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1 | (32) |
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1.1 Brief History of Underwater Sound Transducers |
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2 | (5) |
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1.2 Underwater Transducer Applications |
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7 | (8) |
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1.3 General Description of Linear Electroacoustic Transduction |
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15 | (7) |
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1.4 Transducer Characteristics |
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22 | (5) |
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1.4.1 Electromechanical Coupling Coefficient |
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22 | (2) |
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1.4.2 Transducer Responses, Directivity Index, and Source Level |
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24 | (3) |
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27 | (1) |
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28 | (5) |
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29 | (1) |
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30 | (3) |
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2 Electroacoustic Transduction |
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33 | (58) |
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2.1 Piezoelectric Transducers |
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34 | (11) |
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34 | (5) |
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2.1.2 The 33 Mode Longitudinal Vibrator |
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39 | (4) |
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2.1.3 The 31 Mode Longitudinal Vibrator |
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43 | (2) |
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2.2 Electrostrictive Transducers |
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45 | (4) |
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2.3 Magnetostrictive Transducers |
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49 | (3) |
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2.4 Electrostatic Transducers |
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52 | (3) |
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2.5 Variable Reluctance Transducers |
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55 | (2) |
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2.6 Moving Coil Transducers |
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57 | (3) |
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2.7 Comparison of Transduction Mechanisms |
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60 | (2) |
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62 | (17) |
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2.8.1 Equivalent Circuit Basics |
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62 | (3) |
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65 | (1) |
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2.8.3 Circuit Q and Bandwidth |
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66 | (3) |
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2.8.4 Power Factor and Tuning |
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69 | (4) |
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73 | (2) |
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75 | (3) |
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2.8.7 Hydrophone Circuit and Noise |
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78 | (1) |
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2.9 Thermal Considerations |
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79 | (6) |
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2.9.1 Transducer Thermal Model |
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80 | (3) |
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2.9.2 Power and Heating at Resonance |
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83 | (2) |
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2.10 Extended Equivalent Circuits |
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85 | (1) |
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86 | (5) |
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87 | (2) |
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89 | (2) |
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91 | (62) |
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3.1 Lumped-Parameter Models and Equivalent Circuits |
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92 | (18) |
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3.1.1 Mechanical Single Degree of Freedom Lumped Equivalent Circuits |
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92 | (3) |
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3.1.2 Mechanical Lumped Equivalent Circuits for Higher Degrees of Freedom |
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95 | (4) |
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3.1.3 Piezoelectric Ceramic Lumped-Parameter Equivalent Circuit |
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99 | (5) |
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3.1.4 Magnetostrictive Lumped-Parameter Equivalent Circuit |
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104 | (4) |
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108 | (2) |
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110 | (18) |
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3.2.1 Distributed Mechanical Model |
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111 | (4) |
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3.2.2 Matrix Representation |
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115 | (3) |
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3.2.3 Piezoelectric Distributed Parameter Equivalent Circuit |
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118 | (10) |
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128 | (5) |
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3.3.1 Three Port Matrix Model |
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128 | (3) |
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3.3.2 Two Port ABCD Matrix Model |
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131 | (2) |
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3.4 Finite Element Models |
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133 | (16) |
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3.4.1 A Simple FEM Example |
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133 | (2) |
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3.4.2 FEA Matrix Representation |
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135 | (2) |
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3.4.3 Inclusion of a Piezoelectric Finite Element |
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137 | (1) |
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3.4.4 Application of FEA Without Water Loading |
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138 | (3) |
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3.4.5 Application of FEA with Water Loading |
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141 | (3) |
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3.4.6 Water Loading of Large Arrays |
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144 | (1) |
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3.4.7 Magnetostrictive FEA |
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145 | (2) |
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3.4.8 Equivalent Circuits for FEA Models |
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147 | (2) |
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149 | (4) |
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150 | (1) |
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151 | (2) |
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4 Transducer Characteristics |
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153 | (32) |
