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E-raamat: Transducers and Arrays for Underwater Sound

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This improved and updated second edition covers the theory, development, and design of electro-acoustic transducers for underwater applications. This highly regarded text discusses the basics of piezoelectric and magnetostrictive transducers that are currently being used as well as promising new designs. It presents the basic acoustics as well as the specific acoustics data needed in transducer design and evaluation. A broad range of designs of projectors and hydrophones are described in detail along with methods of modeling, evaluation, and measurement. Analysis of projector and hydrophone transducer arrays, including the effects of mutual radiation impedance and numerical models for elements and arrays, are also covered. The book includes new advances in transducer design and transducer materials and has been completely reorganized to be suitable for use as a textbook, as well as a reference or handbook. The new edition contains corrections to the first edition, end-of-chapter e

xercises, and solutions to selected exercises. Each chapter includes a short introduction, end-of-chapter summary, and an extensive reference list offering the reader more detailed information and historical context. A glossary of key terms is also included at the end.
1 Introduction
1(32)
1.1 Brief History of Underwater Sound Transducers
2(5)
1.2 Underwater Transducer Applications
7(8)
1.3 General Description of Linear Electroacoustic Transduction
15(7)
1.4 Transducer Characteristics
22(5)
1.4.1 Electromechanical Coupling Coefficient
22(2)
1.4.2 Transducer Responses, Directivity Index, and Source Level
24(3)
1.5 Transducer Arrays
27(1)
1.6 Summary
28(5)
Exercises
29(1)
References
30(3)
2 Electroacoustic Transduction
33(58)
2.1 Piezoelectric Transducers
34(11)
2.1.1 General
34(5)
2.1.2 The 33 Mode Longitudinal Vibrator
39(4)
2.1.3 The 31 Mode Longitudinal Vibrator
43(2)
2.2 Electrostrictive Transducers
45(4)
2.3 Magnetostrictive Transducers
49(3)
2.4 Electrostatic Transducers
52(3)
2.5 Variable Reluctance Transducers
55(2)
2.6 Moving Coil Transducers
57(3)
2.7 Comparison of Transduction Mechanisms
60(2)
2.8 Equivalent Circuits
62(17)
2.8.1 Equivalent Circuit Basics
62(3)
2.8.2 Circuit Resonance
65(1)
2.8.3 Circuit Q and Bandwidth
66(3)
2.8.4 Power Factor and Tuning
69(4)
2.8.5 Power Limits
73(2)
2.8.6 Efficiency
75(3)
2.8.7 Hydrophone Circuit and Noise
78(1)
2.9 Thermal Considerations
79(6)
2.9.1 Transducer Thermal Model
80(3)
2.9.2 Power and Heating at Resonance
83(2)
2.10 Extended Equivalent Circuits
85(1)
2.11 Summary
86(5)
Exercises
87(2)
References
89(2)
3 Transducer Models
91(62)
3.1 Lumped-Parameter Models and Equivalent Circuits
92(18)
3.1.1 Mechanical Single Degree of Freedom Lumped Equivalent Circuits
92(3)
3.1.2 Mechanical Lumped Equivalent Circuits for Higher Degrees of Freedom
95(4)
3.1.3 Piezoelectric Ceramic Lumped-Parameter Equivalent Circuit
99(5)
3.1.4 Magnetostrictive Lumped-Parameter Equivalent Circuit
104(4)
3.1.5 Eddy Currents
108(2)
3.2 Distributed Models
110(18)
3.2.1 Distributed Mechanical Model
111(4)
3.2.2 Matrix Representation
115(3)
3.2.3 Piezoelectric Distributed Parameter Equivalent Circuit
