ISBN-13: 9781119851059 / Angielski / Twarda / 2022 / 500 str.
ISBN-13: 9781119851059 / Angielski / Twarda / 2022 / 500 str.
Preface xvii1 Acoustic Waves and Radiation 11.1 Small Signals/Linear Acoustics 11.1.1 Compressibility 21.1.2 Small Signals/Linear Acoustics 21.1.3 Relationship Between Acoustic Pressure and Acoustic Density 21.1.4 Condensation 21.1.5 Time Derivative Using Eulerian and Lagrangian Description 31.2 The Equations of Continuity, Motion, and the Wave Equation in a Fluid Media 31.2.1 Equation of Continuity in a Single Dimension 31.2.2 The Force Equation in a Single Dimension 41.2.3 The Wave Equation in a Single Dimension 51.2.4 Generalization of the Wave Equation to Three Dimensions 51.2.5 Helmholtz Wave Equation 61.2.6 Velocity Potential 61.3 Plane Waves 71.3.1 Harmonic Plane Waves 71.3.2 Plane Waves in an Infinite Media 71.3.3 Plane Wave Acoustic Intensity 81.3.4 Plane Wave Acoustic Impedance 81.4 Radiation from Spheres 81.4.1 General Solution to Radiation from Spheres 91.4.2 Spherical Wave Acoustic Impedance 111.4.3 Axis-Symmetric Radiation from a Sphere - the Spherical Source 111.4.4 The Simple Spherical Source 121.4.5 Source Strength 121.4.6 The General Simple Source 131.4.7 Acoustic Reciprocity and Reciprocity Factor 131.5 Radiation from Sources on a Cylindrical Surface 141.5.1 General Solution to Radiation from Cylinders 151.5.2 Radiation from an Infinitely Long Cylinder 181.5.3 The Simple, Infinitely Long Cylindrical Source 191.5.4 Radiation from an Infinitely Long Strip on an Infinitely Long Cylinder 201.5.5 Radiation from a Finite Source on a Cylinder with a Periodic z Dependence 211.5.6 Radiation from a Finite Source on a Cylinder with a Uniform z Dependence 221.5.7 The Simple Cylindrical Source - Radiation from a Finite Length Cylinder in an Infinitely Long Cylinder Baffle 251.6 Integral Formulations 261.6.1 The Green's Function 271.6.2 Helmholtz Integral Formulations 281.6.3 Far Field Approximation 291.6.4 An Application of the Simple Source Integral Formulation - Radiation from a Finite Cylinder 341.7 Linear Apertures 361.7.1 Far Field Radiation (Beam) Patterns as a Fourier Transform of the Linear Aperture Function - the Directivity Function 361.7.2 A Simple Rectangular Aperture Function as an Example of a Linear Aperture 381.7.3 The Triangular Window Aperture Function as a Linear Aperture 411.7.4 The Cosine Window Aperture Function as a Linear Aperture 431.7.5 Other Linear Apertures 451.7.6 The Far Field Radiation Pattern of a Linear Aperture on a Cylindrical Surface 451.8 Planar Apertures 491.8.1 The Green's Function for Radiation from Planar Apertures Located on a Rigid Plane Baffle 491.8.2 Far Field Radiation Patterns as a Fourier Transform of the Planar Aperture Function 501.8.3 The Rectangular Piston in an Infinite Plane Baffle 521.8.4 The Circular Piston in an Infinite Plane Baffle 541.8.5 The Far Field Radiation Pattern of a Circular Annular Ring 591.8.6 The Elliptical Piston in an Infinite Plane Baffle 601.8.7 Impact of Boundary Impedance on Radiation Patterns from Planar Apertures 601.9 Directivity and Directivity Index (DI) 631.9.1 Definition of Directivity and Directivity Index (DI) 651.9.2 Relationship Between Source Level and