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153 | (4) |
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4.2 Mechanical Quality Factor |
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157 | (4) |
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157 | (2) |
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4.2.2 Effect of the Mass of the Bar |
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159 | (1) |
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4.2.3 Effect of Frequency-Dependent Resistance |
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160 | (1) |
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4.3 Characteristic Mechanical Impedance |
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161 | (2) |
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4.4 Electromechanical Coupling Coefficient |
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163 | (15) |
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4.4.1 Energy Definitions of Coupling and Other Interpretations |
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164 | (5) |
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4.4.2 The Effect of Inactive Components on the Coupling Coefficient |
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169 | (5) |
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4.4.3 The Effect of Dynamic Conditions on the Coupling Coefficient |
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174 | (4) |
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4.5 Parameter Based Figure of Merit (FOM) |
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178 | (3) |
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181 | (4) |
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182 | (1) |
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183 | (2) |
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5 Transducers as Projectors |
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185 | (96) |
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5.1 Principles of Operation |
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187 | (3) |
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5.1.1 Projector Figure of Merit |
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188 | (2) |
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5.2 Ring and Spherical Transducers |
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190 | (17) |
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5.2.1 Piezoelectric 31 Mode Ring |
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190 | (6) |
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5.2.2 Piezoelectric 33 Mode Ring |
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196 | (1) |
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5.2.3 The Spherical Transducer |
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197 | (3) |
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5.2.4 The Magnetostrictive Ring |
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200 | (1) |
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201 | (4) |
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205 | (2) |
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207 | (13) |
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5.3.1 The Tonpilz Projector |
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207 | (9) |
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5.3.2 The Hybrid Transducer |
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216 | (4) |
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5.4 Transmission Line Transducers |
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220 | (17) |
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5.4.1 Sandwich Transducers |
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220 | (5) |
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5.4.2 Wideband Transmission Line Transducers |
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225 | (5) |
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5.4.3 Large Plate Transducers |
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230 | (2) |
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5.4.4 Composite Transducers |
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232 | (5) |
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5.5 Flextensional Transducers |
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237 | (11) |
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5.5.1 The Class IV and VII Flextensional Transducers |
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237 | (5) |
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5.5.2 The Class I Barrel Stave Flextensional |
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242 | (1) |
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5.5.3 The Class V and VI Flextensional Transducers |
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243 | (1) |
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5.5.4 Astroid, Trioid, and X-Spring Transducers |
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244 | (3) |
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5.5.5 Lumped Mode Equivalent Circuit |
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247 | (1) |
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248 | (11) |
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5.6.1 Bender Bar Transducer |
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249 | (4) |
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5.6.2 Bender Disc Transducer |
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253 | (2) |
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5.6.3 Slotted Cylinder Transducer |
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255 | (3) |
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5.6.4 Bender Mode X-Spring Transducer |
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258 | (1) |
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259 | (6) |
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5.7.1 Power Wheel Transducer |
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259 | (3) |
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262 | (1) |
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5.7.3 Leveraged Cylindrical Transducer |
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263 | (2) |
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5.8 Low Profile Piston Transducers |
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265 | (7) |
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5.8.1 Cantilever Mode Piston Transducer |
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265 | (5) |
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5.8.2 Shear Mode Piston Transducer |
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270 | (2) |
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272 | (9) |
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273 | (2) |
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275 | (6) |
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6 Transducers as Hydrophones |
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281 | (68) |
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6.1 Principles of Operation |
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282 | (9) |
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283 | (2) |
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285 | (2) |
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6.1.3 Simplified Equivalent Circuit |
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287 | (1) |
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6.1.4 Other Sensitivity Considerations |
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288 | (3) |
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6.2 Cylindrical and Spherical Hydrophones |
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291 | (6) |
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6.2.1 Performance with Shielded Ends |
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292 | (3) |
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6.2.2 Spherical Hydrophones |
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295 | (1) |
