Smart Structures Theory Inderjit Chopra and Jayant Sirohi Index More Information

Cambridge University Press 978-0-521-86657-6 - Smart Structures Theory Inderjit Chopra and Jayant Sirohi Index More information

Index

Active materials, 739 dissimilar thickness, 330, 371 Actuation double lever (L-L), 761 asymmetric, 327, 347, 368 dual, 361 bending, 476, 478, 497, 559, 565 flextensional, 749 bending moment, 359 comparison, 753 extension, 476, 477, 478, 555, 563 hybrid hydraulic, 775, 778 force, 324, 332, 333, 335, 359 magnetostrictive, 777 induced-strain, 411, 416, 460 piezoelectric, 772, 778 mechanism, 739 SMA, 777 moment, 325, 332, 333, 335 key characteristics, 770 response, 753 LIPCA, 753 solid-state, 743 macro fiber composites (MFC), 748 stroke amplification, 743 magnetostrictive, 747 active material arrangement, 744 Moonie, 749 special geometry, 744 piezoceramic sheet, 743 symmetric, 321, 338, 361 piezoelectric, 747 Actuation displacement, 744 special geometry, 747 Actuation efficiency, 762, 763, 765 types of, 747 effect of stiffness, 763 piezoelectric bimorph, 744 finite support stiffness, 763 piezohydraulic, 776 Actuator piezostacks, 744 available energy, 144 PMN stack, 746 bimorph, 375 pre-stressed stack, 747 bond layer effect, 562 PZT sheet, 743 embedded, 379 PZT stack, 746 load line, 626 RAINBOW, 751 magnetostrictive, 625, 627 smart material, 740 piezoelectric tube, 819 solid-state, 740, 753 single, 347, 368 comparison, 753 strain, 354, 356 THUNDER, 752 strain energy, 144 torsional, 758 Actuators specially arranged, 760 active fiber composites (AFC), 748 structural coupling, 760 assessment, 753 torsional tube, 758 bending, 744 stepper motor, 760 bimorph, 744 unequal voltage, 354, 370 C-block, 755 Adaptive structure, 305 comparison, 747 AFC manufacture, 749 conventional, 740 Ampere’s law, 598 Cymbal, 750 Amplification mechanism dissimilar piezo constants, 332, 355, 371 double lever (L-L), 761

897

898 Index

Amplification mechanisms, 755 Carbon composite, 447 categories, 756 Cement-based piezoelectric composites, 172 comparisons, 756 Centrosymmetric, 113 flexures, 757 Chang, 194 Anisotropic plate, 460 Charge amplifier, 178 Annealing, 211 Circuit model, 171 Antisymmetric angle-ply laminate, 478 Circular coil, 587 Antisymmetric cross-ply laminate, 478 Clark, 583 Antisymmetric laminate, 477 Clark, A. E., 23 Approximate solution, 392, 488 Classical laminated plate theory (CLPT), 446, 486, AS4/3501-6, 447 527 Axial displacement, 365 Classical laminated theory (CLT), 446 Axial strain, 365, 367 Clauser, 3 Compliance matrix, 116, 306, 307, 308 Balanced laminate, 454 isotropic material, 312 Barium Titanate, 12 Composite beam fabrication, 292 Beam Composite beam testing, 294 axial stress, 327 Composite beams bending moment, 315 embedded SMA, 837 boundary conditions, 316 tuning, 837 coordinate system, 315 Composite lamina, 309 deflection, 327 Conductor dual actuator, 321, 329 current carrying, 586 sign convention, 315 finite straight, 586 single actuator, 320, 327 Constitutive models, 217, 609 transverse deflection, 318 Constitutive relations, IEEE standard, 114 Beam equilibrium equations, 391 Constrained recovery, 282 Beam strain, 354, 356 Constrained-recovery behavior, 240 Beam theory, 305 Contracted notation, 314 Bending deformation, 367 Convection coefficient, 267 Bending moment, 456 Coordinate transformation, 309, 448 Bending stiffness matrix, 461 Couette flow, 701 Bimorph sensor, 175 Coupling Bimorphs, 6 bending-bending, 462 Bingham number, 708, 716 bending-shear, 462, 478 Biot-Savart Law, 585 bending-torsion, 462, 474, 477, 481, 502 Blocked force, 140, 626 coefficient, 619, 620 Blocked-force model, 320 electromechanical, 581 Blocked stress, 215 extension-bending, 462, 481 Blocking torque, 759 extension-extension, 462 BM600, 670 extension-shear, 462, 477 small-signal characteristics, 670 extension-torsion, 462, 481, 499 Boundary condition extension-twist, 478 axial-spring supported, 411 in-plane-out-of-plane, 480 bending-spring supported, 317, magneto-mechanical, 581 411 Coupling coefficient clamped, 317, 410 electromechanical, 846 free, 317, 410 Coupling efficiency, 521 hinged, 410 bending-torsion, 523 linear-spring supported, 317 displacement-based, 521 pinned, 410 energy-based, 521 roller supported, 411 extension-torsion, 521 simply supported, 317, 410 torsion vertical-spring supported, 411 extension and bending comparison, 524 Boundary conditions Coupling stiffness matrix, 461 force, 458 Critical stress, 206 geometric, 458 end of transformation, 224 kinematic, 458 start of transformation, 224 Boyd-Lagoudas model, 218, 227 Critical stress-temperature diagram, 220, 223, 243 Brinson model, 221, 263 Cross-ply laminate, 479 Buehler, W. J., 14 Crystal axes, 599

