Applications of ATILA FEM software to smart materials: Case studies in designing devices

Y......Page 0
Woodhead Publishing Series in Electronic and Optical Materials 12......Page 12
1......Page 14
conductance for columns 3......Page 16
problem equations definition, 4-7......Page 17
variational principle, 7......Page 20
transient analysis, 16......Page 29
ATILA simulation comparison, 23......Page 36
new version capacity, 25-44......Page 39
Wilson method, 26......Page 40
contour fill of far-field, Plate IV contour fill of strain, Plate III pre-processor GiD, 27-31......Page 41
icon-elastic shell, 32......Page 46
cylinder model characteristics, 44......Page 58
nonlinearity, 45-56......Page 60
temperature rise for various soft PZT multilayer actuators, 57......Page 72
mesoscopic model, 60......Page 75
curves obtained from the mesoscopic approach, 63......Page 78
64......Page 79
finite element analysis of orthogonally stiffened cylindrical shells with ATILA, 69-92......Page 82
stiffness constant shell, 70-2......Page 83
repeating section of a ring of a cylindrical shell, 73......Page 86
boundary conditions for symmetry and anti-symmetry, 74-8......Page 87
frequency, 92......Page 105
utilisation in ATILA, 94-134......Page 107
stress tensor, 95......Page 108
piezoelectric polarisation Cartesian coordinates, 97-106......Page 110
cylindrical coordinates, 106-21......Page 119
cylindrical polarisation, 115-21......Page 128
original polarisation, 122-33......Page 135
statistical analysis, 133......Page 146
potential profile, 134......Page 147
time domain analysis of piezoelectric device with ATILA, 136-54......Page 150
acoustic signal propagation and reflection, 140-4......Page 154
future trends, 153-4......Page 167
excitation condition optimisation with user defined waveform modifications, 154......Page 168
designing with ATILA, 155-78......Page 169
finite element method (FEM) procedure, 156-7......Page 170
tiny ultrasonic linear motor, 157-66......Page 171
ultrasonic motors (USM) butterfly-shaped ultrasonic linear motor, 166-74......Page 180
7.5 Conclusions 175......Page 189
7.6 References 176......Page 190
overview, 177-8......Page 193
general formulation, 178-83......Page 194
transmitting voltage response (TVR), 183......Page 199
displacement field of the elementary cell, 185......Page 201
frequency variations of the transmitting voltage response (TVR), 188......Page 204
phononic crystal (PC) ATILA, 190-201......Page 206
different periodic lattices, 191......Page 207
modulus of the displacement field for the waveguide mode, Plate X plate of thickness h, 194......Page 210
negative refraction applications, 197-201......Page 213
gradient index phononic crystal, 201......Page 217
sonar piezoelectric single crystal behaviour study using ATILA, 203-28......Page 220
state of the art single crystal technology, 204-8......Page 221
single crystal material behaviour modelling, 209......Page 226
VDB8b, 210......Page 227
comparison of the admittance VDB8b, 217......Page 234
real part of the electrical displacement, 225......Page 243
contour fill of the Z displacement at the resonance frequency, Plate XI imaginary part of the admittance, 228......Page 246
thermal analysis piezoelectric and magnetostrictive materials using ATILA, 230-79......Page 248
heat generation in piezoelectric materials, 231-2......Page 249
piezoelectric materials implementation, 232-45......Page 250
strains and stresses in piezoelectric materials caused by thermal effect, 245-9......Page 263
stress analysis, 249......Page 267
model experimental validation, 253-65......Page 271
heat generation in magnetostrictive materials, 266-72......Page 284
3D inducer element, 272......Page 290
dissipated power for each material, 279......Page 297
11.10 References 280......Page 298
damping modelling with ATILA, 281-304......Page 301
resistor, 282-3......Page 302
equivalent circuit of piezoelectric device, 287......Page 307
dielectric coefficient and electrical network, 289......Page 309
304......Page 324
temperature and stress effect, 305-72......Page 325
material properties, 306-7......Page 326
non-linear analysis, 310-11......Page 330
piezoelectric constant g33, 312......Page 332
analytical solution, 330-3......Page 350
337......Page 357
analytical solution, 342-6......Page 362
temperature iterative computation of the sphere in air, 354......Page 374