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6.2.3 Performance with End Caps |
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296 | (1) |
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297 | (7) |
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6.3.1 Tonpilz Hydrophones |
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298 | (2) |
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6.3.2 The 1-3 Composite Hydrophones |
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300 | (3) |
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6.3.3 Flexible Hydrophones |
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303 | (1) |
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304 | (2) |
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306 | (19) |
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6.5.1 Dipole Vector Sensors, Baffles, and Images |
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307 | (4) |
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6.5.2 Pressure Gradient Vector Sensor |
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311 | (2) |
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6.5.3 Velocity Vector Sensor |
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313 | (1) |
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6.5.4 Accelerometer Sensitivity |
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314 | (2) |
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6.5.5 Multimode Vector Sensor |
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316 | (2) |
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6.5.6 Summed Scalar and Vector Sensors |
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318 | (5) |
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323 | (2) |
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6.6 The Plane Wave Diffraction Constant |
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325 | (3) |
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6.7 Hydrophone Thermal Noise |
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328 | (13) |
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6.7.1 Directivity and Noise |
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330 | (1) |
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6.7.2 Low Frequency Hydrophone Noise |
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331 | (1) |
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6.7.3 More General Description of Hydrophone Noise |
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332 | (3) |
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6.7.4 Comprehensive Hydrophone Noise Model |
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335 | (1) |
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6.7.5 Vector Sensor Internal Noise |
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336 | (2) |
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6.7.6 Vector Sensor Susceptibility to Local Noise |
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338 | (1) |
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6.7.7 Thermal Noise from Radiation Resistance |
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339 | (2) |
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341 | (8) |
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343 | (1) |
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344 | (5) |
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349 | (58) |
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7.1 Array Directivity Functions |
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352 | (18) |
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7.1.1 The Product Theorem |
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352 | (2) |
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7.1.2 Line, Rectangular, and Circular Arrays |
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354 | (3) |
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357 | (2) |
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7.1.4 Beam Steering and Shaping |
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359 | (6) |
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365 | (4) |
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7.1.6 Effects of Random Variations |
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369 | (1) |
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7.2 Mutual Radiation Impedance and the Array Equations |
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370 | (6) |
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7.2.1 Solving the Array Equations |
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370 | (4) |
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374 | (2) |
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7.2.3 Negative Radiation Resistance |
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376 | (1) |
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7.3 Calculation of Mutual Radiation Impedance |
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376 | (9) |
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7.3.1 Planar Arrays of Piston Transducers |
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376 | (6) |
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7.3.2 Nonplanar Arrays, Nonuniform Velocities |
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382 | (3) |
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7.4 Arrays of Non-FVD Transducers |
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385 | (6) |
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7.4.1 Modal Analysis of Radiation Impedance |
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385 | (1) |
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7.4.2 Modal Analysis of Arrays |
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386 | (5) |
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391 | (2) |
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7.6 Near Field of a Projector Array |
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393 | (2) |
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7.7 The Nonlinear Parametric Array |
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395 | (5) |
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7.8 Doubly Steered Arrays |
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400 | (3) |
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403 | (4) |
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403 | (1) |
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404 | (3) |
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407 | (68) |
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8.1 Hydrophone Array Directional Response |
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409 | (12) |
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8.1.1 Directivity Functions |
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409 | (4) |
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413 | (1) |
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8.1.3 Shading and Directivity Factor |
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414 | (6) |
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8.1.4 Wavevector Response of Arrays |
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420 | (1) |
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421 | (4) |
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8.3 Sources and Properties of Noise in Arrays |
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425 | (7) |
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425 | (4) |
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429 | (2) |
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431 | (1) |
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8.4 Reduction of Array Noise |
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432 | (14) |
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8.4.1 Ambient Noise Reduction |
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432 | (3) |
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8.4.2 Structural Noise Reduction |
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435 | (5) |
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8.4.3 Flow Noise Reduction |
