Mechanics of Underwater Noise

Preface

Acknowledgments


1. Introduction

1.1 Noise: Unwanted Sound

Underwater Noise

Noise is Unavoidable

Acoustic Conversion Efficiency

Noise Control

Types of Underwater Noise

1.2 Decibels and Levels

Decibels

Transmission Loss

Levels

Reference Pressures

Source Level

Power Level

spectrum Level

Decibel Arithmetic

1.3 Significance of Spectra

1.4 Passive Sonar Equation

1.5 Some Mathematics

Scalars, Vectors and Tensors

Tensor Notation

Vector Operations

Vector Operators

Scalar Potentials

Spherical Symmetry

Line, Surface and Volume Integrals

Complex Quantities

Fourier Series

Fourier Integrals and Transforms

References


2. Sound Waves in Liquids

2.1 Description of Waves

Plane Waves

Retarded Time

Harmonic Representation of Waves

Helmholtz Equation

Wave Vectors

2.2 Wave Equation for Sound in Fluids

Assumptions

Equation of State

Equation of Continuity

Equation of Motion

Acoustic Wave Equation

Velocity Potential

Harmonic Solutions

2.3 Plane Sound Waves

Acoustic Potential

Particle Velocity

Specific Acoustic Impedance

Acoustic Intensity

2.4 Spherical Waves

Acoustic Potential

Particle Velocity

Specific Acoustic Impedance

Acoustic Intensity

Ideal Transmission Loss

Acoustic Power

Damped Sound Waves

Spherical Waves from Plane Waves

2.5 Transmission at Media Interfaces

Snell's Law

Reflection from a Plane Boundary

Transmission Through a Plane Boundary

Transmission from Air to Water

Transmission from Water into Air

Reflection of Underwater Sound by Ocean Surfaces

2.6 Finite-Amplitude Effects

References


3. Acoustic Radiation Fundamentals

3.1 General Characterization of Noise Sources

Monopoles, Dipoles and Quadrupoles

Radiation Impedance

Radiation Efficiency

3.2 General Equation for Sound Generation

Derivation

Interpretation

3.3 General Spherical Sources

3.4 Hydrodynamic Sources

Radiation Efficiencies

Fluctuating-Volume Acoustic Sources

Fluctuating-Force Sources

Turbulence Noise

Noise from Wake Turbulence

Flow Noise

3.5 Sources in Motion

Dcppler Shift

Effect of Steady Motion on Level

Periodic Motions

References


4. Radiation by Fluctuating-Volume (Monopole) Sources

4.1 Uniformly Pulsating Spherical Source

Intensity and Power

Radiation Impedance

Radiation Efficiency

Entrained Mass

4.2 Monopole Radiation

4.3 Sounds from Gas Bubbles in Liquids

Linear Bubble Pulsations

Frequency of Bubble Oscillation

Damping Mechanisms

Sound Radiation

4.4 Sounds from Splashes

Franz's Measurements

Wind-Generated Ambient Sea Noise

Rain Noise

4.5 Radiation by Two Equal Monopoles

General Equation for Pressure Field

Far-Field Pressure Pattern

Directivity Function

Electrical Steering

Two Equal in-Phase Sources

Out-of-Phase Sources

Dipoles

4.6 Near-Surface Sources

Surface Image

Interference Patterns

Effects on Noise Measurements

4.7 Linear Arrays

Arrays of Equally-Spaced Monopoles

Continuous Line Radiators

Directivity Factor

Directivity Index

Arrays of Directional Sources

Arrays as Spatial Filters

4.8 Radiation from Rigid Pistons

Elementary Piston Radiator

Circular Piston in a Baffle

Near Field of a Piston Radiator

Radiation Impedance and Efficiency

Directivity Factor and Index

Pistons of Other Shapes

Planar Arrays

Pistons in Non-Rigid Baffles