Index 899

Crystal categories, 113 Empirical constants, 243 Curie Pierre, 11, 113 Energy Curie temperature, 172, 584, 593, 601, 677 anisotropy, 615 Curie-Weiss law, 677 elastic, 616 Cyclic loading, 268 exchange, 615 Cycling long-range coupling, 615 AC, 148, 155 magnetic, 616 DC, 148 magneto-elastic coupling, 616 strain, 616 Damping Energy density, 769 active constrained layer, 880 Energy formulation, 392 constrained layer, 877 Energy harvesting, 863 Damping coefficient, 711 cantilever beam, 866 Damping mechanism piezoelectric flow mode, 701 modeling, 864 mixed mode, 704 vibration-based, 863 shear mode, 701 wind-based, 864 squeeze mode, 702 Energy index, 769 types of, 701 Energy methods, 615 DC bias magnetic field, 629 Energy transfer, 782 Delta-E effect, 584, 617, 622 Engineering notation, 314 Demagnetization, 595 Environmental heating, 241 Depoling, 161 Equivalent single-layer (ESL) model, 573 Detwinned martensite, 220 Equivalent single-layer (ESL) theory, 431, Diamagnetic, 593 446 Dielectric breakdown, 161 ER and MR fluid dampers, 700 Differential Scanning Calorimeter, 229, ER/MR fluids, 25, 685 231 behavior, 686 Dipole moment, 120 comparison, 693 Directional solidification, 583 composition, 686 Discrete-layer model, 576 damper modeling, 704 Displacive transformation, 198 annular-flow passage, 725 Dissipation factor, 154, 674 rectangular-flow passage, 705 Domain, 120 device performance, 694 Drift phenomenon, 147, 152 dynamic behavior, 693 Dual actuators, 338 in-use thickening, 29, 693 Duhem, P., 113 models, 694 Bing Max, 699 E-glass, 447 Bingham plastic, 696 Eddy current, 609, 637 biviscous, 697 Effective stiffness, 784 equivalent viscous damping, 695 Electric displacement vector, 116 extended Bingham, 699 Electric enthalpy, 865 Eyring, 700 Electric field vector, 116 Herschel-Bulkley, 697 Electric permittivity matrix, 116 hysteretic biviscous, 698 Electrical impedance, 596 nonlinear viscoelastic-plastic, 699 Electromechanical coupling coefficient, 138 phenomenological, 695 Electromechanical impedance, 163 three-element, 699 Electromechanical variational indicator, MR damper, 28 865 MR sponge, 29 Electrorheological (ER) fluid, 6, 685 temperature dependence, 692 Electromotive force, 598 yield behavior, 690 Electrorheological effect, 685 Euler-Bernouli model, 361, 395 Electrostrictive materials, 662 Ewing, 22 Electrostrictives, 5, 19, 581 Extension-bending coupling, 363, 404 induced-free strain, 20 Extension-bending-torsion beam model, 385 lead magnesium niobate, 20 Extensional stiffness matrix, 461 lead magnesium niobate-lead titanate, 20 Extrinsic effect, 154 Elemental force vector, 414 Elemental mass matrix, 414 Fatigue effect, 153 Elemental stiffness matrix, 414 Ferroelectric ceramics, 114

