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1 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
2 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
3 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
4 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
5 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
6 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
7 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
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