive sound, including manydetails of specific transducer designs as they are used in current applications.Chapters5and6explain the benefits of combining large numbers of transducers

in arrays that often contain more than 1000 individual transducers These largearrays are necessary in many sonar applications, but they introduce other problemsthat are also discussed and analyzed

The remaining six chapters, Chaps.7 12, support the earlier chapters and carrythe discussion of concepts and methods into much more detail for those who seek adeeper understanding of transducer operation Chapter7describes all the principalmethods of transducer modeling, analysis, and design, including an introduction tothe finite element method Chapter8gives further discussion of the most importanttransducer characteristics Chapter9describes the principal nonlinear mechanismsthat occur in all the transducer types and presents methods of analyzing importantnonlinear effects such as harmonic distortion Chapter10presents the basic acous-tics necessary for determining those acoustical quantities, such as directivity pat-terns and radiation impedance, that are essential to transducer and array analysisand design It also includes useful results for such quantities in several typical cases.Chapter 11 extends the discussion of acoustical quantities by introducing moreadvanced methods of analysis that can be applied to more complicated casesincluding a brief introduction to numerical methods Chapter12is a summary ofthe major methods of measurement used for the evaluation of transducer and arrayperformance The book ends with an extensive Appendix containing several types

of specific information that can be used in transducer analysis and design and with aGlossary of Terms

We have attempted to make this monograph suitable for beginners to learn fromand for practitioners in the transducer field to learn more from In addition thoseconcerned in any way with undersea research may find useful guidance regardingapplications of transducers and arrays Although some parts of this book may beuseful 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) units ingeneral, but English units are also occasionally used to clarify the relationship topractical devices

January 2006

The first and second editions are based on the experience of the authors in bothgovernment and industrial organizations We are grateful to our early teachers inthe fields of transducers and acoustics: Dr R S Woollett, E J Parsinnen, and

H 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 Ocean Systems, Inc.); B McTaggart, NUWC; FrankMassa, Massa Products Corporation; and Stan Ehrlich, Raytheon Company Wewould also like to thank Dr W Thompson, Jr and W J Marshall for their review

of the first edition Discussions with the following colleagues were also very helpful

at various points: S C Butler, D T Porter, and Drs H H Schloemer, S H Ko,W.A Strawderman, R T Richards, A E Clark, J E Boisvert, M B Moffett, and

R C Elswick

I am grateful to the many other people who have contributed in specific ways tothis second edition: to Jan F Lindberg for originally encouraging us to take on thetask of the first edition and to Alexander L Butler and Victoria Curtis of ImageAcoustics, Inc for their help with the illustrations, graphs, and analysis I wouldalso like to thank William J Marshall, Jan F Lindberg, and Dr Harold C Robinsonfor their comments, suggestions, and review of the draft of this second edition

I am especially grateful to my wife Nancy Clark Butler, for her encouragementand understanding This second edition was written in memory of Charlie Sherman,coauthor, mentor, colleague, and friend