900 Index

Ferrofluid, 687 Induced response, 377 Ferromagnetic, 593 Inductance, 589 Ferromagnetic shape memory alloy (FSMA), Integrated systems, 739 643 Interdigitated electrodes, 748 Fiber angle, 448 Interior-noise control, 884 Fiber optics, 6 Internal energy, 865, 867 Fiberglass, 447 Interpolation functions, 413 Field-induced magnetostriction, 602 Iron-gallium alloy, 641 Finite element method (FEM), 411 Isotropic material, 313, 448 Finite-thickness bond, 345 Isotropic plate, 457 First-order shear deformation theory (FSDT), antisymmetric actuation, 465 421, 532 symmetric actuation, 463 Flextensional actuators, 31 Isotropic ply, 475 Cymbal, 31 Isotropic symmetry, 311 Moonie, 31 RAINBOW, 31 Jiles-Atherton model, 610 THUNDER, 31 Joule effect, 583, 625 Flexural stiffness, 366 Joule magnetostriction, 603 Flow-passage area, 717 Joule, J., 22, 582 Fluid impedance, 800 Fluid-transfer matrix model, 804 Kennelly convention, 596 Free displacement, 140, 626 Kirchhoff-Love hypothesis, 450, 531 Free-standing zone melt (FSZM), 583 Frequency rectification, 772 Lagrange’s equations, 402, 491, 504, 530 Fringing factor, 589 Lamina, 446 Froude-scaled rotor, 760 Laminate, 446 Laminated plate stiffness matrix, 481 Galerkin method, 392, 397, 489, 496, 498 Langevin, 11, 114 Galfenol, 583, 641 Latent heat, 266 Gauss, 597 Lateral mode, 121 Gauss’s law, 598 Layer-wise model, 576 Generally orthotropic lamina, 449 Layer-wise theory, 546 Giant electrorheological effect, 26 LCR meter, 165 Giant magnetostriction, 582 Lead magnesium niobate (PMN), 5, 117 Gibbs free energy, 206, 227, 666 Lead zirconate titanate (PZT), 4, 117 Gilbert, 597 Liang and Rogers model, 220, 263 Global-force vector, 415 Likhachev model, 257 Global-mass matrix, 415 Lippmann, 11, 113 Global-stiffness matrix, 415 Load line, 140, 142, 779 Longitudinal mode, 121 Hall-effect sensor, 628 Lord Kelvin, 12, 113 Hamilton’s principle, 284, 408 Lorentz force law, 591 Hard piezoelectric material, 118 Loss factor, 853 Heat dissipation, 272 Heat-transfer coefficient, 266 Magnetic anisotropy, 600 Henry, 589 Magnetic circuits, 597 Higher-harmonic control (HHC), 811 Magnetic energy, 594 Higher-order shear-deformable theory (HSDT), Magnetic field, 585, 627 532 Magnetic-field intensity, 590 Hooke’s law, 305 Magnetic flux, 590 Hybrid hydraulic actuation concept, 775 Magnetic-flux density, 585 Hysteresis models, 145 Magnetic induction, 585 Magnetic-induction sense coil, 629 IM7/8552, 447 Magnetic moment, 591 Impedance analyzer, 165 Magnetic saturation, 594 Impedance matching, 143, 144 Magnetic shape memory alloy (MSMA), 643 In-plane forces, 456 Magnetic susceptibility, 593 Inchworm motors, 773 Magnetization, 584, 593 Individual blade control (IBC), 811 Magnetorheological (MR) fluid, 6 Induced-force vector, 461 Magnetomechanical coupling factor, 619 Induced-moment vector, 461 Magnetomechanical hysteresis, 608