temperature iterative computation of the sphere in water, 370......Page 390
circumferential stress along the thickness at start and final step of process, 372......Page 392
Index 374......Page 395
periodic boundary condition, 182......Page 198
Langevin transducer sending and receiving acoustic signals, 142......Page 156
ringing and damping, 144-8......Page 158
transient simulation parameters used for the Langevin transducer, 143......Page 157
modelled device, 137-40......Page 151
Langevin transducer, 138......Page 152
frequency variations, 184......Page 200
large aluminium plate, 298-304......Page 318
central transducer, 301......Page 321
modal analysis of quarter of plate, 302......Page 322
normalised displacement (RC damping at 69.1 Hz), 303......Page 323
320......Page 340
modal analysis results between analytical vs numerical solutions, 334......Page 354
344......Page 364
resonance frequency, 51......Page 66
assembly, 14-15......Page 27
static analysis, 15......Page 28
variational form, 12-14......Page 25
four-node quadrilateral element, 10......Page 23
shape function, 8......Page 21
quality factors derived by simulation and analytical calculation, 56......Page 71
55......Page 70
6......Page 19
contour fill of z-displacement, 31......Page 45
‘A’ node displacements of the ring, 118......Page 131
strained structure, 125......Page 138
illustration, 120......Page 133
fifth resonant frequency of the stiffened target at 121 Hz......Page 134
123......Page 136
ring description, 127......Page 140
piezoelectric ring geometry, 108......Page 121
fifth resonant frequency of the stiffened target at 113 Hz......Page 126
ring deformation, 114......Page 127
radial electric field, 110......Page 123
poled Z-axis, 109......Page 122
ring potential profile, 112......Page 125
illustration, 111......Page 124
piezoelectric disk piezoelectric disk under external impulse shock pressure, 139......Page 153
aluminium tube boundary, 75......Page 88
local coordinate system boundary condition, 77-8......Page 90
circular cylindrical shell, 78-85......Page 91
model test of stiffened shell, 81......Page 94
frequencies (Hz) for a ring-stiffened shell, 82......Page 95
elastic band structures calculated with the ATILA code, 195......Page 211
band structure along the GX direction calculated with a supercell, 196......Page 212
configuration and operating principle, 167......Page 181
illustration, 174......Page 188
butterfly-shaped ultrasonic linear motor, 168-74......Page 182
sixth resonant frequency of the stiffened target at 173 Hz......Page 187
mesh generation, 172......Page 186
electrical potential condition, 171......Page 185
tube boundary condition faces, 76......Page 89
material condition of tiny motor, 170......Page 184
transverse vibration mode 66 kHz,......Page 81
damping of cantilever beam, 292-5......Page 312
deflection of the end of the beam for L damping vs frequency, 296......Page 316
experimental analysis of damping of cantilever beam, 295-8......Page 315
description, 297......Page 317
Young modulus, 294......Page 314
axial displacement with RC damping vs frequency, 293......Page 313
end of beam deflection - R damping, 299......Page 319
numerical results of damping of different circuits, 300......Page 320
finite element inductor, 284......Page 304
cube, 99-106......Page 112
mesh of the cube, 100......Page 113
poled X-axis, 101......Page 114
resistor and inductor in parallel, 285-6......Page 305
resistor, inductor and capacitor in parallel, 286-7......Page 306
inductor, 283-4......Page 303
SAS mode comparison, 79......Page 92
84......Page 97
85......Page 98
nodal patterns, 83......Page 96
358......Page 378
circumferential stress, 357-8......Page 377
piezoelectric transducer, 242-45......Page 260
illustration, 116......Page 129
first and third vibration modes, 21......Page 34
structured mesh for water, 22......Page 35
convert to ATI function for generation ATILA code file, 146......Page 160
operation optimisation with customised waveform, 148-53......Page 162
parameters for the piezoelectric disk simulation, 145......Page 159
project.ati file modification to provide pulse time length, 147......Page 161
transient displacement response of the piezoelectric disk, 149......Page 163
temperature dependence, 307-9......Page 327
real part of the longitudinal stress, 324......Page 344
shell geometry, 346......Page 366
one dimensional heat transfer, 326-8......Page 346