John L Butler

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1 Introduction 1

1.1 Brief History of Underwater Sound Transducers 2

1.2 Underwater Transducer Applications 7

1.3 General Description of Linear Electroacoustic Transduction 15

1.4 Transducer Characteristics 22

1.4.1 Electromechanical Coupling Coefficient 22

1.4.2 Transducer Responses, Directivity Index, and Source Level 24

1.5 Transducer Arrays 27

1.6 Summary 28

Exercises 29

References 30

2 Electroacoustic Transduction 33

2.1 Piezoelectric Transducers 34

2.1.1 General 34

2.1.2 The 33 Mode Longitudinal Vibrator 39

2.1.3 The 31 Mode Longitudinal Vibrator 43

2.2 Electrostrictive Transducers 45

2.3 Magnetostrictive Transducers 49

2.4 Electrostatic Transducers 52

2.5 Variable Reluctance Transducers 55

2.6 Moving Coil Transducers 57

2.7 Comparison of Transduction Mechanisms 60

2.8 Equivalent Circuits 62

2.8.1 Equivalent Circuit Basics 62

2.8.2 Circuit Resonance 65

2.8.3 CircuitQ and Bandwidth 66

2.8.4 Power Factor and Tuning 69

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2.8.5 Power Limits 73

2.8.6 Efficiency 75

2.8.7 Hydrophone Circuit and Noise 78

2.9 Thermal Considerations 79

2.9.1 Transducer Thermal Model 80

2.9.2 Power and Heating at Resonance 83

2.10 Extended Equivalent Circuits 85

2.11 Summary 86

Exercises 87

References 89

3 Transducer Models 91

3.1 Lumped-Parameter Models and Equivalent Circuits 92

3.1.1 Mechanical Single Degree of Freedom Lumped Equivalent Circuits 92

3.1.2 Mechanical Lumped Equivalent Circuits for Higher Degrees of Freedom 95

3.1.3 Piezoelectric Ceramic Lumped-Parameter Equivalent Circuit 99

3.1.4 Magnetostrictive Lumped-Parameter Equivalent Circuit 104

3.1.5 Eddy Currents 108

3.2 Distributed Models 110

3.2.1 Distributed Mechanical Model 111

3.2.2 Matrix Representation 115

3.2.3 Piezoelectric Distributed Parameter Equivalent Circuit 118

3.3 Matrix Models 128

3.3.1 Three Port Matrix Model 128

3.3.2 Two Port ABCD Matrix Model 131

3.4 Finite Element Models 133

3.4.1 A Simple FEM Example 133

3.4.2 FEA Matrix Representation 135

3.4.3 Inclusion of a Piezoelectric Finite Element 137

3.4.4 Application of FEA Without Water Loading 138

3.4.5 Application of FEA with Water Loading 141

3.4.6 Water Loading of Large Arrays 144

3.4.7 Magnetostrictive FEA 145

3.4.8 Equivalent Circuits for FEA Models 147

3.5 Summary 149

Exercises 150

References 151

4 Transducer Characteristics 153

4.1 Resonance Frequency 153

4.2 Mechanical Quality Factor 157

4.2.1 Definitions 157

4.2.2 Effect of the Mass of the Bar 159

4.2.3 Effect of Frequency-Dependent Resistance 160

4.3 Characteristic Mechanical Impedance 161

4.4 Electromechanical Coupling Coefficient 163

4.4.1 Energy Definitions of Coupling and Other Interpretations 164

4.4.2 The Effect of Inactive Components on the Coupling Coefficient 169

4.4.3 The Effect of Dynamic Conditions on the Coupling Coefficient 174

4.5 Parameter Based Figure of Merit (FOM) 178

4.6 Summary 181

Exercises 182

References 183

5 Transducers as Projectors 185

5.1 Principles of Operation 187

5.1.1 Projector Figure of Merit 188

5.2 Ring and Spherical Transducers 190

5.2.1 Piezoelectric 31 Mode Ring 190

5.2.2 Piezoelectric 33 Mode Ring 196

5.2.3 The Spherical Transducer 197

5.2.4 The Magnetostrictive Ring 200

5.2.5 Free-Flooded Rings 201

5.2.6 Multimode Rings 205

5.3 Piston Transducers 207

5.3.1 The Tonpilz Projector 207

5.3.2 The Hybrid Transducer 216

5.4 Transmission Line Transducers 220

5.4.1 Sandwich Transducers 220

5.4.2 Wideband Transmission Line Transducers 225

5.4.3 Large Plate Transducers 230

5.4.4 Composite Transducers 232

5.5 Flextensional Transducers 237

5.5.1 The Class IV and VII Flextensional Transducers 237

5.5.2 The Class I Barrel Stave Flextensional 242

5.5.3 The Class V and VI Flextensional Transducers 243

5.5.4 Astroid, Trioid, and X-Spring Transducers 244

5.5.5 Lumped Mode Equivalent Circuit 247

5.6 Flexural Transducers 248

5.6.1 Bender Bar Transducer 249

5.6.2 Bender Disc Transducer 253

5.6.3 Slotted Cylinder Transducer 255

5.6.4 Bender Mode X-Spring Transducer 258

5.7 Modal Transducers 259

5.7.1 Power Wheel Transducer 259

5.7.2 Octoid Transducer 262

5.7.3 Leveraged Cylindrical Transducer 263

5.8 Low Profile Piston Transducers 265

5.8.1 Cantilever Mode Piston Transducer 265

5.8.2 Shear Mode Piston Transducer 270