118(10)
3.3 Matrix Models
128(5)
3.3.1 Three Port Matrix Model
128(3)
3.3.2 Two Port ABCD Matrix Model
131(2)
3.4 Finite Element Models
133(16)
3.4.1 A Simple FEM Example
133(2)
3.4.2 FEA Matrix Representation
135(2)
3.4.3 Inclusion of a Piezoelectric Finite Element
137(1)
3.4.4 Application of FEA Without Water Loading
138(3)
3.4.5 Application of FEA with Water Loading
141(3)
3.4.6 Water Loading of Large Arrays
144(1)
3.4.7 Magnetostrictive FEA
145(2)
3.4.8 Equivalent Circuits for FEA Models
147(2)
3.5 Summary
149(4)
Exercises
150(1)
References
151(2)
4 Transducer Characteristics
153(32)
4.1 Resonance Frequency
153(4)
4.2 Mechanical Quality Factor
157(4)
4.2.1 Definitions
157(2)
4.2.2 Effect of the Mass of the Bar
159(1)
4.2.3 Effect of Frequency-Dependent Resistance
160(1)
4.3 Characteristic Mechanical Impedance
161(2)
4.4 Electromechanical Coupling Coefficient
163(15)
4.4.1 Energy Definitions of Coupling and Other Interpretations
164(5)
4.4.2 The Effect of Inactive Components on the Coupling Coefficient
169(5)
4.4.3 The Effect of Dynamic Conditions on the Coupling Coefficient
174(4)
4.5 Parameter Based Figure of Merit (FOM)
178(3)
4.6 Summary
181(4)
Exercises
182(1)
References
183(2)
5 Transducers as Projectors
185(96)
5.1 Principles of Operation
187(3)
5.1.1 Projector Figure of Merit
188(2)
5.2 Ring and Spherical Transducers
190(17)
5.2.1 Piezoelectric 31 Mode Ring
190(6)
5.2.2 Piezoelectric 33 Mode Ring
196(1)
5.2.3 The Spherical Transducer
197(3)
5.2.4 The Magnetostrictive Ring
200(1)
5.2.5 Free-Flooded Rings
201(4)
5.2.6 Multimode Rings
205(2)
5.3 Piston Transducers
207(13)
5.3.1 The Tonpilz Projector
207(9)
5.3.2 The Hybrid Transducer
216(4)
5.4 Transmission Line Transducers
220(17)
5.4.1 Sandwich Transducers
220(5)
5.4.2 Wideband Transmission Line Transducers
225(5)
5.4.3 Large Plate Transducers
230(2)
5.4.4 Composite Transducers
232(5)
5.5 Flextensional Transducers
237(11)
5.5.1 The Class IV and VII Flextensional Transducers
237(5)
5.5.2 The Class I Barrel Stave Flextensional
242(1)
5.5.3 The Class V and VI Flextensional Transducers
243(1)
5.5.4 Astroid, Trioid, and X-Spring Transducers
244(3)
5.5.5 Lumped Mode Equivalent Circuit
247(1)
5.6 Flexural Transducers
248(11)
5.6.1 Bender Bar Transducer
249(4)
5.6.2 Bender Disc Transducer
253(2)
5.6.3 Slotted Cylinder Transducer
255(3)
5.6.4 Bender Mode X-Spring Transducer
258(1)
5.7 Modal Transducers
259(6)
5.7.1 Power Wheel Transducer
259(3)
5.7.2 Octoid Transducer
262(1)
5.7.3 Leveraged Cylindrical Transducer
263(2)
5.8 Low Profile Piston Transducers
265(7)
5.8.1 Cantilever Mode Piston Transducer
265(5)
5.8.2 Shear Mode Piston Transducer
270(2)
5.9 Summary
272(9)
Exercises
273(2)
References
275(6)
6 Transducers as Hydrophones
281(68)
6.1 Principles of Operation
282(9)
6.1.1 Sensitivity
283(2)
6.1.2 Figure of Merit
285(2)
6.1.3 Simplified Equivalent Circuit
287(1)
6.1.4 Other Sensitivity Considerations
288(3)
6.2 Cylindrical and Spherical Hydrophones
291(6)
6.2.1 Performance with Shielded Ends
292(3)
6.2.2 Spherical Hydrophones
295(1)
6.2.3 Performance with End Caps
296(1)
6.3 Planar Hydrophones
297(7)
6.3.1 Tonpilz Hydrophones
298(2)
6.3.2 The 1-3 Composite Hydrophones
300(3)
6.3.3 Flexible Hydrophones
303(1)
6.4 Bender Hydrophones
304(2)
6.5 Vector Hydrophones