Directivity Index 671.9.3 The Directivity of Baffled vs. Unbaffled Sources 681.9.4 The Directivity Index of a Baffled Circular Piston 681.9.5 The Directivity Index of a Baffled Rectangular Piston 701.9.6 The Directivity Index of a Line Source 701.10 Scattering and Diffraction 721.10.1 Scattering and Diffraction from a Rigid Cylinder 721.10.1.1 The Incident Wave 721.10.1.2 The Scattered Wave 731.10.1.3 Matching the Boundary Conditions for the Total Field 731.10.1.4 The Scattered Pressure Field in the Far Field 741.10.1.5 The Total Pressure Field 741.10.1.6 The Average Pressure Exerted on the Cylinder by the Total Pressure Field 741.10.2 The Diffraction Constant for a Rigid Cylinder 761.10.3 Diffraction Constant for a Strip on a Rigid Cylinder 761.10.4 Diffraction of a Cylinder with Variable Boundary Admittance 771.10.4.1 The Incident Wave 771.10.4.2 The Boundary Admittance 781.10.4.3 The Scattered Wave 781.10.4.4 Matching the Boundary Conditions 811.10.4.5 The Boundary Reflection Coefficient and the Scattered Field 811.10.4.6 The Total Field 821.10.4.7 The Average Pressure Exerted on the Cylinder With a Variable Boundary Admittance 821.10.4.8 The Diffraction Constant for a Cylinder with Variable Boundary Admittance 821.10.4.9 The Total Diffracted Field in the Far Field 831.10.4.10 The Total Diffracted Field at the Surface of the Cylinder 831.10.5 Scattering and Diffraction from a Rigid Sphere 841.10.5.1 The Incident Wave 841.10.5.2 The Scattered Wave 851.10.5.3 Matching the Boundary Conditions for the Total Field 851.10.5.4 The Total Pressure Field 851.10.5.5 The Scattered Pressure Field in the Far Field 861.10.5.6 The Average Pressure Exerted on the Sphere by the Pressure Field 861.10.6 The Diffraction Constant for a Rigid Sphere 871.10.7 Scattering and Diffraction from a Thin Cylindrical Ring 871.11 Radiation Impedance 891.11.1 Introduction to Radiation Impedance 891.11.2 Units of Acoustic Radiation Impedance 901.11.3 What it Means to be rhoc Loaded 901.11.4 The Relationship Between Resistance and Reactance - The Hilbert Transform 901.11.5 The Relationship Between Radiation Resistance, Directivity, and Diffraction Constant 921.11.6 The Radiation Impedance of a Spherical Radiator 941.11.7 The Radiation Impedance of a Simple Source Radiator 951.11.8 The Radiation Impedance of a Circular Piston Radiator in a Plane Baffle 951.11.9 The Radiation Impedance of a Circular Piston Radiator at the End of a Tube 971.11.10 The Radiation Impedance of a Rectangular Piston Radiator in a Plane Baffle 981.11.11 The Radiation Impedance of an Infinitely Long Strip Radiator in a Plane Baffle 1001.11.12 The Radiation Impedance of a Circular Annular Piston Radiator in a Plane Baffle 1011.11.13 The Radiation Impedance of an Elliptical Piston Radiator in a Plane Baffle 1031.11.14 The Radiation Impedance of an Infinitely Long Cylindrical Radiator 1031.11.15 The Radiation Impedance of a Finite Cylindrical Radiator 1041.11.16 Mutual Radiation Impedance 1051.11.17 The Mutual Radiation Impedance Between Spherical Radiators 1061.11.18 The Mutual Radiation Impedance Between Two Circular Piston Radiators in a Plane Baffle 1081.11.19 The Mutual Radiation Impedance Between Two Square Piston Radiators in a Plane