Index A bsolute calibration of receivers, 248 Absorption (see also Losses), 55, 239 relative coefficient, 240 Accelerometer, 151 Acoustic bond, 56 Acoustic load (see Load) Acoustic pressure transformation, 218 Acoustically bounded and unbounded media, 6 Acoustically transmissive wall section, 48 Addition of vibrational power, 111 Aggressive media, 10, 44 Ammonium dihydrophosphate (ADP), 136 Amplitude measurement, 18, 31, 148,179 Analytical relations flexural waveguide, 69 rod-type waveguide, 153 torsional waveguide, 133 torsional concentrators, table, 160 torsional insulators, 167 Anisotropy, 135 artificial, 137 Antinodes, 108, 118 Attachment modes, 70, 79, 82, 96, 110, 114, 166, 223 table, 86, 171 Automatic retuning, 46 Barium titanate, 136, 141, 217 "Beam" velocity, 44, 72 Boundary conditions (see also Attachment modes, Excitation, Load), 76, 101, 147, 156 table, 83, 171 263 Branching device (see also Division of vibrational power), 42, 114 Calibration absolute, 248 radiometers, 233 receivers, 187, 235, 243, 252 shock wave method, 248 static pressure spike method, 253 topographical relief method, 258 Calorimetric measurements, 120, 189 Cathode follower, 221 Cavitation, 15, 215 Chamber pressure, 254 vacuum, 54 Characteristic number definition, 49 table, 50 Checkerboard polarization of transducer facings, 137 Clamping, 79, 117, 220 Classification of working media, 5 Cleaning, ultrasonic, 42 Coefficients of waveform equation, 86 Compound radiators (see Sectional systems) Concentrator, 46, 126 catenoidal, 14 exponential, 155, 163 grooved, 176 longitudinal-torsional (LT), 174 rod-type, 153 sectional (stepped), 155, 163, 177
264 Concentrator (continued) torsional, 155, 160, 163 Contact area, 56 Cooled radiator, 43 Cophasal radiator, 41 Coupling (see also Matching), 4, 12, 44 irregular objects, 57 several waveguides, 113 ultrasonic receiver, 196 Critical dimensions of radiator, 113 Crust effects (melts), 44 Current loop in magnetic field, 138 Cutting, ultrasonic, 125, 162, 176 Cylindrical receivers, 201 table of parameters, 204 Cylindrical vibrator, 129 Damping factor, 6 Decoupling (acoustic), 9 delimiting contour, 53 hermetic slip-seal, 53 nodal, 52 Deflection nodes, 115 Delimiting contour, 48, 53 Directivity characteristics, 200, 210, 213, 217 Disk torsional-mode transducer,145,151 Disk-type receiver, 203, 205 Disk-type supporting insulator, 168, 170 Disperse media, 10 Dispersion, 66 Distributed parameters, 40 Distortion waves, 128 Division (distribution) of vibrational power., III Drilling, ultrasonic, 180 Driving force, 93 Dual-section nodal decoupling, 52 INDEX End conditions (see Boundary conditions) Eighth-wave section, 19 Equipment considerations, 3, 63 Excess thickness (of melt), 45 Excitation (see also Driving force), 96, 141, 175 in arbitrary plane, 100 Experimental investigations flexural waveguide, 117 longitudinal-torsional systems, 173 Fay equation, 227 Ferrites, 207 Flat radiometer, 233 Flexural modes, 38, 63, 140 Flexural-mode waveguides, 63 table of arrangements, 96 experimental, 11 7 Form factor, 70, 81 Focusing devices (see Concentrators) Free coupling, 79, 108 Frequency characteristics longitudinal-torsional concentrator,174 ultrasonic receiver, 208 Frequency separation, 32, 47 Fric tion losses, 73, 162 Fundamental modes, 130 Furnace (insertion) (see also Heat effects), 52, 108, 120, 197 Generalized impedance, 82 Grooved concentrator, 176 Guided-wave probes, 215 Heat effects, 10, 44, 117, 120 Hinged support, 79 Hydrostatic calibration method, 255 Edge supports, 222 Efficiency radiator, 8, 150 waveguide, 13 Electrodynamic torsional-mode transducer, 142 Immersion techniques, 45, 120 Impedance force, 68 input, 75, 163 moment, 68, 94 radiation, 6
INDEX Impedance (continued) variable-load, 21 wave, 66, 77, 94 Inhomogeneity scale of sound field, 193 Inhomogeneous waveguides, 14, 178 Input impedance flexural waveguide, 75 torsional concentrator, 163 Inserts, mica, 58 Insulation (decoupling), 9, 48, 166 Irregular objects, 55 Junction conditions (see also Boundary conditions), 102 Krylov functions, 71, 85 Langevin stacked transducer, 145 Lathe, 67 Length of waveguide-load system, 26 Liquid media, 39 Limiting gain, 157 Load, 3, 15, 110 active, 81 characteristics for flexural waveguides, 102 elastic (compliant), 81 mass, 81 modes, 96 torsional waveguide, 163 Load frequency band, 34 Load resistance, 15 Load -waveguide mass ratio (coefficient), 33 loaded waveguide, 80 Longitudinal-mode waveguide, 63, ll7, 140 Longitudinal-torsional modes, 125, 173 