5.9 Summary 272

Exercises 273

References 275

6 Transducers as Hydrophones 281

6.1 Principles of Operation 282

6.1.1 Sensitivity 283

6.1.2 Figure of Merit 285

6.1.3 Simplified Equivalent Circuit 287

6.1.4 Other Sensitivity Considerations 288

6.2 Cylindrical and Spherical Hydrophones 291

6.2.1 Performance with Shielded Ends 292

6.2.2 Spherical Hydrophones 295

6.2.3 Performance with End Caps 296

6.3 Planar Hydrophones 297

6.3.1 Tonpilz Hydrophones 298

6.3.2 The 1-3 Composite Hydrophones 300

6.3.3 Flexible Hydrophones 303

6.4 Bender Hydrophones 304

6.5 Vector Hydrophones 306

6.5.1 Dipole Vector Sensors, Baffles, and Images 307

6.5.2 Pressure Gradient Vector Sensor 311

6.5.3 Velocity Vector Sensor 313

6.5.4 Accelerometer Sensitivity 314

6.5.5 Multimode Vector Sensor 316

6.5.6 Summed Scalar and Vector Sensors 318

6.5.7 Intensity Sensors 323

6.6 The Plane Wave Diffraction Constant 325

6.7 Hydrophone Thermal Noise 328

6.7.1 Directivity and Noise 330

6.7.2 Low Frequency Hydrophone Noise 331

6.7.3 More General Description of Hydrophone Noise 332

6.7.4 Comprehensive Hydrophone Noise Model 335

6.7.5 Vector Sensor Internal Noise 336

6.7.6 Vector Sensor Susceptibility to Local Noise 338

6.7.7 Thermal Noise from Radiation Resistance 339

6.8 Summary 341

Exercises 343

References 344

7 Projector Arrays 349

7.1 Array Directivity Functions 352

7.1.1 The Product Theorem 352

7.1.2 Line, Rectangular, and Circular Arrays 354

7.1.3 Grating Lobes 357

7.1.4 Beam Steering and Shaping 359

7.1.5 Staggered Arrays 365

7.1.6 Effects of Random Variations 369

7.2 Mutual Radiation Impedance and the Array Equations 370

7.2.1 Solving the Array Equations 370

7.2.2 Velocity Control 374

7.2.3 Negative Radiation Resistance 376

7.3 Calculation of Mutual Radiation Impedance 376

7.3.1 Planar Arrays of Piston Transducers 376

7.3.2 Nonplanar Arrays, Nonuniform Velocities 382

7.4 Arrays of Non-FVD Transducers 385

7.4.1 Modal Analysis of Radiation Impedance 385

7.4.2 Modal Analysis of Arrays 386

7.5 Volume Arrays 391

7.6 Near Field of a Projector Array 393

7.7 The Nonlinear Parametric Array 395

7.8 Doubly Steered Arrays 400

7.9 Summary 403

Exercises 403

References 404

8 Hydrophone Arrays 407

8.1 Hydrophone Array Directional Response 409

8.1.1 Directivity Functions 409

8.1.2 Beam Steering 413

8.1.3 Shading and Directivity Factor 414

8.1.4 Wavevector Response of Arrays 420

8.2 Array Gain 421

8.3 Sources and Properties of Noise in Arrays 425

8.3.1 Ambient Sea Noise 425

8.3.2 Structural Noise 429

8.3.3 Flow Noise 431

8.4 Reduction of Array Noise 432

8.4.1 Ambient Noise Reduction 432

8.4.2 Structural Noise Reduction 435

8.4.3 Flow Noise Reduction 440

8.4.4 Summary of Noise Reduction 444

8.5 Arrays of Vector Sensors 446

8.5.1 Directionality 448

8.5.2 Vector Sensor Arrays in Ambient Noise 449

8.5.3 Hull-Mounted Arrays in Structural Noise 455

8.6 Steered Planar Circular Arrays 464

8.7 Summary 469

Exercises 469

References 471

9 Transducer Evaluation and Measurement 475

9.1 Electrical Measurement of Transducers in Air 476

9.1.1 Electric Field Transducers 476

9.1.2 Magnetic Field Transducers 480

9.2 Measurement of Transducers in Water 482

9.3 Measurement of Transducer Efficiency 486

9.4 Acoustic Responses of Transducers 488

9.5 Reciprocity Calibration 491

9.6 Tuned Responses 495

9.6.1 Electric Field Transducers 495

9.6.2 Magnetic Field Transducers 498

9.7 Near-Field Measurements 500

9.7.1 Distance to the Far Field 500

9.7.2 Measurements in Tanks 502

9.7.3 Near-to-Far-Field Extrapolation: Small Sources 504

9.7.4 Near-to-Far-Field Extrapolation: Large Sources 506

9.7.5 Effect of Transducer Housings 510

9.8 Calibrated Reference Transducers 511

9.9 Summary 512

Exercises 513

References 514

10 Acoustic Radiation from Transducers 517

10.1 The Acoustic Radiation Problem 517

10.2 Far-Field Acoustic Radiation 524

10.2.1 Line Sources 524

10.2.2 Flat Sources in a Plane 527

10.2.3 Spherical and Cylindrical Sources 533

10.3 Near-Field Acoustic Radiation 53410.3.1 Field on the Axis of a Circular Piston 53410.3.2 The Effect of the Near Field on Cavitation 53610.3.3 Near Field of Circular Sources 53910.4 Radiation Impedance 54010.4.1 Spherical Sources 54010.4.2 Circular Sources in a Plane 54310.5 Dipole Coupling to Parasitic Monopole 54610.6 Summary 551Exercises 551References 552