Baffle 1141.11.20 The Mutual Radiation Impedance Between a Circular Piston and an Outer Annular Ring 1161.11.21 The Mutual Radiation Impedance Between Rectangular or Square Pistons Located on a Cylindrical Baffle 1181.11.22 The Mutual Radiation Impedance Between Bands on a Cylindrical Baffle 1241.12 Transmission Phenomena 1251.12.1 Reflection and Transmission of Plane Waves with Normal Incidence at a Boundary 1261.12.2 Reflection and Transmission of Plane Waves Obliquely Incident at a Plane Boundary 1291.12.2.1 Snell's Law 1301.12.2.2 Reflection and Transmission Factors for Obliquely Incident Plane Waves 1311.12.2.3 Brewster's Angle or the Angle of Zero Reflection 1311.12.2.4 The Critical Angle or the Angle of Complete Reflection 1321.12.2.5 Evanescent Waves 1321.13 Absorption and Attenuation of Sound 1331.13.1 Absorption Phenomena 1331.13.2 Absorption in Seawater 134References 1352 Mechanical/Acoustical Equivalent Circuits 1372.1 Different Forms of Impedance 1382.2 Mechanical Equivalent Circuits 1392.2.1 The Simple Mechanical System 1392.2.1.1 A Simple Mechanical Oscillator 1392.2.1.2 Phasor Form of the Solutions to the Equations of Motion 1392.2.1.3 Damped Oscillations 1402.2.1.4 Forced Oscillations 1412.2.1.5 Complete Solution for a Simple Oscillator 1422.2.1.6 Analogy to Electrical Circuits 1422.2.1.7 Behavior of the Steady State, Forced, Mechanical Oscillator 1432.2.1.8 Equivalent Circuit for a Simple Resonator System 1442.2.2 Introduction to Mobility 1452.2.2.1 Mechanical Generators 1452.2.2.2 Combining Impedance and Mobility Elements 1452.2.2.3 Elements of Mobility and Impedance Analogs 1472.2.2.4 Examples of Mechanical Systems Described by Mobility Analogs 1492.2.2.5 An Example of a Gyrator Conversion 1502.2.2.6 Converting from Mobility to Impedance and Vice Versa 1512.3 Acoustical Equivalent Circuits 1532.3.1 Acoustic Circuit Elements 1532.3.1.1 Acoustic Compliance - the Closed-End Tube 1532.3.1.2 Acoustic Mass - the Open-Ended Tube 1542.3.1.3 Acoustic Resistance 1562.3.1.4 Acoustic Generators 1562.3.1.5 Pressure Equalization Orifices 1562.3.1.6 The Thin Acoustic Orifice 1592.3.1.7 The Narrow Slit 1602.3.1.8 The Acoustic Mesh or Perforated Sheet 1602.3.2 Acoustic Equivalent Circuits 1612.3.2.1 Example of an Acoustic System Described by an Equivalent Circuit 1612.3.2.2 Another Example of an Acoustic Equivalent Circuit - the Helmholtz Resonator 1612.4 Combining Mechanical and Acoustical Equivalent Circuits 1632.5 Introduction to Transduction 1652.5.1 The Transducer as a Two-Port Equivalent Circuit 1652.5.2 Reciprocal and Anti-Reciprocal Transducers 1662.5.3 The Electromechanical Coupling Factor 1662.5.4 Electromechanical Transformation 1672.5.5 Transmitters 1672.5.6 Receivers 1692.5.7 Relationship Between Transmit and Receive Characteristics 170References 1713 Waves in Solid Media 1733.1 Waves in Homogeneous, Isotropic, Elastic, Solid Media 1733.1.1 The Components of Stress 1733.1.2 The Equations of Motion 1743.1.3 The Components of Strain 1753.1.4 The Relationship Between Stress and Strain - The Constitutive Equations 1773.1.4.1 Hooke's Law - Tensor Form 1773.1.4.2 Hooke's Law - Matrix Form 1793.1.4.3 The Differences Between Tensor and Matrix Forms of the Constitutive