conductance for column 5......Page 18
elastic rigidity constant, 309......Page 329
vibration velocity jump and hysteresis during rising and falling frequency, 47......Page 62
stiffened shell of elastic target, 86-92......Page 99
piezoelectric voltage constant coefficient, 316......Page 336
345......Page 365
potential profile in the cube, Plate V parallel to Y-axis, 102-4......Page 115
illustration, 103......Page 116
potential profile in the cube, Plate VI parallel to Z-axis, 104......Page 117
illustration, 105......Page 118
cylindrical coordinates, 107......Page 120
electrical displacement, 317......Page 337
58......Page 73
equifrequency contour (EFC), 199......Page 215
sphere element, 343......Page 363
thermal stress, 246-7......Page 264
axis definition for a poled Z-axis, 98......Page 111
axial stress of the cylinder vs time, 254......Page 272
259......Page 277
approximate analytical vs axisymmetrical FE model for uncoated PZT-8, 257......Page 275
coated cylinder in water in-water cylinder 2 with epoxy......Page 15
coated cylinder, 256-8......Page 274
bare cylinder in air, 258-62......Page 276
uncoated cylinder, 255-6......Page 273
with thermocouple wire, 261......Page 279
piezoelectric ceramic cylinder dimensions and measured small signal properties, 260......Page 278
coated cylinder in air, 262-5......Page 280
thermocouple, 263......Page 281
in-air convection film coefficients for different ceramic cylinders, 264......Page 282
coating, 265......Page 283
stiffened shell, 72-3......Page 85
205......Page 222
transducer material condition, 161......Page 175
fluid pressure, 356-7......Page 376
Gibbs energy curves for various electric field E levels, 61......Page 76
Boltzmann probability, 62......Page 77
247......Page 265
mesh of the bar, 321......Page 341
heat transfer coefficient as a function of applied electric field, 59......Page 74
thermal analysis implementation, 267-8......Page 285
stresses definition in shell coordinates, 71......Page 84
relationship of polarisation vs electric field, 46......Page 61
loss anisotropy, 48-55......Page 63
lead zirconate titanate (PZT), 53-5......Page 68
piezoelectric loss, 54......Page 69
resonance and anti-resonance frequencies of the bar, 322......Page 342
real part of the longitudinal strain, 323......Page 343
steady problem, 325-6......Page 345
losses determination, 315-20......Page 335
tube, 80......Page 93
quality factors derivations, 49-53......Page 64
resonance and antiresonance, 50......Page 65
result, 275......Page 293
steady temperature profile, 276......Page 294
materials definition, 277......Page 295
steady temperature profile, 278......Page 296
material looses, 269-70......Page 287
model description, 274-5......Page 292
variational formulation, 273-4......Page 291
temperature and stress effects on material behaviour, 369-70......Page 389
single crystal properties between start vs final computational steps, 371......Page 391
piezoelectric transformer, 19-21......Page 32
disk shape piezoelectric transformer with crescent curved electrodes, 20......Page 33
resonant frequencies of the stiffened target, 87......Page 100
frequency, 90......Page 103
frequency, 91......Page 104
frequency, 89......Page 102
frequency, 88......Page 101
physical properties of the motor’s elements, 163......Page 177
phononic crystal, 198......Page 214
pressure field for PC-made flat lens, 200......Page 216
flow chart, 314......Page 334
stress iterative computation at the resonance frequency, 336......Page 356
temperature and stress effects on the shell, 352-3......Page 372
temperature effect on the bar non-linear material behaviour, 328-30......Page 348
mesh of the piezoelectric cylinder, 250......Page 268
temperature profile through the cylinder, 252......Page 270
modulus of the shell radial displacement along the thickness, 349......Page 369
1D shell thermal model, 351......Page 371
real part of the shell pressure in fluid vs frequency, 365......Page 385
shell transmitting voltage response (TVR), 367......Page 387
ring behaviour, 128......Page 141
rested and deformed ring, 130......Page 143
numerical results, 129-30......Page 142
ring strained structure, 131......Page 144
project.ati modification, 151......Page 165
project.exc with user defined wave form information, 152......Page 166
transient parameters for the bimorph actuator, 150......Page 164
windmill ultrasonic motor illustration and a metal ring/finger coupled vibration mode, 18......Page 31
