John C. Cochran - Introduction to Sonar Transducer Design

1 Cover

2 Title Page Introduction to Sonar Transducer Design John C. Cochran Raytheon Technologies, RI, USA (Retired)

3 Copyright Page

4 Dedication

5 Preface

6 1 Acoustic Waves and Radiation 1.1 Small Signals/Linear Acoustics 1.2 The Equations of Continuity, Motion, and the Wave Equation in a Fluid Media 1.3 Plane Waves 1.4 Radiation from Spheres 1.5 Radiation from Sources on a Cylindrical Surface 1.6 Integral Formulations 1.7 Linear Apertures 1.8 Planar Apertures 1.9 Directivity and Directivity Index ( DI ) 1.10 Scattering and Diffraction 1.11 Radiation Impedance 1.12 Transmission Phenomena 1.13 Absorption and Attenuation of Sound References

7 2 Mechanical/Acoustical Equivalent Circuits 2.1 Different Forms of Impedance 2.2 Mechanical Equivalent Circuits 2.3 Acoustical Equivalent Circuits 2.4 Combining Mechanical and Acoustical Equivalent Circuits 2.5 Introduction to Transduction References

8 3 Waves in Solid Media 3.1 Waves in Homogeneous, Isotropic, Elastic, Solid Media 3.2 Piezo‐electricity and Piezo‐electric Ceramic Materials 3.3 Waves in Non‐Homogenous, Piezo‐electric Media References

9 4 Sonar Projectors 4.1 Tools for Underwater Sonar Projector Design 4.2 Specific Applications in Underwater Sonar Projector Design 4.3 Special Topics in Underwater Sonar Projector Design References

10 5 Sonar Hydrophones 5.1 Elements of Sonar Hydrophone Design 5.2 Analysis of Noise in Hydrophone/Preamplifier Systems 5.3 Specific Applications in Underwater Sonar Hydrophone Design References

11 AppendixA.1 Summary of Vector Notation A.2 Useful Material Properties References

12 Index

13 End User License Agreement

1 Chapter 1 Table 1.7-1 Properties of linear apertures. Table 1.8-1 Baffle admittance for common materials.

2 Chapter 2Table 2.1‐1 Forms and units of impedance.Table 2.2‐1 Mobility and impedance circuit elements.

3 Chapter 3Table 3.2-1 Elastic, dielectric, and piezo‐electric nomenclature.Table 3.2-2 Coupling coefficients for different geometries.

4 Chapter 4Table 4.2‐1 Geometry factors for tonpilz example.Table 4.2‐2 Calculated parameters for the trilaminar flexural disk example....Table 4.2‐3 Calculated parameters for the bilaminar flexural disk example....

