Оглавление
John C. Cochran. Introduction to Sonar Transducer Design
Table of Contents
List of Tables
List of Illustrations
Guide
Pages
Introduction to Sonar Transducer Design
Preface
1 Acoustic Waves and Radiation
1.1 Small Signals/Linear Acoustics
1.1.1 Compressibility
1.1.2 Small Signals/Linear Acoustics
1.1.3 Relationship Between Acoustic Pressure and Acoustic Density
1.1.4 Condensation
1.1.5 Time Derivative Using Eulerian and Lagrangian Description
1.2 The Equations of Continuity, Motion, and the Wave Equation in a Fluid Media. 1.2.1 Equation of Continuity in a Single Dimension
1.2.2 The Force Equation in a Single Dimension
1.2.3 The Wave Equation in a Single Dimension
1.2.4 Generalization of the Wave Equation to Three Dimensions
1.2.5 Helmholtz Wave Equation
1.2.6 Velocity Potential
1.3 Plane Waves. 1.3.1 Harmonic Plane Waves
1.3.2 Plane Waves in an Infinite Media
1.3.3 Plane Wave Acoustic Intensity
1.3.4 Plane Wave Acoustic Impedance
1.4 Radiation from Spheres
1.4.1 General Solution to Radiation from Spheres
1.4.2 Spherical Wave Acoustic Impedance
1.4.3 Axis‐Symmetric Radiation from a Sphere – the Spherical Source
1.4.4 The Simple Spherical Source
1.4.5 Source Strength
1.4.6 The General Simple Source
1.4.7 Acoustic Reciprocity and Reciprocity Factor
1.5 Radiation from Sources on a Cylindrical Surface
1.5.1 General Solution to Radiation from Cylinders
1.5.2 Radiation from an Infinitely Long Cylinder
1.5.3 The Simple, Infinitely Long Cylindrical Source
1.5.4 Radiation from an Infinitely Long Strip on an Infinitely Long Cylinder
1.5.5 Radiation from a Finite Source on a Cylinder with a Periodic z Dependence
1.5.6 Radiation from a Finite Source on a Cylinder with a Uniform z Dependence
1.5.7 The Simple Cylindrical Source – Radiation from a Finite Length Cylinder in an Infinitely Long Cylinder Baffle
1.6 Integral Formulations
1.6.1 The Green’s Function
1.6.2 Helmholtz Integral Formulations
1.6.3 Far Field Approximation
1.6.4 An Application of the Simple Source Integral Formulation – Radiation from a Finite Cylinder
1.7 Linear Apertures
1.7.1 Far Field Radiation (Beam) Patterns as a Fourier Transform of the Linear Aperture Function – the Directivity Function
1.7.2 A Simple Rectangular Aperture Function as an Example of a Linear Aperture
1.7.3 The Triangular Window Aperture Function as a Linear Aperture
1.7.4 The Cosine Window Aperture Function as a Linear Aperture
1.7.5 Other Linear Apertures
1.7.6 The Far Field Radiation Pattern of a Linear Aperture on a Cylindrical Surface
1.8 Planar Apertures
1.8.1 The Green’s Function for Radiation from Planar Apertures Located on a Rigid Plane Baffle
1.8.2 Far Field Radiation Patterns as a Fourier Transform of the Planar Aperture Function
1.8.3 The Rectangular Piston in an Infinite Plane Baffle
1.8.4 The Circular Piston in an Infinite Plane Baffle
1.8.5 The Far Field Radiation Pattern of a Circular Annular Ring
1.8.6 The Elliptical Piston in an Infinite Plane Baffle
1.8.7 Impact of Boundary Impedance on Radiation Patterns from Planar Apertures