Index 901

Magnetomotive force, 597, 598 Orthotropic material, 307 Magnetorheological (MR) fluid, 685 Orthotropic ply, 475 Magnetostriction, 581, 582, 599 Orthotropic symmetry, 307 Magnetostrictive, 6 actuator Paramagnetic, 584, 593 design, 630 Paul-Jacques Curie, 11, 113 power consumption, 636 Permeability of free space, 585 Magnetostrictive composite, 624 Perovskites, 117 Magnetostrictive material, 599 Phase Magnetostrictive material properties, 616 austenite, 195, 197 Magnetostrictive model, 613 detwinned, 197 linear, 611 martensite, 195, 197 nonlinear constitutive, 613 R-phase, 212, 213 Preisach, 614 twinned, 197 Magnetostrictive particulate actuator, 639 Phase Interaction Energy Function (PIEF), 228, Magnetostrictive sensor, 639 261 Magnetostrictives, 21, 581 Phase transformation, 197 Delta-E effect, 23 stress-induced, 207 Galfenol, 24 temperature-induced, 207 induced-strain, 23 Phase-transformation constant, 219 metglas, 23 Piezo stack actuators, 6 Terfenol-D, 22 Piezoceramic, 114, 117 Martensite volume fraction, 203, 219, 221, actuator equations, 124 227 basic characteristics, 119 Material constant, 306, 311 compliance matrix, 125 Material elastic constants, 305 constitutive equations, 122 Material stiffness matrix, 306 Curie temperature, 124 Matteusi effect, 583 dielectric permittivity, 130, 131 Maximum recoverable strain, 219 electric displacement, 131 Maxwell, 597 piezoelectric coefficient matrix, 126, 130 Mechanical damper, 685 polarization, 123 Mechanical hysteresis, 154 poling, 121 Mechanical systems sensor capacitance, 131 check valve, 772 sensor equations, 130 friction-based typical properties, 129 clamp and release, 772 Piezoceramic actuator, 146 traveling wave, 772 DC bias, 160 output rectification, 772 dynamic behavior, 154 roller clutch, 772 dynamic strain, 156 Metglas, 583 equivalent circuit, 170 Modeling approach, 796 power consumption, 169 Moderately large deflections, 533 static behavior, 147 Modified Bridgman (MB), 583 Piezoceramic sensors, 133 Monoclinic material, 307 Piezoceramic sheet, 123 Monoclinic symmetry, 306 Piezoceramics, 4 Multilayer symmetric laminate, 474 Piezoelectric bending, 474 actuator equation, 114 extension, 474 coefficient matrices, 117 Multimorphs, 6 constant strain, 116 constant stress, 116 Newtonian fluid, 687 constitutive relations, 115 Nickel-titanium alloy (NiTiNOL), 194 coupling coefficients, 137, 140 Nitinol, 6 coupling matrices, 117 Normal stress, 313 electrical boundary conditions, 138 hysteresis, 145 Oersted, 585, 597 open-circuit compliance, 138 Ohm’s law, 599 sensor equation, 114 Ohmic heating, 609 short-circuit compliance, 138 Ohmic loss, 637 symbols, 134 Olander, A., 14 voltage coefficient, 134 Orthotropic lamina, 447, 448 Piezoelectric active valves, 778

902 Index

Piezoelectric actuator Pyroelectric effect, 13, 113 power consumption, 163 PZT, 119 strain hysteresis, 154 spontaneous polarization, 120 Piezoelectric coefficients, 127 unit cell, 120 Piezoelectric pump, 787 PZT-5H, 119, 127, 147, 148 work done per cycle, 783, 785 effect of external stresses, 151 Piezoelectric sensor small-signal characteristics, 127 effect of temperature, 189 static free strain, 149 Poisson’s ratio effect, 182 PZT-8, 127 shear lag effect, 183 signal-to-noise ratio, 185 Quadratic response, 671 Piezoelectric sensors, 173 Quasi-static analysis, 798 Piezoelectric shunting, 842 capacitive shunt, 850 R-Phase, 220 damping, 844 R-phase transformation, 213 effective impedance, 844 Rabinow Jacob, 686 inductive shunt, 854 Rayleigh-Ritz method, 392, 401, 490, 497, 530 open-circuit compliance, 846 Read, 194 resistive shunt, 844, 849 Recovery stress, 215 shunt circuits, 847 Reissner-Mindlin model, 532 shunt impedence, 847 Reluctance, 597 stiffness ratio, 847 Remanent field, 594 Piezoelectric transducer, 137 Repoling, 163 Piezoelectricity, 11, 113 Resistive heating, 241 converse effect, 11 Restrained recovery, 249 Curie temperature, 12 Rochelle salt, 11, 113 direct effect, 11 Rotary motors, 773 hysteresis, 13 Rotor vibratory loads, 811 induced-free-strain, 13 poling, 13 S-glass, 447 Piezoelectrics, 4 Seignette salt, 12 Piezoelectrics and electrostrictors Self-sensing actuation, 9 differences, 665 Semi-active device, 686 Piezomagnetic equations, 611 Sensor calibration, 181 Pin-force model, 320 Sensors, 8 Piston area, 717 Shape functions, 413 Plastic limit, 312 Shape memory alloy, 6, 194 Plastic viscosity, 690 alloying elements, 195 Plate analysis, 446 austenite, 14 PMN-15, 665 constrained recovery, 15 PMN-38, 665 crystal structure, 195 PMN-85, 665 low-temperature stress-strain curve, 201 PMN-PT, 665 martensite, 14 Pockels, F., 113 Nitinol, 14 Poiseulle flow, 701 phase transformation, 16 Polarization, 677 pseudoelasticity, 15 Polyvinylidene fluoride, 7, 133 R-phase, 16 Porous SMA, 214 solid engine, 19 Post-yield condition, 690 thermo-mechanical behavior, 195 Pre-yield condition, 690 Shape memory alloy hybrid composites, 19 Preisach model, 159 Shape memory alloys, 14 Pressure electricity, 113 Shape memory ceramic actuators, 172 Principal axes, 309 Shape memory effect, 15, 194, 195, 197 Principle of virtual work, 393, 396, 418 all-round shape memory effect (ARSME), 212 Pseudoelastic hysteresis, 208 one-way (OWSME), 16, 202 Pseudoelasticity, 195, 204 reversible, 209 Pumping cycle, 780 two-way (TWSME), 16, 209 Pure bending, 323, 338, 366, 381 Shape memory properties, 195 Pure extension, 322, 340, 365, 381 Shear correction factor, 423, 542 PVDF sensor, 184 Shear lag, 183, 337