11 Mathematical Models for Acoustic Radiation 55511.1 Mutual Radiation Impedance 55611.1.1 Piston Transducers on a Sphere 55611.1.2 Piston Transducers on a Cylinder 56011.1.3 Hankel Transform 56611.1.4 Hilbert Transform 56811.2 Green’s Theorem and Acoustic Reciprocity 56911.2.1 Green’s Theorem 56911.2.2 Acoustic Reciprocity 57111.2.3 Green’s Function Solutions 57211.2.4 The Helmholtz Integral Formula 57611.3 Scattering and the Diffraction Constant 57911.3.1 The Diffraction Constant 58011.3.2 Scattering from Cylinders 58311.4 Numerical Methods for Acoustic Calculations 58611.4.1 Mixed Boundary Conditions: Collocation 58711.4.2 Boundary Element Methods 58811.5 Summary 591Exercises 592References 594

12 Nonlinear Mechanisms and Their Effects 59712.1 Nonlinear Mechanisms in Lumped-Parameter

Transducers 59812.1.1 Piezoelectric Transducers 59812.1.2 Electrostrictive Transducers 60312.1.3 Magnetostrictive Transducers 60512.1.4 Electrostatic and Variable Reluctance

Transducers 60712.1.5 Moving Coil Transducers 60912.1.6 Other Nonlinear Mechanisms 611

12.2 Analysis of Nonlinear Effects 61112.2.1 Harmonic Distortion: Direct Drive

Perturbation Analysis 61212.2.2 Harmonic Distortion for Indirect Drive 62112.2.3 Instability in Electrostatic and Variable Reluctance

Transducers 62212.3 Nonlinear Analysis of Distributed Parameter Transducers 62512.4 Nonlinear Effects on the Electromechanical

Coupling Coefficient 63212.5 Summary 633Exercises 634References 635

13 Appendix 63713.1 Conversions and Constants 63713.1.1 Conversions 63713.1.2 Constants 63713.2 Materials for Transducers Ordered by Impedance,ρc 63813.3 Time Averages, Power Factor, Complex Intensity 63913.3.1 Time Average 63913.3.2 Power 64013.3.3 Intensity 64013.3.4 Radiation Impedance 64113.3.5 Complex Intensity 64113.4 Relationships Between Piezoelectric Coefficients 64113.5 Small Signal Properties of Piezoelectric Materials 64313.5.1 Comparison of Small Signal Properties

of Textured Ceramic, PZT-8 Ceramic,and Commercial Grade Single CrystalPiezoelectric Materials 64513.6 Piezoelectric Ceramic Approximate Frequency

Constants (See Footnote 1) 64613.7 Small Signal Properties of Magnetostrictive Materials 64713.7.1 Nominal 33 Magnetostrictive Properties 64713.7.2 Three-Dimensional Terfenol-D Properties 64713.8 Voltage Divider and Thevenin Equivalent Circuit 64813.8.1 Voltage Divider 64813.8.2 Thevenin Equivalent Circuit 64913.9 Magnetic Circuit Analysis 64913.9.1 Equivalent Circuit 64913.9.2 Example 65013.10 Norton Circuit Transformations 65113.11 Integral Transform Pairs 652

13.12 Stiffness, Mass, and Resistance 65313.12.1 Mechanical Stiffness [K¼ F/x] 65313.12.2 Piezoelectric Compliance [CE¼ x/F] 65313.12.3 Mass [m¼ F/a] 65413.12.4 Resonance [ω0¼ 1/√(mC)] 65413.12.5 Resistance [R¼ F/u] 65513.13 Frequently Used Formulas 65513.13.1 Transduction 65513.13.2 Radiation 65713.14 Stress, Field Limits, and Aging for Piezoelectric

Ceramics 66113.15 Development of a Comprehensive Hydrophone

Noise Model 66513.16 Cables and Transformers 67113.16.1 Cables 67113.16.2 Transformers 67213.17 Complex Algebra 67413.18 Transducer Publications 2000–2015 677