Equations 1803.1.4.4 Lame's Constants 1823.1.4.5 Stiffness vs. Compliance Matrices 1833.1.4.6 Modified Constitutive Equations 1843.1.5 Acoustic Waves in Isotropic Solids 1843.1.5.1 The Acoustic Wave Equation for Isotropic Solids 1843.1.5.2 Waves of Dilatation and Distortion 1843.1.5.3 Acoustic Plane Waves in Isotropic Solids 1863.1.6 Longitudinal Waves in Bars 1863.1.6.1 Vibrations in a Bar with Clamped Boundary Conditions 1883.1.6.2 Vibrations in a Bar with Free Boundary Conditions 1893.1.6.3 Equivalent Circuit Representation for Longitudinal Vibrations in a Bar with Arbitrary Boundary Conditions 1903.1.6.4 A Two-Port Representation of Longitudinal Vibrations Within a Bar 1923.1.6.5 Impact of Different Load Impedances on the Longitudinal Vibrations Within a Bar 1933.1.6.6 Equivalent Circuit Representation for a Mass-Loaded Bar with One Free End 1943.1.6.7 Equivalent Circuit Representation for a Mass-loaded Bar with One End Clamped 1963.1.6.8 Lumped Parameter Equivalent Circuit for a Longitudinal Resonator 1983.1.6.9 The Effective Mass of a Spring 2003.1.7 Equivalent Circuit Representations for Solid Elements 2023.1.7.1 Longitudinal Vibrations Within a Hollow Cylinder 2023.1.7.2 Longitudinal Vibrations Within a Conical Section 2043.1.7.3 Longitudinal Vibrations Within an Exponential Section 2063.2 Piezo-electricity and Piezo-electric Ceramic Materials 2083.2.1 The Nature of Piezo-electricity 2083.2.2 Piezo-electric Ceramic Materials 2113.2.3 The Piezo-electric Ceramic Constitutive Equations 2123.2.4 The Meaning of the Piezo-electric Coefficients 2143.2.5 Piezo-electric, Elastic, and Dielectric Coefficient Nomenclature 2153.2.6 Piezo-electric Ceramic Material Properties 2163.2.7 The Electromechanical Coupling Coefficient 2193.2.8 Further Observations on the Piezo-electric Constitutive Equations 2203.3 Waves in Non-Homogenous, Piezo-electric Media 2223.3.1 Vibrations in Rods and Disks 2233.3.1.1 Constitutive Equations 2233.3.1.2 Equations of Motion and Strain in Cylindrical Coordinates 2243.3.1.3 Radial Mode Vibrations in Thin Disks 2243.3.1.4 Thickness Mode Vibrations in Thin Disks 2283.3.1.5 The Relationship Between Dielectric Constant and Coupling Factor for Vibrations in Thin Disks 2333.3.1.6 Length Longitudinal Mode Vibrations in Long, Thin Rods or Bars 2353.3.1.7 Radial Mode Vibrations in Long, Thin Rods or Bars 2373.3.1.8 The Relationship Between Dielectric Constant and Coupling Factor for Vibrations in Long, Thin Rods 2403.3.1.9 Frequency Constants for Vibrations in Rods and Disks 2413.3.2 Vibrations in Piezo-electric Plates and Parallelepipeds 2423.3.2.1 Equations of Motion and Strain in Rectangular Coordinates 2433.3.2.2 Length Expander Bar with Electric Field Perpendicular to Width - The 31 Mode Bar 2443.3.2.3 Length Expander Bar with Electric Field Parallel to Width - The 33 Mode Bar 2483.3.2.4 Thickness Mode Vibrations in Thin Piezo-electric Plates with the Electric Field Parallel to the Thickness 2503.3.2.5 Coupled Mode Vibrations in Parallelepipeds with One Large Dimension 2543.3.2.6 Coupled Mode Vibrations in Thin Piezo-electric Plates with the Electric Field Perpendicular to the Thickness 2563.3.2.7 Coupled Mode Vibrations in Thin Piezo-electric Plates with