1.9 Directivity and Directivity Index (DI)
1.9.1 Definition of Directivity and Directivity Index (DI)
1.9.2 Relationship Between Source Level and Directivity Index
1.9.3 The Directivity of Baffled vs. Unbaffled Sources
1.9.4 The Directivity Index of a Baffled Circular Piston
1.9.5 The Directivity Index of a Baffled Rectangular Piston
1.9.6 The Directivity Index of a Line Source
1.10 Scattering and Diffraction
1.10.1 Scattering and Diffraction from a Rigid Cylinder
1.10.1.1 The Incident Wave
1.10.1.2 The Scattered Wave
1.10.1.3 Matching the Boundary Conditions for the Total Field
1.10.1.4 The Scattered Pressure Field in the Far Field
1.10.1.5 The Total Pressure Field
1.10.1.6 The Average Pressure Exerted on the Cylinder by the Total Pressure Field
1.10.2 The Diffraction Constant for a Rigid Cylinder
1.10.3 Diffraction Constant for a Strip on a Rigid Cylinder
1.10.4 Diffraction of a Cylinder with Variable Boundary Admittance
1.10.4.1 The Incident Wave
1.10.4.2 The Boundary Admittance
1.10.4.3 The Scattered Wave
1.10.4.4 Matching the Boundary Conditions
1.10.4.5 The Boundary Reflection Coefficient and the Scattered Field
1.10.4.6 The Total Field
1.10.4.7 The Average Pressure Exerted on the Cylinder With a Variable Boundary Admittance
1.10.4.8 The Diffraction Constant for a Cylinder with Variable Boundary Admittance
1.10.4.9 The Total Diffracted Field in the Far Field
1.10.4.10 The Total Diffracted Field at the Surface of the Cylinder
1.10.5 Scattering and Diffraction from a Rigid Sphere
1.10.5.1 The Incident Wave
1.10.5.2 The Scattered Wave
1.10.5.3 Matching the Boundary Conditions for the Total Field
1.10.5.4 The Total Pressure Field
1.10.5.5 The Scattered Pressure Field in the Far Field
1.10.5.6 The Average Pressure Exerted on the Sphere by the Pressure Field
1.10.6 The Diffraction Constant for a Rigid Sphere
1.10.7 Scattering and Diffraction from a Thin Cylindrical Ring
1.11 Radiation Impedance
1.11.1 Introduction to Radiation Impedance
1.11.2 Units of Acoustic Radiation Impedance
1.11.3 What it Means to be ρc Loaded
1.11.4 The Relationship Between Resistance and Reactance – The Hilbert Transform
1.11.5 The Relationship Between Radiation Resistance, Directivity, and Diffraction Constant
1.11.6 The Radiation Impedance of a Spherical Radiator
1.11.7 The Radiation Impedance of a Simple Source Radiator
1.11.8 The Radiation Impedance of a Circular Piston Radiator in a Plane Baffle
1.11.9 The Radiation Impedance of a Circular Piston Radiator at the End of a Tube
1.11.10 The Radiation Impedance of a Rectangular Piston Radiator in a Plane Baffle
1.11.11 The Radiation Impedance of an Infinitely Long Strip Radiator in a Plane Baffle
1.11.12 The Radiation Impedance of a Circular Annular Piston Radiator in a Plane Baffle
1.11.13 The Radiation Impedance of an Elliptical Piston Radiator in a Plane Baffle
1.11.14 The Radiation Impedance of an Infinitely Long Cylindrical Radiator
1.11.15 The Radiation Impedance of a Finite Cylindrical Radiator
1.11.16 Mutual Radiation Impedance