Answers to Odd-Numbered Exercises 681

Glossary 691

Index 703

About the Authors

John L Butler is chief scientist at Image Acoustics, Inc and has had over 40 years

of both practical and theoretical experiences in the design and analysis of water sound transducers and arrays He has worked for and consulted to a number ofunderwater acoustics firms as well as Parke Mathematical Laboratories and the USNavy He has also taught courses in acoustics at Northeastern University, Naval AirDevelopment Center, Raytheon Company, Harris Transducer Products, HazeltineCorporation (now Ultra Ocean Systems, Inc.), Massa Products Corporation, EtremaProducts, Plessey Australia, and Lund Institute of Technology, Sweden He holds

under-27 patents and has presented or published well over 30 papers on electroacoustictransducers In 1977 he was elected fellow of the Acoustical Society of Americaand has received their 2015 Silver Medal Award for advancing the field of acoustictransducers and transducer arrays His education includes Ph.D., NortheasternUniversity, Boston, MA, and Sc.M., Brown University, Providence, RI

Charles H Sherman (1928–2009) received a B.S degree in physics from theMassachusetts Institute of Technology in 1950 After his first job at TracerLab, Inc

in Boston, he became a research physicist at the Navy Underwater Sound tory in New London, CT He received M.S and Ph.D degrees from the University

Labora-of Connecticut and was elected Fellow Labora-of the Acoustical Society Labora-of America in

1974 He became a prominent expert in underwater transducers and arrays,presenting and publishing over 30 papers related to underwater acoustics He alsoworked at Parke Mathematical Laboratories in Carlisle, MA, and taught advancedacoustics at the University of Connecticut and in the Ocean Engineering Depart-ment of the University of Rhode Island He received the prestigious Decibel Award,which is presented to a scientist or engineer for outstanding contributions to sonarand underwater acoustics After his retirement from the Navy Underwater SoundLaboratory in 1988, he worked for Image Acoustics, Inc and, in 2007, coauthoredthe first edition of Transducers and Arrays for Underwater Sound, a technicalmonograph commissioned by the Office of Naval Research and the most compre-hensive treatment to date of underwater transducers and arrays

xxv

The development of underwater electroacoustic transducers expanded rapidlyduring the twentieth century, and continues to be a growing field of knowledgethat combines mechanics, electricity, magnetism, solid state physics, and acousticswith many significant applications In the most general sense a transducer is aprocess 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 thunderstorm

is 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, afamiliar man-made transducer is the moving coil loudspeaker used in radio, tele-vision, and other sound systems Loudspeakers are so common that they probablyoutnumber people in developed parts of the world The familiar designationsloudspeaker and microphone for transducers used as sources and receivers ofsound in air become projector and hydrophone for sources and receivers in water.The term SONAR (SOund Navigation And Ranging) is used for the process ofdetecting and locating objects by receiving the sounds they emit (passive sonar), or

by receiving the echoes reflected from them when they are “insonified” in echoranging (active sonar) Every use of sound in the water requires transducers for itsgeneration and reception, and most are based on electroacoustics Severalnon-electroacoustic transducers also find applications in water, e.g., projectorsbased on explosions, sparks, and hydroacoustics as well as optical hydrophones,but they are not included in this book

This book presents the theory and practice of underwater sound electroacoustictransducers at the beginning of the twenty-first century Chapter1 begins with abrief historical survey of the development of electroacoustics and its many appli-cations to underwater sound It also introduces the basic concepts of electroacoustictransduction in a general way applicable to all types of electroacoustic transducers.Chapter 2 describes and compares major types of electroacoustic transductionmechanisms and shows why certain piezoelectric materials now dominate thefield of underwater transducers Chapter 3 introduces the transducer models and

© Springer International Publishing Switzerland 2016

J.L Butler, C.H Sherman, Transducers and Arrays for Underwater Sound,

Modern Acoustics and Signal Processing, DOI 10.1007/978-3-319-39044-4_1

1

analysis methods and Chap.4discusses transducer characteristics Specific tor and hydrophone designs are presented in Chaps.5and6and arrays of projectorsand hydrophones are discussed in Chaps.7 and8 Chapter9 presents means fortransducer evaluation and measurement Chapter10presents a discussion of acous-tic radiation from transducers and Chap.11discusses and implements advancedmathematical models for acoustic radiation And finally, Chap 12 provides ananalysis of nonlinear effects in transducers which was introduced in Chap.2.

projec-1.1 Brief History of Underwater Sound Transducers

Electroacoustics began to develop more than 200 years ago with observations of themechanical effects associated with electricity and magnetism, and found an impor-tant place in underwater sound early in the twentieth century F V Hunt has giventhe most complete historical survey of the development of electroacoustics includ-ing a section entitled Electroacoustics Goes to Sea [1] R J Urick’s brief historicalintroduction concentrates on underwater applications of electroacoustics [2] R