306(19)
6.5.1 Dipole Vector Sensors, Baffles, and Images
307(4)
6.5.2 Pressure Gradient Vector Sensor
311(2)
6.5.3 Velocity Vector Sensor
313(1)
6.5.4 Accelerometer Sensitivity
314(2)
6.5.5 Multimode Vector Sensor
316(2)
6.5.6 Summed Scalar and Vector Sensors
318(5)
6.5.7 Intensity Sensors
323(2)
6.6 The Plane Wave Diffraction Constant
325(3)
6.7 Hydrophone Thermal Noise
328(13)
6.7.1 Directivity and Noise
330(1)
6.7.2 Low Frequency Hydrophone Noise
331(1)
6.7.3 More General Description of Hydrophone Noise
332(3)
6.7.4 Comprehensive Hydrophone Noise Model
335(1)
6.7.5 Vector Sensor Internal Noise
336(2)
6.7.6 Vector Sensor Susceptibility to Local Noise
338(1)
6.7.7 Thermal Noise from Radiation Resistance
339(2)
6.8 Summary
341(8)
Exercises
343(1)
References
344(5)
7 Projector Arrays
349(58)
7.1 Array Directivity Functions
352(18)
7.1.1 The Product Theorem
352(2)
7.1.2 Line, Rectangular, and Circular Arrays
354(3)
7.1.3 Grating Lobes
357(2)
7.1.4 Beam Steering and Shaping
359(6)
7.1.5 Staggered Arrays
365(4)
7.1.6 Effects of Random Variations
369(1)
7.2 Mutual Radiation Impedance and the Array Equations
370(6)
7.2.1 Solving the Array Equations
370(4)
7.2.2 Velocity Control
374(2)
7.2.3 Negative Radiation Resistance
376(1)
7.3 Calculation of Mutual Radiation Impedance
376(9)
7.3.1 Planar Arrays of Piston Transducers
376(6)
7.3.2 Nonplanar Arrays, Nonuniform Velocities
382(3)
7.4 Arrays of Non-FVD Transducers
385(6)
7.4.1 Modal Analysis of Radiation Impedance
385(1)
7.4.2 Modal Analysis of Arrays
386(5)
7.5 Volume Arrays
391(2)
7.6 Near Field of a Projector Array
393(2)
7.7 The Nonlinear Parametric Array
395(5)
7.8 Doubly Steered Arrays
400(3)
7.9 Summary
403(4)
Exercises
403(1)
References
404(3)
8 Hydrophone Arrays
407(68)
8.1 Hydrophone Array Directional Response
409(12)
8.1.1 Directivity Functions
409(4)
8.1.2 Beam Steering
413(1)
8.1.3 Shading and Directivity Factor
414(6)
8.1.4 Wavevector Response of Arrays
420(1)
8.2 Array Gain
421(4)
8.3 Sources and Properties of Noise in Arrays
425(7)
8.3.1 Ambient Sea Noise
425(4)
8.3.2 Structural Noise
429(2)
8.3.3 Flow Noise
431(1)
8.4 Reduction of Array Noise
432(14)
8.4.1 Ambient Noise Reduction
432(3)
8.4.2 Structural Noise Reduction
435(5)
8.4.3 Flow Noise Reduction
440(4)
8.4.4 Summary of Noise Reduction
444(2)
8.5 Arrays of Vector Sensors
446(18)
8.5.1 Directionality
448(1)
8.5.2 Vector Sensor Arrays in Ambient Noise
449(6)
8.5.3 Hull-Mounted Arrays in Structural Noise
455(9)
8.6 Steered Planar Circular Arrays
464(5)
8.7 Summary
469(6)
Exercises
469(2)
References
471(4)
9 Transducer Evaluation and Measurement
475(42)
9.1 Electrical Measurement of Transducers in Air
476(6)
9.1.1 Electric Field Transducers
476(4)
9.1.2 Magnetic Field Transducers
480(2)
9.2 Measurement of Transducers in Water
482(4)
9.3 Measurement of Transducer Efficiency
486(2)
9.4 Acoustic Responses of Transducers
488(3)
9.5 Reciprocity Calibration
491(4)
9.6 Tuned Responses
495(5)
9.6.1 Electric Field Transducers
495(3)
9.6.2 Magnetic Field Transducers
498(2)
9.7 Near-Field Measurements
500(11)
9.7.1 Distance to the Far Field
500(2)
9.7.2 Measurements in Tanks
502(2)
9.7.3 Near-to-Far-Field Extrapolation: Small Sources
504(2)
9.7.4 Near-to-Far-Field Extrapolation: Large Sources
506(4)
9.7.5 Effect of Transducer Housings
510(1)