1.11.17 The Mutual Radiation Impedance Between Spherical Radiators
1.11.18 The Mutual Radiation Impedance Between Two Circular Piston Radiators in a Plane Baffle
1.11.19 The Mutual Radiation Impedance Between Two Square Piston Radiators in a Plane Baffle
1.11.20 The Mutual Radiation Impedance Between a Circular Piston and an Outer Annular Ring
1.11.21 The Mutual Radiation Impedance Between Rectangular or Square Pistons Located on a Cylindrical Baffle
1.11.22 The Mutual Radiation Impedance Between Bands on a Cylindrical Baffle
1.12 Transmission Phenomena
1.12.1 Reflection and Transmission of Plane Waves with Normal Incidence at a Boundary
1.12.2 Reflection and Transmission of Plane Waves Obliquely Incident at a Plane Boundary
1.12.2.1 Snell’s Law
1.12.2.2 Reflection and Transmission Factors for Obliquely Incident Plane Waves
1.12.2.3 Brewster’s Angle or the Angle of Zero Reflection
1.12.2.4 The Critical Angle or the Angle of Complete Reflection
1.12.2.5 Evanescent Waves
1.13 Absorption and Attenuation of Sound. 1.13.1 Absorption Phenomena
1.13.2 Absorption in Seawater
References
2 Mechanical/Acoustical Equivalent Circuits
2.1 Different Forms of Impedance
2.2 Mechanical Equivalent Circuits. 2.2.1 The Simple Mechanical System. 2.2.1.1 A Simple Mechanical Oscillator
2.2.1.2 Phasor Form of the Solutions to the Equations of Motion
2.2.1.3 Damped Oscillations
2.2.1.4 Forced Oscillations
2.2.1.5 Complete Solution for a Simple Oscillator
2.2.1.6 Analogy to Electrical Circuits
2.2.1.7 Behavior of the Steady State, Forced, Mechanical Oscillator
2.2.1.8 Equivalent Circuit for a Simple Resonator System
2.2.2 Introduction to Mobility
2.2.2.1 Mechanical Generators
2.2.2.2 Combining Impedance and Mobility Elements
2.2.2.3 Elements of Mobility and Impedance Analogs
2.2.2.4 Examples of Mechanical Systems Described by Mobility Analogs
2.2.2.5 An Example of a Gyrator Conversion
2.2.2.6 Converting from Mobility to Impedance and Vice Versa
2.3 Acoustical Equivalent Circuits. 2.3.1 Acoustic Circuit Elements
2.3.1.1 Acoustic Compliance – the Closed‐End Tube
2.3.1.2 Acoustic Mass – the Open‐Ended Tube
2.3.1.3 Acoustic Resistance
2.3.1.4 Acoustic Generators
2.3.1.5 Pressure Equalization Orifices
2.3.1.6 The Thin Acoustic Orifice
2.3.1.7 The Narrow Slit
2.3.1.8 The Acoustic Mesh or Perforated Sheet
2.3.2 Acoustic Equivalent Circuits. 2.3.2.1 Example of an Acoustic System Described by an Equivalent Circuit
2.3.2.2 Another Example of an Acoustic Equivalent Circuit – the Helmholtz Resonator
2.4 Combining Mechanical and Acoustical Equivalent Circuits
2.5 Introduction to Transduction. 2.5.1 The Transducer as a Two‐Port Equivalent Circuit
2.5.2 Reciprocal and Anti‐Reciprocal Transducers
2.5.3 The Electromechanical Coupling Factor
2.5.4 Electromechanical Transformation
2.5.5 Transmitters
2.5.6 Receivers
2.5.7 Relationship Between Transmit and Receive Characteristics
References
3 Waves in Solid Media
3.1 Waves in Homogeneous, Isotropic, Elastic, Solid Media
3.1.1 The Components of Stress
3.1.2 The Equations of Motion