the Electric Field Parallel to the Width 2583.3.2.8 Coupled Mode Vibrations in Parallelepipeds with Arbitrary Dimensions 2593.3.3 Vibrations in Piezo-electric Ceramic Cylinders 2613.3.3.1 Longitudinal Vibrations in Axially Polarized, Piezo-ceramic Cylinders 2633.3.3.2 Longitudinal Vibrations in Radially Polarized, Piezo-ceramic Cylinders 2723.3.3.3 Radial Vibrations in Radially Polarized, Piezo-ceramic Cylinders 2813.3.3.4 Longitudinal Vibrations in Circumferentially Polarized, Segmented, Piezo-ceramic Cylinders 2853.3.3.5 Radial Vibrations in Circumferentially Polarized, Segmented, Piezo-ceramic Cylinders 2943.3.4 Vibrations in Radially Polarized Spherical Shells 2973.3.4.1 Boundary Conditions 2973.3.4.2 Constitutive Equations 2983.3.4.3 The Equations of Motion and Strain 2983.3.4.4 Kinetic Energy and Equivalent Mass 2993.3.4.5 Internal Energy 2993.3.4.6 Electromechanical Coupling Coefficient 3003.3.4.7 In-Air Resonance Frequency of a Spherical Shell 3003.3.4.8 Equivalent Circuit Model for a Radially Polarized Spherical Shell 300References 3034 Sonar Projectors 3054.1 Tools for Underwater Sonar Projector Design 3054.1.1 Assembling Circuit Elements 3054.1.1.1 Two-Port Representations for Non-Piezoelectric Components 3054.1.1.2 Series Combination of Two-Port Networks for Non-Piezoelectric Components 3074.1.1.3 Parallel Combinations of Two-Port Networks for Non-Piezoelectric Components 3074.1.1.4 Two-Port Representations of Piezoelectric Components 3084.1.1.5 Cascaded Combinations of Two-Port Networks for Piezoelectric Components 3094.1.1.6 Ladder Network Analysis 3114.1.2 How to Specify a Projector 3124.2 Specific Applications in Underwater Sonar Projector Design 3134.2.1 Frequency Ranges for Different Types of Projectors 3134.2.2 Spherical Projectors 3144.2.2.1 The Lossless, Air-Backed Spherical Projector 3144.2.2.2 The Lossy, Air-Backed Spherical Projector 3204.2.2.3 Fluid-Filled Spherical Projectors 3214.2.3 The Radially Polarized Cylindrical Projector 3234.2.3.1 The Radially Polarized, Air-Backed Cylindrical Projector 3234.2.3.2 Prestressing for Increased Power-Handling Capability 3284.2.3.3 The Radially Polarized, Fluid-Filled Cylindrical Projector 3304.2.3.4 The Radially Polarized, Squirter Projector 3324.2.3.5 The Radially Polarized, Free-Flooded Cylindrical Projector 3394.2.3.6 The Free-Flooded Cylindrical Projector with a Reflector Plate 3424.2.4 Circumferentially Polarized Cylindrical Projectors - The Barrel Stave Projector 3434.2.4.1 The Circumferentially Polarized, Air-Backed Cylindrical Projector 3434.2.4.2 The Circumferentially Polarized, Free-Flooded Cylindrical Projector 3464.2.4.3 The Circumferentially Polarized Striped Cylindrical Projector 3484.2.5 The Tonpilz Transducer 3524.2.5.1 The End Mass-Loaded Tonpilz Transducer 3534.2.5.2 The Nodally Mounted Tonpilz Transducer 3554.2.6 The Flexural Disk Transducer 3554.2.6.1 The Trilaminar Flexural Disk Transducer 3574.2.6.2 The Bilaminar Flexural Disk Transducer 3754.2.7 Flat Oval Flextensional Projectors 3854.2.8 Slotted Cylinder Projectors 3874.2.8.1 Geometry and Description 3884.2.8.2 Wall Thickness, Radii, and Taper Factors 3904.2.8.3 Neutral Axis 3914.2.8.4 Displacement Profiles 3924.2.8.5 Stress and Strain