Index 903

Shear lag parameter, 342, 347 tip twist, 816 Shear stress, 313 tracking tab, 823 Signal-conditioning electronics, 177 trailing-edge flaps, 813 Single-layer generally orthtropic plate Smart structure technology bending, 473 applications, 741, 770 extension, 472 automotive industry, 742 Single-layer specially orthtropic plate civil structures, 741 bending, 471 electronic equipment, 742 extension, 469 energy harvesting, 743 Slender beam, 315 fixed-wing aircraft, 741 Slip, 200 jet engines, 741 SMA machine tools, 742 constitutive-model parameters, 246 marine systems, 742 annealing, 230 medical systems, 742 constrained recovery, 215 rail systems, 743 damping capacity, 256 robotics, 743 electrical resistance, 269 rotorcraft, 741 free recovery, 215 space systems, 741 macroscopic phenomenological models, 217 Smart structures, 3 micromechanics-based thermodynamics active structures, 4 macroscopic models, 217 adaptive structures, 4 microscopic thermodynamics models, 217 controlled structures, 4 non-quasi-static behavior, 259 intelligent structures, 4 power requirements, 269, 289 sensory structures, 4 quasi-static conditions, 259 Smart structures programs, 31 quasi-static loading, 260 active aeroelastic wing, 43, 49 quasi-static macroscopic phenomenological active automobile suspension, 72 models, 217 active engine mount, 74 resistance variation, 270 active flow control, 46 strain energy change rate, 265 active interior-noise control, 51 strain-rate effect, 261 active knee brace, 77 stress-relaxation, 260 active palpation sensor, 81 tension and compression, 258 active railway-vehicle relief buffer, 88 thermomechanical energy equilibrium, 264 active space truss, 37 torsional analysis, 272 active twist rotor blade, 57 torsional testing, 276 actively controlled response of buffet-affected SMA actuator tail, 50 load line, 216 adaptive reflector, 41 SMA damping, 257 adaptive satellite mirror, 41 SMA embedded composite, 281, 286, 296 adaptive skin, 44 SMA wire, 214 ADAPTRONIK, 32 cycling, 229 artificial fingers, 78 material constants, 267 artificial hand, 78 SMA wire testing, 229 artificial muscles, 78 SMA-in-sleeve, 282, 284, 292, 294 ASSET, 32 Smart actuators, 7 automobile interior-noise control, 74 output energy density, 8 automotive systems, 71 Smart helicopter rotor, 810 beam-steering antennae, 88 active blade tip, 816 bending-torsion coupled beam, 56 active twist, 812 biocompatible MR fluid, 81 adaptive controller, 819 CHAP, 32 bending-torsion coupling, 816 civil structures, 61 extension-torsion coupling, 817 CLAS, 32 Froude-scaled, 813 deformable-mirror control, 37 full-scale, 818 double-lever amplification mechanism, 56 Mach-scaled, 813 earthquake mitigation, 67 model-scale, 812 electronic-damping control, 35 piezoelectric tube, 818 electronics equipment, 86 SMA torsional rod, 824 energy harvesting, 90 SMA wire, 824 ER/MR dampers for large civil structures, 67