9.8 Calibrated Reference Transducers
511(1)
9.9 Summary
512(5)
Exercises
513(1)
References
514(3)
10 Acoustic Radiation from Transducers
517(38)
10.1 The Acoustic Radiation Problem
517(7)
10.2 Far-Field Acoustic Radiation
524(10)
10.2.1 Line Sources
524(3)
10.2.2 Flat Sources in a Plane
527(6)
10.2.3 Spherical and Cylindrical Sources
533(1)
10.3 Near-Field Acoustic Radiation
534(6)
10.3.1 Field on the Axis of a Circular Piston
534(2)
10.3.2 The Effect of the Near Field on Cavitation
536(3)
10.3.3 Near Field of Circular Sources
539(1)
10.4 Radiation Impedance
540(6)
10.4.1 Spherical Sources
540(3)
10.4.2 Circular Sources in a Plane
543(3)
10.5 Dipole Coupling to Parasitic Monopole
546(5)
10.6 Summary
551(4)
Exercises
551(1)
References
552(3)
11 Mathematical Models for Acoustic Radiation
555(42)
11.1 Mutual Radiation Impedance
556(13)
11.1.1 Piston Transducers on a Sphere
556(4)
11.1.2 Piston Transducers on a Cylinder
560(6)
11.1.3 Hankel Transform
566(2)
11.1.4 Hilbert Transform
568(1)
11.2 Green's Theorem and Acoustic Reciprocity
569(10)
11.2.1 Green's Theorem
569(2)
11.2.2 Acoustic Reciprocity
571(1)
11.2.3 Green's Function Solutions
572(4)
11.2.4 The Helmholtz Integral Formula
576(3)
11.3 Scattering and the Diffraction Constant
579(7)
11.3.1 The Diffraction Constant
580(3)
11.3.2 Scattering from Cylinders
583(3)
11.4 Numerical Methods for Acoustic Calculations
586(5)
11.4.1 Mixed Boundary Conditions: Collocation
587(1)
11.4.2 Boundary Element Methods
588(3)
11.5 Summary
591(6)
Exercises
592(2)
References
594(3)
12 Nonlinear Mechanisms and Their Effects
597(40)
12.1 Nonlinear Mechanisms in Lumped-Parameter Transducers
598(13)
12.1.1 Piezoelectric Transducers
598(5)
12.1.2 Electrostrictive Transducers
603(2)
12.1.3 Magnetostrictive Transducers
605(2)
12.1.4 Electrostatic and Variable Reluctance Transducers
607(2)
12.1.5 Moving Coil Transducers
609(2)
12.1.6 Other Nonlinear Mechanisms
611(1)
12.2 Analysis of Nonlinear Effects
611(14)
12.2.1 Harmonic Distortion: Direct Drive Perturbation Analysis
612(9)
12.2.2 Harmonic Distortion for Indirect Drive
621(1)
12.2.3 Instability in Electrostatic and Variable Reluctance Transducers
622(3)
12.3 Nonlinear Analysis of Distributed Parameter Transducers
625(7)
12.4 Nonlinear Effects on the Electromechanical Coupling Coefficient
632(1)
12.5 Summary
633(4)
Exercises
634(1)
References
635(2)
13 Appendix
637(44)
13.1 Conversions and Constants
637(1)
13.1.1 Conversions
637(1)
13.1.2 Constants
637(1)
13.2 Materials for Transducers Ordered by Impedance, pc
638(1)
13.3 Time Averages, Power Factor, Complex Intensity
639(2)
13.3.1 Time Average
639(1)
13.3.2 Power
640(1)
13.3.3 Intensity
640(1)
13.3.4 Radiation Impedance
641(1)
13.3.5 Complex Intensity
641(1)
13.4 Relationships Between Piezoelectric Coefficients
641(2)
13.5 Small Signal Properties of Piezoelectric Materials
643(3)
13.5.1 Comparison of Small Signal Properties of Textured Ceramic, PZT-8 Ceramic, and Commercial Grade Single Crystal Piezoelectric Materials
645(1)
13.6 Piezoelectric Ceramic Approximate Frequency Constants (See Footnote 1)
646(1)
13.7 Small Signal Properties of Magnetostrictive Materials
647(1)
13.7.1 Nominal 33 Magnetostrictive Properties
647(1)
13.7.2 Three-Dimensional Terfenol-D Properties
647(1)
13.8 Voltage Divider and Thevenin Equivalent Circuit