T Beyer’s history of the past 200 years of acoustics also contains many references

to underwater sound transducers [3] A few historical items, taken from thesebooks, will be briefly described here Daniel Colladon and Charles Sturm collab-orated in 1826 on the first direct measurement of the speed of sound in the freshwater of Lake Geneva in Switzerland [3] They had no electroacoustic transducer togenerate sound in the water; instead their projector was a mechanoacoustic trans-ducer—the striking of a bell under water At one point on the lake the bell wasstruck simultaneously with a flash of light, while an observer in a boat 13 km awaymeasured the time interval between the flash and the arrival of the sound Theobserver also had no electroacoustic transducer for detecting the arrival of thesound; his hydrophone consisted of his ear placed at one end of a tube with theother end in the water Their measured value at a water temperature of 8C is given

by Beyer as 1438 m/s [3], and by Rayleigh as 1435 m/s [4] A modern value forfresh 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 s

Interest in telegraphy in the latter part of the eighteenth and the first part of thenineteenth centuries provided the first practical impetus for the development ofelectrical 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 ormagnetomechanical transducers Electroacoustic transducers were introduced intotelegraphy by Joseph Henry in 1830 using a moving armature transducer (now oftencalled variable reluctance transducer) in which the transmitted signal was observed

by the sound of the armature striking its stops These developments led to theinvention of the telephone, primarily by Alexander Graham Bell in 1876, using

moving armature electroacoustic transducers on both ends of the line and makingpossible transmission of the human voice.

James Joule is usually credited with the discovery of magnetostriction based onhis quantitative experiments between 1842 and 1847 including measurement of thechange in length of an iron bar when it is magnetized, although various manifes-tations of magnetostriction had been observed earlier by others [1] In 1880piezoelectricity was discovered in quartz and other crystals by Jacques and PierreCurie [1] The discoveries of magnetostriction and piezoelectricity would eventu-ally have tremendous importance for underwater sound, since materials with suchproperties are now used in most underwater transducers Magnetostrictive andpiezoelectric materials change dimensions when placed in magnetic or electricfields, respectively, and have other properties that make them very suitable forradiating or receiving sound in water Interest in the mechanical effects of electricand magnetic fields was also closely associated with the development during thenineteenth century of a theoretical understanding of electricity, magnetism, andelectromagnetism

The first application of underwater sound to navigation was made by theSubmarine Signal Company (later a Division of the Raytheon Company) early inthe twentieth century It required the crew of a ship to measure the time intervalbetween 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 illustrated

in Fig.1.1, and binaural means for determining the direction of sound as shown inFig.1.2

Fig 1.1 Early simple underwater signaling system using hammer, rod, and piston, courtesy Raytheon Company [ 6 ]

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, probablybecause 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 which, by 1914, was successfully used for signalingbetween submarines and for echo ranging On 27 April, 1914 an iceberg wasdetected by underwater echo ranging at a distance of nearly 2 miles These

“Fessenden Oscillators” operating at 500 and 1000 Hz were installed on UnitedStates submarines during World War I This was probably the first practicalapplication of underwater electroacoustic transducers [6 8]

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 available forpractical signaling through the water For the first time a significant submarinemenace existed [9], and many underwater echo ranging experiments were initiated

In France, Paul Langevin and others started work early in 1915 using an static transducer as a projector and a waterproofed carbon microphone as a hydro-phone Although some success was had in receiving echoes from targets at shortrange, numerous problems made it clear that improved transducers were necessary.When the French results were communicated to the British, a group under

electro-R W Boyle (the Allied Submarine Detection Investigation Committee, ASDIC)

Fig 1.2 Early binaural

detection and localization

air tube underwater sensor,

courtesy Raytheon

Company [ 6 ]

began similar experiments in 1916 While both sides realized that use of thepiezoelectric effect in quartz had the potential for improved transducers, it wasLangevin 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 submarine

in early 1918 The major design improvement consisted of making a resonator bysandwiching the quartz between steel plates (see Fig.1.3), an approach still used inmodern transducers

These successes greatly improved the outlook for effective echo ranging onsubmarines, and the efforts increased in France, Great Britain, the United States andalso 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 in NewLondon, Connecticut with supporting research, especially on piezoelectric mate-rials, from several other laboratories Although none of this work progressedrapidly enough to have a significant role in WWI, it did provide the basis forcontinued research in echo ranging that would soon be needed in WWII

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 suitable forunderwater use However, both electrical and magnetic losses in magnetostrictivematerials resulted in lower efficiency compared to piezoelectric transducers Othertransducer concepts were also explored including one that used the extensionalmotion of magnetostriction to drive a radiating surface in flexure (called aflextensional transducer; see Fig.1.4)

After WWI Rochelle salt, which was known to have a stronger piezoelectriceffect than quartz, also became available in the form of synthetic crystals to provide

Fig 1.3 British patent

another possibility for improved transducers Synthetic Rochelle salt was probablythe first example of what would become the most important type of innovation inthe field of electroacoustic transducers: new man-made materials with improvedelectromechanical properties.