3.1.3 The Components of Strain
3.1.4 The Relationship Between Stress and Strain – The Constitutive Equations
3.1.4.1 Hooke’s Law – Tensor Form
3.1.4.2 Hooke’s Law – Matrix Form
3.1.4.3 The Differences Between Tensor and Matrix Forms of the Constitutive Equations
3.1.4.4 Lame’s Constants
3.1.4.5 Stiffness vs. Compliance Matrices
3.1.4.6 Modified Constitutive Equations
3.1.5 Acoustic Waves in Isotropic Solids. 3.1.5.1 The Acoustic Wave Equation for Isotropic Solids
3.1.5.2 Waves of Dilatation and Distortion
3.1.5.3 Acoustic Plane Waves in Isotropic Solids
3.1.6 Longitudinal Waves in Bars
3.1.6.1 Vibrations in a Bar with Clamped Boundary Conditions
3.1.6.2 Vibrations in a Bar with Free Boundary Conditions
3.1.6.3 Equivalent Circuit Representation for Longitudinal Vibrations in a Bar with Arbitrary Boundary Conditions
3.1.6.4 A Two‐Port Representation of Longitudinal Vibrations Within a Bar
3.1.6.5 Impact of Different Load Impedances on the Longitudinal Vibrations Within a Bar
3.1.6.6 Equivalent Circuit Representation for a Mass‐Loaded Bar with One Free End
3.1.6.7 Equivalent Circuit Representation for a Mass‐loaded Bar with One End Clamped
3.1.6.8 Lumped Parameter Equivalent Circuit for a Longitudinal Resonator
3.1.6.9 The Effective Mass of a Spring
3.1.7 Equivalent Circuit Representations for Solid Elements
3.1.7.1 Longitudinal Vibrations Within a Hollow Cylinder
3.1.7.2 Longitudinal Vibrations Within a Conical Section
3.1.7.3 Longitudinal Vibrations Within an Exponential Section
3.2 Piezo‐electricity and Piezo‐electric Ceramic Materials
3.2.1 The Nature of Piezo‐electricity
3.2.2 Piezo‐electric Ceramic Materials
3.2.3 The Piezo‐electric Ceramic Constitutive Equations
3.2.4 The Meaning of the Piezo‐electric Coefficients
3.2.5 Piezo‐electric, Elastic, and Dielectric Coefficient Nomenclature
3.2.6 Piezo‐electric Ceramic Material Properties
3.2.7 The Electromechanical Coupling Coefficient
3.2.8 Further Observations on the Piezo‐electric Constitutive Equations
3.3 Waves in Non‐Homogenous, Piezo‐electric Media
3.3.1 Vibrations in Rods and Disks
3.3.1.1 Constitutive Equations
3.3.1.2 Equations of Motion and Strain in Cylindrical Coordinates
3.3.1.3 Radial Mode Vibrations in Thin Disks
3.3.1.4 Thickness Mode Vibrations in Thin Disks
3.3.1.5 The Relationship Between Dielectric Constant and Coupling Factor for Vibrations in Thin Disks
3.3.1.6 Length Longitudinal Mode Vibrations in Long, Thin Rods or Bars
3.3.1.7 Radial Mode Vibrations in Long, Thin Rods or Bars
3.3.1.8 The Relationship Between Dielectric Constant and Coupling Factor for Vibrations in Long, Thin Rods
3.3.1.9 Frequency Constants for Vibrations in Rods and Disks
3.3.2 Vibrations in Piezo‐electric Plates and Parallelepipeds
3.3.2.1 Equations of Motion and Strain in Rectangular Coordinates
3.3.2.2 Length Expander Bar with Electric Field Perpendicular to Width – The 31 Mode Bar
3.3.2.3 Length Expander Bar with Electric Field Parallel to Width – The 33 Mode Bar
3.3.2.4 Thickness Mode Vibrations in Thin Piezo‐electric Plates with the Electric Field Parallel to the Thickness