Losses (acoustic), 41, 51, 73, ll9, 162 Lumped parameters, 33, 36, 39 Magnetostrictive elements, 135, 137, 188, 206 Matching of load to transducer (waveguide system), 4, 8, 12, 18, 105 265 Materials for waveguides, ll7 Materials testing, 125 Measurement of ultrasonic field, 187, 245 Measuring section of concentrator, 15 Mechanical pressure transformation, 218 Media, 3 aggressive, 10, 44 disperse, 10 liquid, measurements, 39, 137 processed, gener ai, 3, 5 Melts, 43 Metals, treatment, 43 Microminiature receivers, 192 Miniature wideband piezoelectric receivers, 192 Misalignment coefficient, 32 Mosaic element, 214 Multiresonance domains, 143 Navier- Stokes equation, 238 Nodal circle (contour), 49 Nodal decoupling, 49, 52 Nodes, nodal plane (see also attachment modes), 23, 68, ll5, 132, 166 tracking of, 47, 94 Nonlinear parameter, 237 Optical measurements, 188 Optimum load, 12 Particle velocity, 13 Piezoelectric anisotropy, 135 Piezoelectric elements, 188, 206 Piston radiator, 39 Plane waves, 41 Polar moment of inertia, 133 Polarization, checkerboard, 137 Porous transition (compensation) layer,196 Power, 15 addition and division (distribution), III Ptessure bomb for calibration measurements, 254 Pressure coupling, 56, 108 Probes (see Receivers) Pulsed operation, 21, 197
266 Quarter-wave section, 19 Quartz, 136 Radiation impedance, 6 Radiation pressure measurements, 245 Radiometers, 189, 226 Reactive load, 19 Receivers, 187, 191 Reflected pulse, 22 Reflection coefficient, 13, 56, 247 Requirements, engineering, 13, 39, 66 Resistance (active) loading, 118 Resonance condition, 23, 94, 119, 143, 157,213 Resonance frequencies, 29,47,88,130, 146, 151 tables, 92 Resonance-type receivers, 206 Reynolds number, 238 Rigidity (see Stiffness) RK-19 cable, 217 Rod-type concentrators, 153 Rotation modes, 116 Rotational inertia, 69 Sawtooth wave for sensitivity calibration, 236 spectrum, 238 Sectional systems, 36, 53 Sensitive element of receiver, 195 Sensitivity characteristics, 193, 206,214, 222, 233, 243, 259 specific, 208 Sheffield multiple-spindle lathe, 67 Shock-wave absolute calibration, 248 SHit oven, 197 Slip-seal decoupling, 53 Solenoid, 28, 31 Sound field in medium, 55 Specific sensitivity, 208 Spherical elements, 198, 231 Spherical radiometer, 231 Stacked (Langevin) transducer, 145 Standing waves, 13 Static pressure spike calibration, 253 INDEX Stiffness, 40, 192 Structural problems, 4 Supporting insulators, 166 Supports (see Attachment modes) Symmetry of driving force and load, 97 Tank, ultrasonic, 48, 53 Thermocouple measurements, 119 Thermoelectric measurements, 189 Thickness modes, 44 Tool, ultr asonic, 12, Ill, 125 Topographical relief calibration method, 258 Torque acting on rod, 134 Torsional-mode systems, 125, 128, 135 special configurations, 139, 153 table, 160 Tracking of nodal planes, 47 Tr ansd ucer, 3 disk-type torsional, 145, 151 Langevin, 145 parameters, 3 stacked, 145 torsional, 135 ultrasonic, 3, 187, 191 Transformation coefficient, 223 devices (see Waveguides, Coupling) energy, 18 modes, 56, 67, 126 pressure, 218 reactive loads, 19 Transmission into working medium, 4 flexural waveguide, 110 through container wall, 48 Traveling-wave ratio, 12, 163 Tuning, 12, 23 device, 29 automatic, 46 Ultrasonic applications, 3 cleaning, 42 cutting, 125, 162, 176 drilling, 180 lathe, 67
INDEX Ultrasonic applications (continued) materials testing, 125 tank, 48, 53 zone refinement, 120 Ultrasonic receivers (see Receivers) Ultrasonic waveguides (see Waveguides) Unhinged support, 79 UZG-10U generator, 23 Vacuum chambers, 54 Variable-load impedance, 21 Variable-parameter media, 7, 26, 29 Velocity dispersion, 66 Vibrational pressure, 13 Viscoelastic model, 74 Wall or bottom transmission, 48 Wave equation, 69, 154 Wave impedance flexural waveguide, 66, 77 force, 68 moment, 68, 94 Waveform of vibration, 70, 101 table of coefficients, 86 distortion (see Sawtooth wave) 267 Waveguide properties of torsional concentrators' 162 Waveguides (see also Concentrators), 4 catenoidal, 14, 134, 160 conical, 14, U8 elementary, 97 exponential, 40, 42, 134, 155, 159,163 flexural-mode, 38, 46, 63, 65 homogeneous, 15 inhomogeneous, 14, 178 joined and separate, 97 loaded, 80, U8 longitudinal-mode, 63, U7, 140 materials, U 7 reflect ing, 58 sectional (stepped), 36, 97, 155, 160, 164,178 separate and joined, 97 table, 17 torsional-mode, 155, 163 uniform, 15 wideband, 31 Webster equation, 134 Welding, ultrasonic, 68, 125, 162, 176 Windings for receivers, 209 Zone refinement, ultrasonic, 120