Friction, 99, 145, 364, 377, 387, 398–400, 404,
410, 417, 419, 421, 435, 437, 446
Stribeck, 188
table of coefficients, 495
Friction-induced vibrations, 171, 188, 191,
192, 435
Functional, 22, 67
variation of, 22
Function classes
admissible functions, 64
comparison functions, 64
eigenfunctions, 64
test functions, 64
G
Galerkin
discretization, 27, 284, 429, 449
equations, 78
method, 27
Galilei, Galileo, vii
Galloping vibrations, 145
General EVP, 67
Generalized
analytical resonance prediction, 429
coordinate, 6, 20
damping, 17
force, 6, 16
load, 21
mass, 14
no-resonance prediction, 427
system with HF-excitation, 389, 403, 405,
426
Generic
bifurcations, 275
models, 228
GLE, 454
Global analysis, 96, 110
GLUT, 453, 455
GnuPlot, 454
Golden Gate, 227
Grammel’s method, 87
Granular materials, 381
Graphics programming, 455
Graphs, plotting, 454
Gyroscopic
force, 43
system, 44
H
Hamiltonian
chaos, 330
Hamilton’s principle, 22
applied to a string problem, 243
Hard
bifurcation. See Subcritical b.
excitation, 160
Hardening nonlinearity, 98
Harmonic
balance, method of, 116
distortion, 173
Hausdorff dimension, 339
Hermitian
EVP, 50
matrix, 50, 480
Heteroclinic orbit, 107, 354
Higher harmonics, 124, 128, 156
High-Frequency (HF) effects, 387
biasing, 397, 400, 403, 407, 416, 437, 438,
443
smoothening, 400, 403, 407, 419, 425, 426,
435, 436
stiffening, 404, 407, 412–414, 441
High-order systems
dimensional reduction, 274, 280, 284
displaying chaos, 376
History of vibrations, vii
Holonomic constraints, 21, 22
Homoclinic
intersections, 350, 351, 354
loops, 378
orbit, 107, 351, 352, 354
points, 351
tangling, 350, 352
Hooke, Robert, vii
Hooke’s law, 12, 56, 59, 150
Hopf bifurcation, 145, 234, 278
conditions, 233, 282
secondary, 293
set, 234
subcritical (hard), 145, 279, 283, 371
supercritical (soft), 279, 283
theorem, 282
third, 344, 350
Horizon of predictability, 337, 338
Horseshoe maps, 350
Horseshoes, 353
Hurwitz determinant, 480
Hyperbolic singular point, 273
Hyper-chaos, 335
Hysteresis, 294, 305
I
Impact
analysis, 175
damper, 368
kinematic, 175, 176
522
Index
410, 417, 419, 421, 435, 437, 446
Stribeck, 188
table of coefficients, 495
Friction-induced vibrations, 171, 188, 191,
192, 435
Functional, 22, 67
variation of, 22
Function classes
admissible functions, 64
comparison functions, 64
eigenfunctions, 64
test functions, 64
G
Galerkin
discretization, 27, 284, 429, 449
equations, 78
method, 27
Galilei, Galileo, vii
Galloping vibrations, 145
General EVP, 67
Generalized
analytical resonance prediction, 429
coordinate, 6, 20
damping, 17
force, 6, 16
load, 21
mass, 14
no-resonance prediction, 427
system with HF-excitation, 389, 403, 405,
426
Generic
bifurcations, 275
models, 228
GLE, 454
Global analysis, 96, 110
GLUT, 453, 455
GnuPlot, 454
Golden Gate, 227
Grammel’s method, 87
Granular materials, 381
Graphics programming, 455
Graphs, plotting, 454
Gyroscopic
force, 43
system, 44
H
Hamiltonian
chaos, 330
Hamilton’s principle, 22
applied to a string problem, 243
Hard
bifurcation. See Subcritical b.
excitation, 160
Hardening nonlinearity, 98
Harmonic
balance, method of, 116
distortion, 173
Hausdorff dimension, 339
Hermitian
EVP, 50
matrix, 50, 480
Heteroclinic orbit, 107, 354
Higher harmonics, 124, 128, 156
High-Frequency (HF) effects, 387
biasing, 397, 400, 403, 407, 416, 437, 438,
443
smoothening, 400, 403, 407, 419, 425, 426,
435, 436
stiffening, 404, 407, 412–414, 441
High-order systems
dimensional reduction, 274, 280, 284
displaying chaos, 376
History of vibrations, vii
Holonomic constraints, 21, 22
Homoclinic
intersections, 350, 351, 354
loops, 378
orbit, 107, 351, 352, 354
points, 351
tangling, 350, 352
Hooke, Robert, vii
Hooke’s law, 12, 56, 59, 150
Hopf bifurcation, 145, 234, 278
conditions, 233, 282
secondary, 293
set, 234
subcritical (hard), 145, 279, 283, 371
supercritical (soft), 279, 283
theorem, 282
third, 344, 350
Horizon of predictability, 337, 338
Horseshoe maps, 350
Horseshoes, 353
Hurwitz determinant, 480
Hyperbolic singular point, 273
Hyper-chaos, 335
Hysteresis, 294, 305
I
Impact
analysis, 175
damper, 368
kinematic, 175, 176
522
Index