3.3.2.5 Coupled Mode Vibrations in Parallelepipeds with One Large Dimension
3.3.2.6 Coupled Mode Vibrations in Thin Piezo‐electric Plates with the Electric Field Perpendicular to the Thickness
3.3.2.7 Coupled Mode Vibrations in Thin Piezo‐electric Plates with the Electric Field Parallel to the Width
3.3.2.8 Coupled Mode Vibrations in Parallelepipeds with Arbitrary Dimensions
3.3.3 Vibrations in Piezo‐electric Ceramic Cylinders
3.3.3.1 Longitudinal Vibrations in Axially Polarized, Piezo‐ceramic Cylinders
3.3.3.1.1 Constitutive Equations
3.3.3.1.2 Boundary Conditions and Assumptions
3.3.3.1.3 Equations of Motion, Strain, and Constitutive Equations
3.3.3.1.4 Stress and Strain in the Axially Polarized Cylinder
3.3.3.1.5 The Voltage Across the Electrodes
3.3.3.1.6 Equivalent Circuit for Longitudinal Vibrations in an Axially Polarized Cylinder
3.3.3.1.7 Short Circuit Admittance
3.3.3.1.8 Resonance Frequencies for Longitudinal Vibrations in an Axially Polarized Cylinder
3.3.3.2 Longitudinal Vibrations in Radially Polarized, Piezo‐ceramic Cylinders
3.3.3.2.1 Constitutive Equations
3.3.3.2.2 The Equations of Motion and Strain
3.3.3.2.3 Boundary Conditions and Assumptions
3.3.3.2.4 Simplified Equations of Motion, Strain, and Constitutive Equations
3.3.3.2.5 Stress and Strain in the Radially Polarized Cylinder
3.3.3.2.6 The Voltage Across the Electrodes
3.3.3.2.7 Equivalent Circuit for Longitudinal Vibrations in a Radially Polarized Cylinder
3.3.3.2.8 Short Circuit Admittance
3.3.3.2.9 Resonance Frequencies for Longitudinal Vibrations in a Radially Polarized Cylinder
3.3.3.3 Radial Vibrations in Radially Polarized, Piezo‐ceramic Cylinders
3.3.3.3.1 Boundary Conditions
3.3.3.3.2 Constitutive Equations
3.3.3.3.3 The Equations of Motion and Strain
3.3.3.3.4 Equivalent Circuit for Radial Vibrations in Radially Polarized Cylinders
3.3.3.4 Longitudinal Vibrations in Circumferentially Polarized, Segmented, Piezo‐ceramic Cylinders
3.3.3.4.1 Constitutive Equations
3.3.3.4.2 The Equations of Motion and Strain
3.3.3.4.3 Boundary Conditions and Assumptions
3.3.3.4.4 Simplified Equations of Motion, Strain, and Constitutive Equations
3.3.3.4.5 Stress and Strain in the Circumferentially Polarized Cylinder
3.3.3.4.6 The Voltage Across the Electrodes
3.3.3.4.7 Equivalent Circuit for Longitudinal Vibrations in a Circumferentially Polarized Cylinder
3.3.3.4.8 Short Circuit Admittance for Longitudinal Vibrations in a Circumferentially Polarized Cylinder
3.3.3.4.9 Resonance Frequencies for Longitudinal Vibrations in a Circumferentially Polarized Cylinder
3.3.3.5 Radial Vibrations in Circumferentially Polarized, Segmented, Piezo‐ceramic Cylinders
3.3.3.5.1 Boundary Conditions
3.3.3.5.2 Constitutive Equations
3.3.3.5.3 The Equations of Motion and Strain
3.3.3.5.4 Equivalent Circuit for Radial Vibrations in a Circumferentially Polarized Cylinder
3.3.4 Vibrations in Radially Polarized Spherical Shells
3.3.4.1 Boundary Conditions
3.3.4.2 Constitutive Equations
3.3.4.3 The Equations of Motion and Strain
