Stiffening. See High-Frequency (HF) effects
Stiffness
[influence] coefficients, 40
load-dependent, 371
matrix, 6, 37
method, 37, 40
Stitching, method of, 176
Stochastic models, 324
Straightforward expansion, 118
Strain energy, 23, 244
Strange attractor, 330, 334
Stribeck friction, 188
Strict stability, 296
Strings
HF excited, 441
HF excited, 426, 432
natural frequencies and mode shapes, 486
with sliding point mass, 242
Strong nonlinearity, 170
Structural stability, 273, 297
Strutt diagram, 481
Stutts’ sliding bar, 46
Subcritical
bifurcation, 145, 276, 279, 362
damping, 105, 110, 371, 387
Subharmonic
motion, 328
resonance, 161
Submanifold, 286
Subspace iteration, 51
Supercritical
bifurcation, 145, 276, 279
operating speed, 457
Superharmonic resonance, 161
Supertransient chaos, 349
Suspension trick, 288, 289
Sweep-response, 254
Sylvester’s Criterion, 480
Synchronous motion, 308
System
circulatory, 44
classification, 44
conservative system, 44
dissipative, 44
gyroscopic system, 44
instationary, 44
non-conservative, 44
non-gyroscopic, 44
purely dissipative/circulatory/instationary,
44
stability, 44, 297
T
Tacoma Narrows Bridge, 228
Tangent bifurcation, 277, 293
Tangling, homoclinic, 350
Targeted energy transfer, 210
Temple quotients, 79
Tension control, 364, 377, 457
Test
function, 27, 64
vector, 51
Theorem
averaging, 179
averaging, extended, 180
center manifold, 284, 285
comparison-EVPs, 71
eigenfunction orthogonality, 69
eigenvector orthogonality, 51
inclusion, 73
Lyapunov exponents, 333, 334
minimizing eigenvalues, 70, 71
real-valueness of eigenvalues, 50, 67
saddle-node, 281
sign of eigenvalues, 68
Thermal expansion coefficients, 496
Three-torus, 344
Timoshenko
beam, 489
theory, 489
Topological dimension, 330, 336, 338
Topology of orbits, 111
Torus, 334
Trajectory. See Orbits
Transcendent equation, 55
Transcritical
bifurcation, 277, 293
conditions, 282
Transient
chaos, 349, 371
cut-off time, 345
period, 35
response, 8, 11
route to chaos, 345
Transmission shafts, 457
Transversality conditions, 281
Transverse intersection, 281, 354
Traveling wave, 18
Trefftz’s method, 87
Truncation
error, 82, 84
of mode shape expansion, 16
of Taylor expansion, 148
528
Index
Stiffness
[influence] coefficients, 40
load-dependent, 371
matrix, 6, 37
method, 37, 40
Stitching, method of, 176
Stochastic models, 324
Straightforward expansion, 118
Strain energy, 23, 244
Strange attractor, 330, 334
Stribeck friction, 188
Strict stability, 296
Strings
HF excited, 441
HF excited, 426, 432
natural frequencies and mode shapes, 486
with sliding point mass, 242
Strong nonlinearity, 170
Structural stability, 273, 297
Strutt diagram, 481
Stutts’ sliding bar, 46
Subcritical
bifurcation, 145, 276, 279, 362
damping, 105, 110, 371, 387
Subharmonic
motion, 328
resonance, 161
Submanifold, 286
Subspace iteration, 51
Supercritical
bifurcation, 145, 276, 279
operating speed, 457
Superharmonic resonance, 161
Supertransient chaos, 349
Suspension trick, 288, 289
Sweep-response, 254
Sylvester’s Criterion, 480
Synchronous motion, 308
System
circulatory, 44
classification, 44
conservative system, 44
dissipative, 44
gyroscopic system, 44
instationary, 44
non-conservative, 44
non-gyroscopic, 44
purely dissipative/circulatory/instationary,
44
stability, 44, 297
T
Tacoma Narrows Bridge, 228
Tangent bifurcation, 277, 293
Tangling, homoclinic, 350
Targeted energy transfer, 210
Temple quotients, 79
Tension control, 364, 377, 457
Test
function, 27, 64
vector, 51
Theorem
averaging, 179
averaging, extended, 180
center manifold, 284, 285
comparison-EVPs, 71
eigenfunction orthogonality, 69
eigenvector orthogonality, 51
inclusion, 73
Lyapunov exponents, 333, 334
minimizing eigenvalues, 70, 71
real-valueness of eigenvalues, 50, 67
saddle-node, 281
sign of eigenvalues, 68
Thermal expansion coefficients, 496
Three-torus, 344
Timoshenko
beam, 489
theory, 489
Topological dimension, 330, 336, 338
Topology of orbits, 111
Torus, 334
Trajectory. See Orbits
Transcendent equation, 55
Transcritical
bifurcation, 277, 293
conditions, 282
Transient
chaos, 349, 371
cut-off time, 345
period, 35
response, 8, 11
route to chaos, 345
Transmission shafts, 457
Transversality conditions, 281
Transverse intersection, 281, 354
Traveling wave, 18
Trefftz’s method, 87
Truncation
error, 82, 84
of mode shape expansion, 16
of Taylor expansion, 148
528
Index