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440 | (4) |
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8.4.4 Summary of Noise Reduction |
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444 | (2) |
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8.5 Arrays of Vector Sensors |
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446 | (18) |
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448 | (1) |
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8.5.2 Vector Sensor Arrays in Ambient Noise |
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449 | (6) |
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8.5.3 Hull-Mounted Arrays in Structural Noise |
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455 | (9) |
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8.6 Steered Planar Circular Arrays |
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464 | (5) |
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469 | (6) |
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469 | (2) |
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471 | (4) |
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9 Transducer Evaluation and Measurement |
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475 | (42) |
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9.1 Electrical Measurement of Transducers in Air |
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476 | (6) |
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9.1.1 Electric Field Transducers |
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476 | (4) |
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9.1.2 Magnetic Field Transducers |
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480 | (2) |
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9.2 Measurement of Transducers in Water |
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482 | (4) |
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9.3 Measurement of Transducer Efficiency |
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486 | (2) |
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9.4 Acoustic Responses of Transducers |
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488 | (3) |
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9.5 Reciprocity Calibration |
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491 | (4) |
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495 | (5) |
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9.6.1 Electric Field Transducers |
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495 | (3) |
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9.6.2 Magnetic Field Transducers |
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498 | (2) |
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9.7 Near-Field Measurements |
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500 | (11) |
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9.7.1 Distance to the Far Field |
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500 | (2) |
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9.7.2 Measurements in Tanks |
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502 | (2) |
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9.7.3 Near-to-Far-Field Extrapolation: Small Sources |
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504 | (2) |
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9.7.4 Near-to-Far-Field Extrapolation: Large Sources |
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506 | (4) |
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9.7.5 Effect of Transducer Housings |
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510 | (1) |
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9.8 Calibrated Reference Transducers |
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511 | (1) |
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512 | (5) |
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513 | (1) |
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514 | (3) |
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10 Acoustic Radiation from Transducers |
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517 | (38) |
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10.1 The Acoustic Radiation Problem |
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517 | (7) |
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10.2 Far-Field Acoustic Radiation |
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524 | (10) |
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524 | (3) |
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10.2.2 Flat Sources in a Plane |
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527 | (6) |
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10.2.3 Spherical and Cylindrical Sources |
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533 | (1) |
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10.3 Near-Field Acoustic Radiation |
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534 | (6) |
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10.3.1 Field on the Axis of a Circular Piston |
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534 | (2) |
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10.3.2 The Effect of the Near Field on Cavitation |
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536 | (3) |
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10.3.3 Near Field of Circular Sources |
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539 | (1) |
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540 | (6) |
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540 | (3) |
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10.4.2 Circular Sources in a Plane |
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543 | (3) |
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10.5 Dipole Coupling to Parasitic Monopole |
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546 | (5) |
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551 | (4) |
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551 | (1) |
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552 | (3) |
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11 Mathematical Models for Acoustic Radiation |
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555 | (42) |
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11.1 Mutual Radiation Impedance |
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556 | (13) |
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11.1.1 Piston Transducers on a Sphere |
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556 | (4) |
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11.1.2 Piston Transducers on a Cylinder |
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560 | (6) |
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566 | (2) |
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568 | (1) |
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11.2 Green's Theorem and Acoustic Reciprocity |
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569 | (10) |
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569 | (2) |
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11.2.2 Acoustic Reciprocity |
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571 | (1) |
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11.2.3 Green's Function Solutions |
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572 | (4) |
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11.2.4 The Helmholtz Integral Formula |
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576 | (3) |
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11.3 Scattering and the Diffraction Constant |
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579 | (7) |
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11.3.1 The Diffraction Constant |
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580 | (3) |
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11.3.2 Scattering from Cylinders |
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583 | (3) |
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11.4 Numerical Methods for Acoustic Calculations |
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586 | (5) |