Early in World War II these accomplishments in transducers, combined withadvances in electronics and better understanding of the propagation of sound in theocean, provided the basis for development of sonar systems with useful but limitedcapability The potential for significant improvement was clear, and, with Germansubmarines causing serious damage to shipping off the east coast of the UnitedStates, the need was great [9] The work had already started in 1941 with ColumbiaUniversity’s Division of War Research in New London, Harvard University’sUnderwater Sound Laboratory (HUSL) in Cambridge, and the University ofCalifornia’s Division of War Research in San Diego Their work resulted in manyAmerican ships being equipped with echo ranging and passive listening systems.Other types of equipment employing transducers and underwater sound were alsodeveloped such as acoustic homing torpedoes, acoustic mines, and sonobuoys Alarge 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 [10]

At the end of WWII the Columbia work at New London continued under thedirection of the Naval Research Laboratory [11] The New London facility wascalled the Navy Underwater Sound Laboratory with John M Ide as TechnicalDirector and J Warren Horton as Chief Consultant Later in 1945 the sonar projects

at the Harvard Underwater Sound Laboratory, and about half the personnel, went toNew 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 Major developments in sonar andelectromagnetics continued at New London for many years including a wide variety

Fig 1.4 An experimental flextensional transducer built at NRL in May 1929 for in-air operation with magnified shell motion driven by three magnetostrictive tubes [ 10 ]

of research and development on transducers and arrays [11] During the sameperiod similar research on transducers and arrays was conducted at the NavalResearch Laboratory in Washington, DC and Orlando, Florida and also at theNavy Electronics Laboratory in San Diego.

WWII, and the Cold War that followed, strongly motivated the search for newman-made transduction materials which led to ammonium dihydrogen phosphate(ADP), lithium sulfate, and other crystals in the early 1940s Then, in 1944,piezoelectricity was discovered by A R von Hippel in permanently polarizedbarium titanate ceramics [12], and in 1954 even stronger piezoelectricity wasfound in polarized lead-zirconate-titanate ceramics [13] The discovery of thesematerials initiated the modern era of piezoelectric transducers in time to play animportant role in, once again, meeting the threat of submarines off the east coast ofthe United States, this time Soviet submarines armed with long range nuclearmissiles

At the end of the twentieth century lead-zirconate-titanate (PZT) ceramic pounds are still being used in most underwater sound transducers However, othersimilar materials such as lead manganese niobate (PMN), textured ceramic andsingle crystals of related compounds, such as lead indium niobate-lead magnesiumniobate-lead titanate (PIN-PMN-PT) and the magnetostrictive materials Terfenol-Dand Galfenol, have been developed which have the potential for improvement overPZT in some applications Piezoelectric ceramics and ceramic-elastomer compos-ites can be made in a great variety of shapes and sizes with many variations ofcomposition that provide specific properties of interest The characteristics of thesematerials have led to the development and manufacture of innovative, relativelyinexpensive transducer designs that would have been unimaginable in the earlydays of electroacoustics

com-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 Forexample, acoustic communication over thousands of kilometers is possible in theoceans, but frequencies below about 100 Hz are required because the absorption ofsound increases rapidly as the frequency increases [2] On the other hand, depthsounding in water as shallow as 1 m is important for small boats, but it requiresshort pulses of sound at a few hundred kHz to separate the echo from the transmis-sion High resolution, short-range active sonar has used frequencies up to 1.5 MHz.Applications over this wide frequency range require many different transducerdesigns

Naval applications of underwater sound require a large number and variety oftransducers Acoustic communication between two submerged submarines requires

a projector to transmit sound and a hydrophone to receive sound on each submarine;echo ranging requires a projector and a hydrophone usually on the same ship;

passive listening requires only a hydrophone However, hydrophones and tors are often used in large groups of up to 1000 or more transducers closely packed

projec-in planar, cylprojec-indrical, or spherical arrays mounted on naval ships

Other naval applications include acoustic mines activated by the voltage from ahydrophone sensitive to the low frequency sound radiated by a moving ship Specialprojectors and hydrophones are required for acoustic communication betweensubmerged submarines or from a surface ship to a submarine Torpedoes withactive acoustic homing systems require high frequency, directional arrays, whilethose with passive homing require lower frequency capability to detect ship radi-ated noise Submarines are usually equipped with other specialized hydrophones tomonitor their self-noise or to augment the major sonar systems Sonobuoys areexpendable hydrophone/radio transmitter combinations dropped into the waterfrom an aircraft The radio floats on the surface, with the tethered hydrophone at