Unbaffled and Partially Baffled Pistons

Pistons on Non-Planar Baffles

Effect of Flow on Piston Radiation

4.9 Radiation from Hull Openings

Radiation from Pipe Ends

Radiation from Tank Resonances

Radiation from Exhaust Pipes

4.10 Radiation from Arbitrary Bodies

Integral Equation Methods

Spheroidal Wave Functions

Slender Body Theory

Radiation from Cylinders

Finite-Element Methods

4.11 Radiation from Hulls

Definition of Frequency Regimes

Low Frequencies

Medium Frequencies

High Frequencies

References


5. Structural Vibrations

5.1 Structure-Borne Sound

5.2 Wave Motions in Solids

Longitudinal Waves in Bars

Shear Waves

Compressional Waves in Bulk Solids

Poisson's Ratio

Longitudinal Waves in Plates

Surface Waves

Flexural (Bending) Waves

5.3 Beam Bending Equations

Forces and Moments

Transverse Acceleration

Rotational Acceleration

Considerations of Shear

Differential Equation for Bending

Equation for Uniform Beams

Euler-Bernoulli (E-B) Equation

5.4 Speed of Flexural Waves

Harmonic Solutions of the Timoshenko Equation

Low-Frequency Approximation

High-Frequency Limit

Intermediate-Frequency Approximation

Solid Rectangular Bars

5.5 Flexural Resonances

Uniform Thin Beams

Correction for Shear and Rotatory Inertia

Wave Approach

5.6 Non-Uniform Beams

Finite-Element Methods

Wave Method

Tapered Cantilever Beams

5.7 Forced Vibrations of Non-Resonant Structures

Mechanical Impedances

Semi-Infinite Beams

Infinite Beams

Role of Damping

5.8 Forced Vibrations of Resonant Structures

Role of Resonances

Modal Responses

Broadband Excitation

5.9 Attenuation of Structural Vibrations

Isolation Mounts

Applied Damping

Impedance Mismatches

Vibration Absorbers and Suppressors

5.10 Fluid Loading

Entrained Mass

Hydrodynamic Damping

Sound Radiation

5.11 Flexural Resonances of Ship Hulls

References


6. Radiation by Plate Flexural Vibrations

6.1 Plate Flexural Vibrations

Bending Rigidity of Plates

Thick Plate Bending Equations

Flexural Wave speed

Plate Vibrations

Input Impedance

6.2 Fluid Loading

Boundary Conditions

Coincidence

Entrained Mass

radiation

6.3 Point-Excited Infinite Plates

Radiation Below Coincidence

Directional Radiation at High Frequencies

6.4 Radiation from Finite Plates

Radiation Resistance

Modal Approach

Effect of Damping

Orthotropic Plates

Beam on a Plate

Periodic Structures

Cylindrical Shells

Radiation from Hull Sections

6.5 Transmission Through Structures

Response of Structures to Sound Waves

Low-Frequency Transmission Through Walls

Use of Impedance Concepts

Role of Flexural Vibrations

Sound Isolation by Walls

6.6 Boundary-Layer Flow Noise

Turbulent Boundary Layers

Boundary-Layer Friction

Boundary-Layer Turbulence

Intermittency Effects

Wall Pressure Fluctuations

Self-Noise of Flush-Mounted Hydrophones

Arrays of Flush-Mounted Hydrophones

Radiated Flow Noise

Domed Sonar Self-Noise

References


7. Cavitation

7.1 Introduction

7.2 Tensile Strength of Liquids

Static Tensile Strength

Cavitation Nuclei

Dynamic Tensile Strengths

7.3 Single Bubble Growth and Collapse

Classical Theory

Pressure Inside a Bubble

Effects of Compressibility

Effects of Permanent Gases

Asymmetrical Bubble Collapse

Summary and Conclusions

7.4 Single Bubble Cavitation Noise

Expression for Radiated Energy

Growth Phase

Collapse Phase

