S
Saddle, 113
Saddle-node
bifurcation, 277
perturbation stability, 294
conditions, 281
Saturated mode, 217, 225
Schmidt-orthogonalization, 71
Schwartz’s quotients, 76
Secondary
Hopf bifurcation, 293
resonance, 161
Secular terms, 119, 120, 122
Self-adjoint
EVP, 64
matrix, 50, 480
Self-excited vibrations, 171, 188, 191, 192, 435
Semidefinite EVP, 65, 66
Sequential continuation, 298
Shareware, 454
Shells, 227, 376, 494
Ships, rolling, 227, 358, 362, 376
Similarity
matrix, 111
transform, 111
Simple zero, 354
eigenvalue, 274, 279, 280, 282, 314
Singular orbit, 107
Singular point
center, 107, 115
definition of, 106
degenerate, 273
focus, 115
hyperbolic, 273
isolated, 108
marginally stable, 115
neutrally stable, 107, 115, 296
node, 113
non-degenerate, 273
non-hyperbolic, 273
saddle, 113
stability, 107
Skeleton curve. See Backbone curve
Slenderness ratio, 152
Sliding bar, Stutts’, 46
Sliding of mass, vibration induced, 210, 238,
242, 377, 437
Slow
force, 389, 410
motions, 388–391, 393, 394, 404, 406, 408,
427
time, 121, 214, 390, 392, 394, 411
Smale horseshoes, 353
Small divisor terms, 132
Smoothed image, 420
Smoothening. See High-Frequency (HF) effects
Soft bifurcation. See Supercritical b.
Softening nonlinearity, 98
Soliton, 378, 381
Solvability condition, 122, 132
Southwell’s formula, 85
Space ball, 383
Spatial chaos, 381
Spatiotemporal chaos, 381
Special EVP, 67
Spectrum
Fourier, 329
frequency, 329
of Lyapunov exponents, 333
Stability
assessment, 44
bounded, 296
confusions, 297
diagram, 143, 227, 232
engineering, 296
Lagrange, 296
local, 108, 116, 232
Lyapunov, 296
marginal, 44, 107, 115, 296
meta-, 296
neutral, 107, 115, 296
notions of, 296
of bifurcations to perturbations, 294, 297
of pitchfork bifurcation, 295
of saddle-node bifurcation, 294
of stationary solutions, 137, 157
of systems, 44, 297
orbital, 297
Poincaré, 297
strict, 296
structural, 273, 297
sufficiently small disturbances, 144
uniform, 296
Stabilizing unstable orbits, 382
Stable
equilibrium, 44
manifold, 285
State
space, 104, 107
variables, 104
Statical-dynamical analogy, 381
Static bifurcation, 294
Stationary response, 8, 133, 135, 137, 139, 168
Steel tape, twisted, 381
Step-loading, 371
Stick-slip vibrations, 188
Index
527
Saddle, 113
Saddle-node
bifurcation, 277
perturbation stability, 294
conditions, 281
Saturated mode, 217, 225
Schmidt-orthogonalization, 71
Schwartz’s quotients, 76
Secondary
Hopf bifurcation, 293
resonance, 161
Secular terms, 119, 120, 122
Self-adjoint
EVP, 64
matrix, 50, 480
Self-excited vibrations, 171, 188, 191, 192, 435
Semidefinite EVP, 65, 66
Sequential continuation, 298
Shareware, 454
Shells, 227, 376, 494
Ships, rolling, 227, 358, 362, 376
Similarity
matrix, 111
transform, 111
Simple zero, 354
eigenvalue, 274, 279, 280, 282, 314
Singular orbit, 107
Singular point
center, 107, 115
definition of, 106
degenerate, 273
focus, 115
hyperbolic, 273
isolated, 108
marginally stable, 115
neutrally stable, 107, 115, 296
node, 113
non-degenerate, 273
non-hyperbolic, 273
saddle, 113
stability, 107
Skeleton curve. See Backbone curve
Slenderness ratio, 152
Sliding bar, Stutts’, 46
Sliding of mass, vibration induced, 210, 238,
242, 377, 437
Slow
force, 389, 410
motions, 388–391, 393, 394, 404, 406, 408,
427
time, 121, 214, 390, 392, 394, 411
Smale horseshoes, 353
Small divisor terms, 132
Smoothed image, 420
Smoothening. See High-Frequency (HF) effects
Soft bifurcation. See Supercritical b.
Softening nonlinearity, 98
Soliton, 378, 381
Solvability condition, 122, 132
Southwell’s formula, 85
Space ball, 383
Spatial chaos, 381
Spatiotemporal chaos, 381
Special EVP, 67
Spectrum
Fourier, 329
frequency, 329
of Lyapunov exponents, 333
Stability
assessment, 44
bounded, 296
confusions, 297
diagram, 143, 227, 232
engineering, 296
Lagrange, 296
local, 108, 116, 232
Lyapunov, 296
marginal, 44, 107, 115, 296
meta-, 296
neutral, 107, 115, 296
notions of, 296
of bifurcations to perturbations, 294, 297
of pitchfork bifurcation, 295
of saddle-node bifurcation, 294
of stationary solutions, 137, 157
of systems, 44, 297
orbital, 297
Poincaré, 297
strict, 296
structural, 273, 297
sufficiently small disturbances, 144
uniform, 296
Stabilizing unstable orbits, 382
Stable
equilibrium, 44
manifold, 285
State
space, 104, 107
variables, 104
Statical-dynamical analogy, 381
Static bifurcation, 294
Stationary response, 8, 133, 135, 137, 139, 168
Steel tape, twisted, 381
Step-loading, 371
Stick-slip vibrations, 188
Index
527