a suitable depth for detecting submarines Some types of sonobuoys listen sively, while others echo range, but both radio information back to the aircraft.Urick [2] discusses most of these naval applications

pas-As sonar technology matured it began to have significant commercial 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 importantnot only to the Navy but also to all mariners from those aboard the largest ships tothose on small recreational boats Sonar can do more than find the water depth at thepoint 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 miles ofocean 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 importance

applica-in the fishapplica-ing applica-industry where systems have been developed specifically for locatapplica-ingschools of fish Underwater transducers can even be used to kill mosquito larva byirradiating them with ultrasonic energy [14]

Bottom mapping with sonar is an important part of oceanography, and it can beextended to sub-bottom mapping and determination of bottom characteristics Forexample, the bottom of Peconic Bay, Long Island, New York has been studied bysonar in an attempt to determine the reasons for the decrease in the scalloppopulation [15] 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 and gasdeep in the ocean or laying underwater cables or pipelines A combination ofunderwater 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 related to

a wide variety of topics The Acoustic Thermometry of Ocean Climate project(ATOC) measures the acoustic travel time over ocean paths thousands of kilome-ters long to determine whether the average sound speed is increasing as timepasses Since an increasing sound speed in ocean waters means an increasingaverage temperature over a large portion of the earth, it may be one of the bestmeasures of global warming This project requires very low frequency projectorsand hydrophones as well as very careful signal processing [16] The SoundSurveillance System has been used to study the behavior of sperm whales bydetecting the “clicks,” which they emit, and to detect earthquakes and volcaniceruptions under the sea [17] In what may become the ultimate version of thesonobuoy concept, plans have been made to land acoustic sensors on Jupiter’smoon Europa in about the year 2020 Cracks, which are thought to occur naturally

in the ice that covers the surface of Europa, generate sound in the ice and in theocean that may lie beneath the ice The sounds received by the acoustic sensorsmay be interpretable in terms of the ice thickness and the depth and temperature ofthe underlying ocean Such information may give clues about the possible exis-tence of extraterrestrial life [18] Underwater sound may even play a role in thefield of particle physics if physicists succeed in showing that hydrophone arrays arecapable of detecting the sounds caused by high energy neutrinos passing throughthe ocean [19]

All these applications of underwater sound require large numbers of ducers, with a great variety of special characteristics for use over a wide range offrequency, power, size, weight, and water depth The problems raised by thevariety of applications and the numerous possibilities for solutions continue tomake underwater sound transducer research and development a challengingsubject Figures 1.5, 1.6, 1.7, 1.8, 1.9, 1.10, 1.11, 1.12, 1.13, 1.14, 1.15, 1.16,and 1.17 illustrate several more recent underwater sound transducers, Fig 1.9shows an early low frequency array, Figs 1.10, 1.11, and 1.12 illustrate morecurrent arrays, Figs.1.13and1.14show flextensional transducers and Figs.1.15,1.16, and 1.17 illustrate transducers that use newer materials, Terfenol-D andsingle crystal PMN-PT

trans-Fig 1.5 Sketch of a Tonpilz transducer with nodal plate mounting system

Fig 1.6 Sketch of high power low frequency Tonpilz transducer with head and tail mounting system and steel housing case

Fig 1.7 Photograph of a

low frequency high power

Tonpilz transducer showing

rubber molded piston,

fiberglass wrapped drive

stack of six piezoelectric

ceramic rings, tail mass,

transformer, and housing

Fig 1.9 Photograph of large array of very low frequency magnetic variable reluctance dipole

“shaker box” transducers ready for deep submergence testing, courtesy of Massa products [ 30 ]

Fig 1.10 Cylindrical scanning array of Tonpilz transducers

Fig 1.11 Submarine sonar

spherical array

undergoing tests

submarine conformal array

during testing

Fig 1.13 Sketch of various classes of flextensional transducers [ 31 ]

Fig 1.14 Sketch of a Class IV flextensional transducer with inactive central section for operation

in a dipole mode [ 32 ] Shell and interface by John Oswin, British Aerospace England

Fig 1.15 An experimental

ring mode magnetostrictive

transducer (without top

end cap) driven by

16 Terfenol-D

magnetostrictive rods [ 33 ]

Fig 1.16 A high power magnetostrictive/piezoelectric hybrid transducer with square piston, piezoelectric ceramic drive, centermass, magnetostrictive drive, and tail mass along with water- tight housing and electrical connector [ 34 ]