p-shaped linear motor dimensions, 17......Page 30
eight-node quadrilateral element, 11......Page 24
description of one unit cell of the doubly periodic structure, 192......Page 208
Alberich anechoic coating, 179......Page 195
description of a doubly periodic structure, 180......Page 196
displacement field real and imaginary parts, 187......Page 203
frequency variations of the free field voltage sensitivity (FFVS), 186......Page 202
piezoelectric cylinder, 234-42......Page 252
axial displacement with no damping vs frequency, 291......Page 311
parallel electric field, 235......Page 253
1D thermal modelling, 239......Page 257
real part of the displacement, 238......Page 256
steady temperature profile, 241......Page 259
thermal harmonic analysis piezoelectric cylinder, 40-2......Page 54
illustration, 41......Page 55
piezoelectric cylinder, 42-4......Page 56
real time from a transient analysis for the cylinder., 43......Page 57
quartz oscillator, 206-7......Page 223
piezoelectric relations, 96-7......Page 109
233......Page 251
VDB8e, 213-15......Page 230
212......Page 229
VDB9e, 215......Page 232
comparison of the admittance VDB8b, 218......Page 235
model geometry, 222......Page 240
224......Page 242
imaginary part of the pressure, 226......Page 244
real part of the impedance, 227......Page 245
real part of the axial displacement, 223......Page 241
comparison of the impedance VDB8b, 219......Page 237
mock-up transducer tested in water, 211......Page 228
new item-eigenvalue shift, 33......Page 47
real time from a modal analysis for the structure, 36......Page 50
fluid, 37-40......Page 51
structure model characteristics, 35......Page 49
modal resonance, 34......Page 48
244......Page 262
element analysis, Plate XII, Plate XIII, Plate XIV tonpilz transducer, 243......Page 261
transducer model characteristics, 38......Page 52
real time from a harmonic analysis for the transducer, 39......Page 53
transducer configuration, 158......Page 172
polarisation three resonant modes, 208......Page 225
ATILA code architecture, 28......Page 42
condition icon-initial surface or displacement, 29......Page 43
material icon, 30......Page 44
illustration, 207......Page 224
124......Page 137
strained structure with Eq electric field, 126......Page 139
1D thermal modelling, 327......Page 347
temperature iterative computation of the bar, 329......Page 349
13......Page 26
generalised n-node linear element, 9......Page 22
piezoelectric constant g33, 313......Page 333
elastic compliance constant, 311......Page 331
piezoelectric constant d33, 308......Page 328
axial stress of the driver at the resonance frequency, 340......Page 360
single crystal properties between start vs final computational steps, 339......Page 359
modal analysis results between analytical vs numerical solution, 338......Page 358
temperature in the driver, 341......Page 361
fluid shell mesh in fluid, 359......Page 379
real part of the far field pressure in fluid vs frequency, 366......Page 386
real part of the shell circumferential deformation in fluid vs frequency, 362......Page 382
real part of the shell circumferential stress in fluid vs frequency, 364......Page 384
real part of the shell radial deformation in fluid vs frequency, 361......Page 381
real part of the shell radial displacement in fluid vs frequency, 360......Page 380
real part of the shell radial stress in fluid vs frequency, 363......Page 383
shell mesh, 347......Page 367
modulus of the shell circumferential stress along the thickness, 350......Page 370
modulus of the shell radial displacement vs frequency, 348......Page 368
shell temperature along the thickness, 353......Page 373
single crystal properties between start vs final computational steps, 355......Page 375
mesh, 333......Page 353
axial stress of the driver at the resonance frequency, 335......Page 355
free bodies diagram, 332......Page 352
model, 331......Page 351
electroded surfaces, 132......Page 145
ring potential profile, 119......Page 132
section, 270......Page 288
2D inducer element, 271......Page 289
transient potential boundary and transient parameters, 141......Page 155
elongation and contraction, 159......Page 173
sawtooth electrical potential, 160......Page 174
fabrication, 165-6......Page 179
material condition, 162......Page 176
admittance, 216......Page 233
comparison of the admittance VDB8b, 214......Page 231