3.3.4.4 Kinetic Energy and Equivalent Mass
3.3.4.5 Internal Energy
3.3.4.6 Electromechanical Coupling Coefficient
3.3.4.7 In‐Air Resonance Frequency of a Spherical Shell
3.3.4.8 Equivalent Circuit Model for a Radially Polarized Spherical Shell
References
4 Sonar Projectors
4.1 Tools for Underwater Sonar Projector Design. 4.1.1 Assembling Circuit Elements
4.1.1.1 Two‐Port Representations for Non‐Piezoelectric Components
4.1.1.2 Series Combination of Two‐Port Networks for Non‐Piezoelectric Components
4.1.1.3 Parallel Combinations of Two‐Port Networks for Non‐Piezoelectric Components
4.1.1.4 Two‐Port Representations of Piezoelectric Components
4.1.1.5 Cascaded Combinations of Two‐Port Networks for Piezoelectric Components
4.1.1.6 Ladder Network Analysis
4.1.2 How to Specify a Projector
4.2 Specific Applications in Underwater Sonar Projector Design. 4.2.1 Frequency Ranges for Different Types of Projectors
4.2.2 Spherical Projectors
4.2.2.1 The Lossless, Air‐Backed Spherical Projector
4.2.2.2 The Lossy, Air‐Backed Spherical Projector
4.2.2.3 Fluid‐Filled Spherical Projectors
4.2.3 The Radially Polarized Cylindrical Projector
4.2.3.1 The Radially Polarized, Air‐Backed Cylindrical Projector
4.2.3.2 Prestressing for Increased Power‐Handling Capability
4.2.3.2.1 Beam Patterns for the Air‐Backed Cylindrical Projector
4.2.3.2.2 The Radially Polarized, Air‐Backed Cylindrical Projector Example
4.2.3.3 The Radially Polarized, Fluid‐Filled Cylindrical Projector
4.2.3.4 The Radially Polarized, Squirter Projector
4.2.3.5 The Radially Polarized, Free‐Flooded Cylindrical Projector
4.2.3.6 The Free‐Flooded Cylindrical Projector with a Reflector Plate
4.2.4 Circumferentially Polarized Cylindrical Projectors – The Barrel Stave Projector
4.2.4.1 The Circumferentially Polarized, Air‐Backed Cylindrical Projector
4.2.4.2 The Circumferentially Polarized, Free‐Flooded Cylindrical Projector
4.2.4.3 The Circumferentially Polarized Striped Cylindrical Projector
4.2.5 The Tonpilz Transducer
4.2.5.1 The End Mass‐Loaded Tonpilz Transducer
4.2.5.2 The Nodally Mounted Tonpilz Transducer
4.2.6 The Flexural Disk Transducer
4.2.6.1 The Trilaminar Flexural Disk Transducer
4.2.6.1.1 Orientation, Boundary Conditions, and Material Properties
4.2.6.1.2 Displacement Profile, Boundary Moment, and Terms
4.2.6.1.3 Strain and Stress in the Disk Assembly
4.2.6.1.4 Kinetic Energy and Equivalent Mass
4.2.6.1.5 Electric Field and Voltage Across the Ceramic Element
4.2.6.1.6 Internal Energy of the Flexural Disk Assembly
4.2.6.1.7 Coupling Coefficient for the Flexural Disk Assembly
4.2.6.1.8 Flexural Stiffness
4.2.6.1.9 In‐Air Resonance Frequency for the Flexural Disk Assembly
4.2.6.1.10 Radiation Loading for the Flexural Disk Assembly
4.2.6.1.11 In‐Water Resonance Frequency for the Flexural Disk Assembly
4.2.6.1.12 Mechanical Q m for the Flexural Disk Transducer
4.2.6.1.13 Mechanical Compliance for the Flexural Disk Transducer
4.2.6.1.14 Blocked Capacitance for the Flexural Disk Transducer