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11.4.1 Mixed Boundary Conditions: Collocation |
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587 | (1) |
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11.4.2 Boundary Element Methods |
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588 | (3) |
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591 | (6) |
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592 | (2) |
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594 | (3) |
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12 Nonlinear Mechanisms and Their Effects |
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597 | (40) |
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12.1 Nonlinear Mechanisms in Lumped-Parameter Transducers |
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598 | (13) |
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12.1.1 Piezoelectric Transducers |
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598 | (5) |
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12.1.2 Electrostrictive Transducers |
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603 | (2) |
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12.1.3 Magnetostrictive Transducers |
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605 | (2) |
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12.1.4 Electrostatic and Variable Reluctance Transducers |
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607 | (2) |
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12.1.5 Moving Coil Transducers |
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609 | (2) |
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12.1.6 Other Nonlinear Mechanisms |
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611 | (1) |
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12.2 Analysis of Nonlinear Effects |
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611 | (14) |
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12.2.1 Harmonic Distortion: Direct Drive Perturbation Analysis |
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612 | (9) |
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12.2.2 Harmonic Distortion for Indirect Drive |
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621 | (1) |
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12.2.3 Instability in Electrostatic and Variable Reluctance Transducers |
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622 | (3) |
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12.3 Nonlinear Analysis of Distributed Parameter Transducers |
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625 | (7) |
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12.4 Nonlinear Effects on the Electromechanical Coupling Coefficient |
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632 | (1) |
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633 | (4) |
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634 | (1) |
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635 | (2) |
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637 | (44) |
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13.1 Conversions and Constants |
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637 | (1) |
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637 | (1) |
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637 | (1) |
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13.2 Materials for Transducers Ordered by Impedance, pc |
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638 | (1) |
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13.3 Time Averages, Power Factor, Complex Intensity |
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639 | (2) |
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639 | (1) |
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640 | (1) |
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640 | (1) |
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13.3.4 Radiation Impedance |
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641 | (1) |
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641 | (1) |
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13.4 Relationships Between Piezoelectric Coefficients |
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641 | (2) |
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13.5 Small Signal Properties of Piezoelectric Materials |
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643 | (3) |
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13.5.1 Comparison of Small Signal Properties of Textured Ceramic, PZT-8 Ceramic, and Commercial Grade Single Crystal Piezoelectric Materials |
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645 | (1) |
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13.6 Piezoelectric Ceramic Approximate Frequency Constants (See Footnote 1) |
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646 | (1) |
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13.7 Small Signal Properties of Magnetostrictive Materials |
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647 | (1) |
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13.7.1 Nominal 33 Magnetostrictive Properties |
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647 | (1) |
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13.7.2 Three-Dimensional Terfenol-D Properties |
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647 | (1) |
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13.8 Voltage Divider and Thevenin Equivalent Circuit |
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648 | (1) |
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648 | (1) |
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13.8.2 Thevenin Equivalent Circuit |
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649 | (1) |
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13.9 Magnetic Circuit Analysis |
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649 | (2) |
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13.9.1 Equivalent Circuit |
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649 | (1) |
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650 | (1) |
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13.10 Norton Circuit Transformations |
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651 | (1) |
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13.11 Integral Transform Pairs |
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652 | (1) |
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13.12 Stiffness, Mass, and Resistance |
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653 | (2) |
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13.12.1 Mechanical Stiffness [ K = F/x] |
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653 | (1) |
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13.12.2 Piezoelectric Compliance [ CE = x/F] |
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653 | (1) |
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654 | (1) |
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13.12.4 Resonance [ ω0 = 1/√(mC)] |
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654 | (1) |
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13.12.5 Resistance [ R = F/u] |
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655 | (1) |
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13.13 Frequently Used Formulas |
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655 | (6) |
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655 | (2) |
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657 | (4) |
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13.14 Stress, Field Limits, and Aging for Piezoelectric Ceramics |
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661 | (4) |
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13.15 Development of a Comprehensive Hydrophone Noise Model |
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|
665 | (6) |
|
13.16 Cables and Transformers |
|
|
671 | (3) |
|
|
671 | (1) |
|
|
672 | (2) |
|
|
674 | (3) |
|
13.18 Transducer Publications 2000--2015 |
|
|
677 | (4) |
Answers to Odd-Numbered Exercises |
|
681 | (10) |
Glossary |
|
691 | (12) |
Index |
|
703 | |