in the SCP 3974.2.8.6 Kinetic Energy and Equivalent Mass 3984.2.8.7 Constitutive Equations for the Piezoceramic Component 3984.2.8.8 Voltage Across Electrodes and Dielectric Displacement 3984.2.8.9 Internal Energy 3994.2.8.10 Flexural Stiffness 4004.2.8.11 In-Air Resonance Frequency 4004.2.8.12 Effective Electromechanical Coupling Factor, k eff 4014.2.8.13 In-water Performance 4014.2.8.14 An SCP Example 4074.2.9 Moving Coil Transducers 4074.2.10 The Line-in-Cone Transducer 4124.2.11 Quarter-Wavelength Resonators 4154.2.12 Disk Projectors 4184.2.13 The High-Frequency Line Projector 4204.3 Special Topics in Underwater Sonar Projector Design 4224.3.1 Techniques for Increasing Bandwidth 4224.3.1.1 Bandwidth Increases with Coupling 4224.3.1.2 Mechanical Tuning with Matching Layers 4234.3.2 Power Limitations in Sonar Projectors 4244.3.2.1 Electric Field Limitations 4244.3.2.2 Loss Tangent Limitations 4254.3.2.3 Stress Limitations 4264.3.2.4 Thermal Limitations 4274.3.2.5 Cavitation Limitations 433References 4365 Sonar Hydrophones 4395.1 Elements of Sonar Hydrophone Design 4395.1.1 An Equivalent Circuit for a Sonar Hydrophone 4405.1.2 The Importance of the Piezo-Ceramic g Constant 4425.1.3 An Equivalent Circuit for a Dielectrically Lossy Sonar Hydrophone 4425.1.4 The Effect of Cable Capacitance 4435.1.5 Typical Response of a Sonar Hydrophone 4445.2 Analysis of Noise in Hydrophone/Preamplifier Systems 4455.2.1 Ambient Noise 4455.2.2 Types of Equivalent Noise Sources 4465.2.3 Ambient Noise Coupling into a Sensor 4475.2.4 Sensor Self-Noise 4485.2.5 Sensor Signal to Noise Ratio 4505.2.6 Preamplifier Noise 4505.2.7 Combined Sensor and Preamp System Noise, the Equivalent Noise Pressure 4525.2.8 The Equivalent Noise Pressure at Low Frequencies 4535.2.9 Comparison of Sensor Noise with Ambient Noise Example 4555.2.10 Hydrophone Figure of Merit 4565.2.11 The Effect of Cable Capacitance - Insertion Loss 4575.3 Specific Applications in Underwater Sonar Hydrophone Design 4585.3.1 Unidirectional Hydrophone 4595.3.1.1 Boundary Conditions 4605.3.1.2 Equation of Motion and Strain 4605.3.1.3 Constitutive Equations 4605.3.1.4 Open Circuit Voltage Sensitivity 4605.3.2 Hydrostatic Hydrophone 4615.3.3 Spherical Hydrophone 4625.3.3.1 Boundary Conditions 4635.3.3.2 Constitutive Equations 4645.3.3.3 The Equations of Motion and Strain 4645.3.3.4 Stress Profile in a Spherical Hydrophone 4645.3.3.5 The Open Circuit Sensitivity of the Spherical Hydrophone 4655.3.3.6 Spherical Hydrophone Depth Limitations 4665.3.3.7 The Effect of a Fill Fluid on Hydrophone Performance 4675.3.4 Cylindrical Hydrophones 4685.3.4.1 The Radially Polarized Cylindrical Hydrophone 4705.3.4.2 The Circumferentially Polarized Cylindrical Hydrophone 4885.3.4.3 The Axially Polarized Cylindrical Hydrophone 4935.3.5 PVDF Polymer Hydrophones 496References 497Appendix 499Index 509
John C. Cochran, PhD, is a former Principal Engineering Fellow in the Advanced Technology Department of Raytheon Integrated Defense Systems responsible for sonar system design and operation. He is a subject matter expert in the design and development of advanced sensors, sensor arrays, and undersea sensing systems.
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