904 Index

Smart structures programs (cont.) SPICES, 32 evaluation of new actuators in buffet loads structural acoustic control, 40 environment, 49 synthetic jets, 46 fiber bragg grating sensors, 40 trailing-edge flaps, 55 fixed-wing aircraft, 41 ultrasonic motors, 87 German buffet suppression program, 50 URI, 31 haptic feedback devices, 75 variable geometry chevrons, 52 health monitoring of civil structures, 62 variable geometry nozzles, 52 helicopter interior-noise control, 60 variable resistance exercise machine, 80 high-speed machining, 68 vibration isolation, suppression, and steering, high-speed train bogies, 89 40 high-speed traversing mechanism, 70 X-frame mechanism, 56 human blood vessel microrobot, 82 Soft piezoelectric material, 118 inflatable space structures, 39 Solenoid, 588 integrated vehicle health monitoring, 45 Sommerfeld convention, 596 intelligent press, 71 Specific energy index, 769 jet engines, 51 Specific heat, 266 machine tools, 68 Spontaneous magnetostriction, 602 magnetorheological finishing, 71 Squeeze mode, 734 marine systems, 75 State-space method, 799 medical systems, 77 Static free strain, 159 minimally invasive surgery, 81 Stiffness matrix, 308 MR force feedback system, 81 Storage modulus, 853 multifunctional structures, 45 Strain energy NASA morphing project, 34, 50 bending, 404 piezoelectric fuel injectors, 75 extensional, 404 piezoelectric transformer, 87 Strain energy distribution, 565 prosthetic devices, 77 Strain hysteresis, 608, 673 rail, 88 Strain sensors, 173 reconfigurable wing, 44 Strain vector, 115 robotic gripper, 90 Strain-force index, 144 robots, 89 Strain-temperature curve, 235 rotary-wing aircraft, 53 Stress Sandia gamma truss, 39 axial, 362 satellite ultra-quiet isolation technology normal, 362 experiment, 40 Stress-induced martensite, 204 shape memory alloy thermal tailoring Stress-influence coefficient, 219 experiment, 38 Stress resultant, 454 SMA actuated hydrofoil, 76 Stress vector, 115 SMA anal sphincter, 80 Stress-induced martensite volume fraction, SMA catheter, 83 221 SMA eye prosthesis, 79 Stress-strain-temperature diagram, 204 SMA eyeglass frames, 83 Stroke amplification SMA implants, 85 mechanisms, 744 SMA stents, 83 Superelasticity, 204 SMA torsional tube actuator, 59 Swashplateless rotor, 812 SMA tracking tab, 58 Symmetric laminated plate, 492 smart aircraft and marine propulsion system demonstration project, 53 Tanaka model, 218, 263 smart material actuated rotor technology, 60 Temperature effect, 607, 676 smart materials and structural systems, 33 Temperature-induced martensite volume fraction, smart papermill, 70 221 smart skins structures technology demonstrator, Tensorial notation, 314 32 Terfenol-D, 6, 581, 582, 600, 601, 612, 613, 617, smart sleeve demonstration system, 76 621, 624, 625, 627 smart structural systems, 33 material properties, 617 smart tip rotor, 56 Tesla, 591, 597 smart wing program, 47 Thermo-elastic constant, 219 space experiment and mid-deck active control Thin bond, 346 experiment, 40 Timoshenko beam theory, 421, 532 space systems, 35 Tip slope, 384

Index 905

Tonpilz transducer, 625 MKSA (Meter-Kilogram-Second-Ampere), 596 Training SI, 596 two-way shape memory effect, 210 Transformation function, 223 Variable-stiffness composite beams, 282 Transformation temperature, 202, 231, 233 Variable-geometry truss, 33 austenite finish (Af ), 202 Villari effect, 22, 583, 625 austenite start (As), 202 Virtual strain energy, 488 martensite finish (Mf ), 202 Virtual work, 491 martensite start (Ms), 202 Viscoelastic material, 848, 878 Transmission-line approach, 804 Viscosity measurement techniques, 687 Transresistance amplifier, 180 Voigt, W., 12, 113 Transverse shear forces, 455 Voltage follower, 177 Transversely isotropic symmetry, 311 Volume factor, 694 Trigger line, 207 von Hippel, 12 Twin pair, 198 von Karman analysis, 537 Twin variant, 644 von Karman nonlinear strain, 534 field-preferred, 645 stress-preferred, 646 Weber, 597 Twinning, 198 Wiedemann effect, 583 Type I material, 202 Winslow, W., 26, 685

Ultrasonic motor, 626 Yield behavior, 690 Ultrasonic motors, 774 Yield strain rate, 699 Uniform-strain model, 337, 392 Yield stress Units system dynamic, 691 CGSM (Centimeter-Gram-Second-abampere), static, 691 596 Young’s modulus, 678