648(1)
13.8.1 Voltage Divider
648(1)
13.8.2 Thevenin Equivalent Circuit
649(1)
13.9 Magnetic Circuit Analysis
649(2)
13.9.1 Equivalent Circuit
649(1)
13.9.2 Example
650(1)
13.10 Norton Circuit Transformations
651(1)
13.11 Integral Transform Pairs
652(1)
13.12 Stiffness, Mass, and Resistance
653(2)
13.12.1 Mechanical Stiffness [ K = F/x]
653(1)
13.12.2 Piezoelectric Compliance [ CE = x/F]
653(1)
13.12.3 Mass [ m = F/a]
654(1)
13.12.4 Resonance [ ω0 = 1/√(mC)]
654(1)
13.12.5 Resistance [ R = F/u]
655(1)
13.13 Frequently Used Formulas
655(6)
13.13.1 Transduction
655(2)
13.13.2 Radiation
657(4)
13.14 Stress, Field Limits, and Aging for Piezoelectric Ceramics
661(4)
13.15 Development of a Comprehensive Hydrophone Noise Model
665(6)
13.16 Cables and Transformers
671(3)
13.16.1 Cables
671(1)
13.16.2 Transformers
672(2)
13.17 Complex Algebra
674(3)
13.18 Transducer Publications 2000--2015
677(4)
Answers to Odd-Numbered Exercises 681(10)
Glossary 691(12)
Index 703
Dr. John L. Butler is Chief Scientist at Image Acoustics, Inc. and has had over forty years of both practical and theoretical experience in the design and analysis of underwater sound transducers and arrays.  He has worked for and consulted to a number of underwater acoustics firms as well as Parke Mathematical Laboratories and the U. S. Navy. He has also taught courses in acoustics at Northeastern University, Naval Air Development Center, Raytheon Company, Harris Transducer Products and Hazeltine Corporation (now Ultra Ocean Systems, Inc.), Massa Products Corporation, Etrema Products, Plessey Australia, and Lund Institute of Technology, Sweden. He holds twenty seven patents and has presented or published well over thirty papers on electro-acoustic transducers. In 1977 he was elected fellow of the Acoustical Society of America and has received their 2015 Silver Medal Award for advancing the field of acoustic transducers and transducer arrays.  His education includes Ph. D., Northeastern University, Boston, MA, and Sc. M., Brown University, Providence, RI.   

Dr. Charles H. Sherman (1928-2009) received a B. S. degree in physics from the Massachusetts Institute of Technology in 1950. After his first job at TracerLab, Inc. in Boston, he became a research physicist at the Naval Underwater Sound Laboratory in New London, CT. He received M.S. and Ph.D. Degrees from the University of Connecticut and was elected Fellow of the Acoustical Society of America in 1974. He became a prominent expert in underwater transducers and arrays, presenting and publishing over thirty papers related to underwater acoustics. He also worked at Parke Mathematical Laboratories in Carlisle, MA, and taught advanced acoustics at the University of Connecticut and in the Ocean Engineering Department of the University of Rhode Island. He received the prestigious Decibel Award, which is presented to a scientist or engineer for outstanding contributions to sonar and underwateracoustics. After his retirement from the Sound Lab in 1988, he worked for Image Acoustics, Inc. and in 2007, co-authored the first edition of Transducers and Arrays for Underwater Sound, a technical monograph commissioned by the Office of Naval Research and the most comprehensive treatment to date of underwater transducers and arrays.