1 Chapter 1 Figure 1.4‐1 Spherical coordinate system for radiation from spheres. Figure 1.5‐1 Cylindrical coordinate system for radiation from cylinder‐shape... Figure 1.5‐2 Cylindrical coordinates for radiation from a piston on a cylind... Figure 1.5‐3 Geometry for radiation from a segment of an infinitely long cyl... Figure 1.6‐1 Geometry for radiation from an arbitrary planar aperture. Figure 1.6‐2 Geometry of line source to illustrate far field approximation.... Figure 1.6‐3 Geometry of line source to illustrate far field approximation.... Figure 1.6‐4 Geometry of line source illustrating far field approximation. Figure 1.6‐5 Geometry for radiation from a finite cylinder. Figure 1.7‐1 A linear aperture geometry for determining the far field direct... Figure 1.7-2 Example of beam pattern for a linear aperture showing the main ... Figure 1.7-3 Geometry for a linear aperture with a rectangular aperture func... Figure 1.7-4 Normalized beam patterns for a linear aperture with a rectangul... Figure 1.7-5 A linear rectangular aperture function. Figure 1.7-6 Normalized beam patterns for a linear aperture with a rectangul... Figure 1.7-7 A cosine aperture function. Figure 1.7-8 Normalized beam patterns for a cosine aperture function. Figure 1.7-9 Geometry for the beam pattern of a linear source on a cylindric... Figure 1.7-10 Beam pattern for source on a cylindrical surface. Figure 1.8-1 Geometry for radiation into a half‐space. Figure 1.8-2 Geometry for radiation into a half‐space. Figure 1.8-3 Geometry for far field radiation from a rectangular piston in a... Figure 1.8-4 Geometry for far field radiation from a circular piston in an i... Figure 1.8-5 Normalized beam patterns for a circular piston aperture in an i... Figure 1.8-6 Circular annular piston geometry. Figure 1.8-7 Beam patterns for a circular annular piston in an infinite baff... Figure 1.8-8 Elliptical piston coordinate system. Figure 1.8-9 Beam patterns for an elliptical piston in an infinite baffle wi... Figure 1.8-10 The impact of a baffle impedance can be determined by examinin... Figure 1.8-11 (Top) −3 dB beamwidth vs. kL /2 for a linear aperture and (bott... Figure 1.9-1 Geometry of an aperture and beam pattern showing the main respo... Figure 1.9-2 Beam pattern and geometry for a circular piston aperture in an ... Figure 1.9-3 The directivity index (DI) for a circular piston aperture in an... Figure 1.9-4 Geometry for determining the directivity index of a linear aper... Figure 1.9-5 Directivity Index (DI) for a linear aperture with a high‐freque... Figure 1.10-1 The geometry for scattering and diffraction around a rigid cyl... Figure 1.10-2 Scattered wave beam pattern from a rigid cylinder for differen... Figure 1.10-3 Diffraction constant for rigid cylinder vs. ka . Figure 1.10‐4 Diffraction constant for a strip on a rigid cylinder vs. ka . Figure 1.10‐5 The geometry for scattering and diffraction around a cylinder.... Figure 1.10-6 Diffraction constant for a cylinder vs. ka with variable bound... Figure 1.10-7 Beam patterns for diffraction around a cylinder vs. ka with va... Figure 1.10-8 The geometry for scattering and diffraction around a sphere. Figure 1.10-9 Diffraction constant for a rigid sphere vs. ka . Figure 1.10-10 The geometry for scattering and diffraction around a thin rin... Figure 1.11-1 Impedance using Hilbert transform ka .Figure 1.11-2 The geometry for radiation impedance between two bodies.Figure 1.11-3 Radiation impedance of a spherical radiator of radius a .Figure 1.11-4 Geometry for radiation from a circular piston in an infinite, ...Figure 1.11-5 Radiation impedance of a circular piston of radius a in a baff...Figure 1.11-6 Equivalent circuit for the radiation impedance from a circular...Figure 1.11-7 Radiation impedance of a circular piston of radius a at the en...Figure 1.11-8 Geometry for radiation from a rectangular piston in a baffle....Figure 1.11-9 Radiation resistance and reactance for a rectangular piston in...Figure 1.11-10 Radiation impedance of an infinite strip of width w in a baff...Figure 1.11-11 Radiation impedance of an annular piston radiator in a baffle...Figure 1.11-12 Radiation resistance of an elliptical piston radiator in a ba...Figure 1.11-13 Radiation impedance per unit length for an infinitely long cy...Figure 1.11-14 Geometry of a finite cylindrical radiator in a baffle.Figure 1.11-15 Radiation impedance of a finite cylinder in a baffle.Figure 1.11-16 The geometry of two spheres illustrating mutual radiation imp...Figure 1.11-17 Mutual radiation resistance and reactance for two identical s...Figure 1.11-18 The geometry of two circular piston radiators located in a ba...Figure 1.11-19 Mutual radiation resistance and reactance for two identical p...Figure 1.11-20 Mutual radiation resistance and reactance for two identical p...Figure 1.11-21 Geometry for the mutual radiation impedance for two identical...Figure 1.11-22 Mutual radiation resistance and reactance for two identical s...Figure 1.11-23 Geometry for a disk with an annular piston.Figure 1.11-24 Mutual radiation resistance and reactance between an inner ci...Figure 1.11-25 Geometry for mutual impedance between rectangular pistons on ...Figure 1.11-26 Normalized mutual radiation impedance between two square pist...Figure 1.11-27 Geometry for mutual impedance between bands on a cylinder.Figure 1.11-28 Normalized mutual radiation impedance between two bands on a ...Figure 1.12-1 Geometry for plane wave reflection and transmission at a bound...Figure 1.12-2 T‐Network equivalent for input impedance at a point x = − l fro...Figure 1.12-3 Geometry for acoustic transmission at multiple boundaries.Figure 1.12-4 Geometry showing oblique reflection and transmission at a boun...Figure 1.12-5 Geometry illustrating the angle of complete reflection and zer...Figure 1.13-1 Attenuation coefficient for sound in the ocean vs. frequency a...