4.2.6.1.15 Equivalent Circuit Model of the Flexural Disk Transducer
4.2.6.1.16 A Trilaminar Flexural Disk Transducer Example
4.2.6.2 The Bilaminar Flexural Disk Transducer
4.2.6.2.1 Displacement Profile
4.2.6.2.2 Strain and Stress in the Disk Assembly
4.2.6.2.3 Neutral Axis
4.2.6.2.4 Kinetic Energy and Equivalent Mass
4.2.6.2.5 Electric Field and Voltage Across the Ceramic Element
4.2.6.2.6 Internal Energy of the Flexural Disk Assembly
4.2.6.2.7 Coupling Coefficient for the Bilaminar Flexural Disk Assembly
4.2.6.2.8 Flexural Stiffness
4.2.6.2.9 In‐Air Resonance Frequency for the Bilaminar Flexural Disk Assembly
4.2.6.2.10 Radiation Loading for the Bilaminar Flexural Disk Assembly
4.2.6.2.11 In‐Water Resonance Frequency for the Bilaminar Flexural Disk Assembly
4.2.6.2.12 Mechanical Q m for the Bilaminar Flexural Disk Transducer
4.2.6.2.13 Mechanical Compliance for the Flexural Disk Transducer
4.2.6.2.14 Blocked Capacitance for the Flexural Disk Transducer
4.2.6.2.15 Equivalent Circuit Model of the Bilaminar Flexural Disk Transducer
4.2.6.2.16 A Bilaminar Flexural Disk Transducer Example
4.2.7 Flat Oval Flextensional Projectors
4.2.8 Slotted Cylinder Projectors
4.2.8.1 Geometry and Description
4.2.8.2 Wall Thickness, Radii, and Taper Factors
4.2.8.3 Neutral Axis
4.2.8.4 Displacement Profiles
4.2.8.5 Stress and Strain in the SCP
4.2.8.6 Kinetic Energy and Equivalent Mass
4.2.8.7 Constitutive Equations for the Piezoceramic Component
4.2.8.8 Voltage Across Electrodes and Dielectric Displacement
4.2.8.9 Internal Energy
4.2.8.10 Flexural Stiffness
4.2.8.11 In‐Air Resonance Frequency
4.2.8.12 Effective Electromechanical Coupling Factor, keff
4.2.8.13 In‐water Performance
4.2.8.14 An SCP Example
4.2.9 Moving Coil Transducers
4.2.10 The Line‐in‐Cone Transducer
4.2.11 Quarter‐Wavelength Resonators
4.2.12 Disk Projectors
4.2.13 The High‐Frequency Line Projector
4.3 Special Topics in Underwater Sonar Projector Design. 4.3.1 Techniques for Increasing Bandwidth. 4.3.1.1 Bandwidth Increases with Coupling
4.3.1.2 Mechanical Tuning with Matching Layers
4.3.2 Power Limitations in Sonar Projectors
4.3.2.1 Electric Field Limitations
4.3.2.2 Loss Tangent Limitations
4.3.2.3 Stress Limitations
4.3.2.4 Thermal Limitations
4.3.2.5 Cavitation Limitations
References
5 Sonar Hydrophones
5.1 Elements of Sonar Hydrophone Design
5.1.1 An Equivalent Circuit for a Sonar Hydrophone
5.1.2 The Importance of the Piezo‐Ceramic g Constant
5.1.3 An Equivalent Circuit for a Dielectrically Lossy Sonar Hydrophone
5.1.4 The Effect of Cable Capacitance
5.1.5 Typical Response of a Sonar Hydrophone
5.2 Analysis of Noise in Hydrophone/Preamplifier Systems
5.2.1 Ambient Noise
5.2.2 Types of Equivalent Noise Sources
5.2.3 Ambient Noise Coupling into a Sensor
5.2.4 Sensor Self‐Noise
5.2.5 Sensor Signal to Noise Ratio
5.2.6 Preamplifier Noise
5.2.7 Combined Sensor and Preamp System Noise, the Equivalent Noise Pressure
5.2.8 The Equivalent Noise Pressure at Low Frequencies
5.2.9 Comparison of Sensor Noise with Ambient Noise Example
5.2.10 Hydrophone Figure of Merit