Acoustic Pressures

Spectrum

Experimental Results

7.5 Broadband Cavitation Noise

7.6 Other Effects of Cavitation

Sonoluminescence

Chemical Reactions

Erosion Damage

7.7 Hydrodynamically-Produced Cavitation

Cavitation Parameter

Body Cavitation

Scale Effects

Effects of Surface Roughness

Vortex Cavitation

Wakes and Jets

7.8 Hydrofoil Cavitation

Symmetric Struts

Lifting Hydrofoils

Effects of Cavitation on Section Performance Scale Effects

Wing-Tip Vortex Cavitation

Supercavitating Hydrofoils

7.9 Hydraulic Cavitation

Pipe Constructions

Valves

Pipe Bends

Hydraulic Machinery

7.10 Underwater Explosions

References


8. Propeller Cavitation Noise

8.1 Types of Propeller Cavitation

8.2 Blade-Surface Cavitation Noise

Rotating Blade Experiments

Scaling Relationships

Dependence of Noise on Depth

Effect of Gas Content

8.3 Propellers in Uniform Inflows

Blade-Element Analysis

Momentum Theory Analysis

cavitation in Uniform Inflows

8.4 Wake-Operating Propellers

Wake Diagrams

Effect of Radially Varying Inflow

Effects of Circumferential Variations

Effect on Cavitation

Low-Frequency Cavitation Tonals

8.5 Submarine Propeller Cavitation

8.6 Surface Ship Radiated Noise

Importance of Propeller Cavitation

World War II Noise Data

Dependence on Speed

Estimation Formulas

Acoustic Efficiencies of Surface Ships

Modulation Effects

Tonal Spectra

Merchant Ship Trends

8.7 Ship-Generated Ambient Noise

Recognition of Ships as Sources of Ambient Noise

Reverberant Room Theory of Ambient Noise

Geographical Variations

Importance of Coastal Shipping

Directional Characteristics

Temporal Fluctuations

Long-Term Trends

References


9. Radiation by Fluctuating-Force (Dipole) Sources

9.1 Dipole Sound Sources

Acoustic Field of a Concentrated Force

Oscillating Rigid Sphere

Spheres Pulsating Out of Phase

Dipole Fields from Monopole Fields

9.2 Propeller Blade Tonals

General Oscillating Hydrodynamic Force

Noise from Oscillating Thrust

Factors Affecting Oscillating Thrust

Propeller-Induced Hull Forces

Blade-Vortex Interaction Noise

Shaft-Rate Components

Rotor-Stator Interactions

Blade-Turbulence Interactions

9.3 Vortex Shedding Sounds

Aeolian Tones

Vortex Wakes of Bluff Bodies

Oscillating Forces Associated with Vortex Wakes

Three-Dimensional Character of Vortex Wakes

Effects of Vibration

Effects of Sound Fields

Vortex Sounds from Cylinders

Sounds from Rotating Rods

Vortex Wakes of Airfoils

Vortex Sounds from Rotating Blades

9.4 Noise from Fans and Blowers

Noise Mechanisms

Spectra

Noise Levels

Positive Displacement Blowers

9.5 Propeller Singing

9.6 Flow-Excited Cavity Resonances

References


10. Mechanical Noise Sources

10.1 Mechanical Unbalances

Rotational Unbalances

Reciprocating Unbalances

10.2 Electromagnetic Force Fluctuations

Magnetostriction

Magnetic Force Variations

10.3 Impact Sounds

Impact Vibratory Relations

Gear Noise

10.4 Piston-Slap Noise in Reciprocating Machinery

Piston Slap

Significance of Piston Slap

Piston Impact Velocity

Cylinder Wall Vibrations

Experimental Verification

Empirical Noise Formulas

Underwater Noise Implications

10.5 Bearing Noise

References

Appendix A Nomenclature

General

Nomenclature by Chapter

Nomenclature Used in References

Appendix B Decibel Arithmetic

Author Index

Subject Index