5.2.11 The Effect of Cable Capacitance – Insertion Loss
5.3 Specific Applications in Underwater Sonar Hydrophone Design
5.3.1 Unidirectional Hydrophone
5.3.1.1 Boundary Conditions
5.3.1.2 Equation of Motion and Strain
5.3.1.3 Constitutive Equations
5.3.1.4 Open Circuit Voltage Sensitivity
5.3.2 Hydrostatic Hydrophone
5.3.3 Spherical Hydrophone
5.3.3.1 Boundary Conditions
5.3.3.2 Constitutive Equations
5.3.3.3 The Equations of Motion and Strain
5.3.3.4 Stress Profile in a Spherical Hydrophone
5.3.3.5 The Open Circuit Sensitivity of the Spherical Hydrophone
5.3.3.6 Spherical Hydrophone Depth Limitations
5.3.3.7 The Effect of a Fill Fluid on Hydrophone Performance
5.3.4 Cylindrical Hydrophones
5.3.4.1 The Radially Polarized Cylindrical Hydrophone
5.3.4.1.1 Boundary Conditions
5.3.4.1.2 Constitutive Equations
5.3.4.1.3 The Equations of Motion and Strain
5.3.4.1.4 Stress Profile in a Radially Polarized Cylindrical Hydrophone
5.3.4.1.5 The Open Circuit Sensitivity of a Radially Polarized, Air‐Backed Cylindrical Hydrophone
5.3.4.1.6 Cylindrical Hydrophone Depth Limitations
5.3.4.1.7 The Effect of Fill Fluid on Hydrophone Performance
5.3.4.1.8 The Effect of Endcap Construction on Hydrophone Performance
5.3.4.1.8.1 Boundary Conditions
5.3.4.1.8.2 Deflection Profile in the Endcap
5.3.4.1.8.3 Deflection Profile in the Ceramic Cylinder
5.3.4.1.8.4 Determining the Boundary Moment
5.3.4.1.8.5 Displacement Profile in an Endcapped Ceramic Cylinder
5.3.4.1.8.6 Stresses in the Ceramic Cylinder
5.3.4.1.8.7 Impact to Receive Sensitivity in an Endcapped Ceramic Cylinder
5.3.4.2 The Circumferentially Polarized Cylindrical Hydrophone
5.3.4.2.1 Boundary Conditions
5.3.4.2.2 Constitutive Equations
5.3.4.2.3 The Equations of Motion and Strain
5.3.4.2.4 Stress Profile in a Circumferentially Polarized Cylindrical Hydrophone
5.3.4.2.5 The Open Circuit Sensitivity of a Circumferentially Polarized Cylindrical Hydrophone
5.3.4.2.6 The Effect of a Fill Fluid on Hydrophone Performance
5.3.4.3 The Axially Polarized Cylindrical Hydrophone
5.3.4.3.1 Stress Profile in an Axially Polarized Cylindrical Hydrophone
5.3.4.3.2 The Axially Polarized Cylindrical Hydrophone
5.3.4.3.3 The Effect of a Fill Fluid on Hydrophone Performance
5.3.5 PVDF Polymer Hydrophones
References
Appendix. A.1 Summary of Vector Notation
A.1.1 Unit Vectors
A.1.2 Definition of a Vector
A.1.3 Definition of a Tensor
A.1.4 Vector and Tensor Arithmetic. A.1.4.1 Basic Operations
A.1.4.2 Scalar (Dot) Product of Two Vectors
A.1.4.3 Cross Product of Two Vectors
A.1.5 The Del (∇) Operator. A.1.5.1 The Vector Differential (Del) Operator
A.1.5.2 Gradient of a Scalar Field
A.1.5.3 Divergence of a Vector Field
A.1.5.4 Curl of a Vector Field
A.1.5.5 Gradient of a Vector Field
A.1.5.6 Other Operations with the Del Operator
A.1.6 The Laplace (∇2) Operator. A.1.6.1 The Laplacian of a Scalar Field
A.1.6.2 The Laplacian of a Vector Field
A.2 Useful Material Properties
References
Index. a
b
c
d
e
f
g
h
i
k
l
m
n
o
p
q
r
s
t
u
v
w
WILEY END USER LICENSE AGREEMENT
