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Nayfeh A.H., Mook D.T. — Nonlinear Oscillations
Nayfeh A.H., Mook D.T. — Nonlinear Oscillations



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Название: Nonlinear Oscillations

Авторы: Nayfeh A.H., Mook D.T.

Аннотация:

A self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. Begins with fundamental concepts and techniques of analysis and progresses through recent developments. Provides an overview that abstracts and introduces main nonlinear phenomena. Treats systems having a single degree of freedom, introducing basic concepts and analytical methods; extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Uses simple physical examples to explain nonlinear dispersive and nondispersive waves. Unifies notation and modifies analysis to conform to discussions. Solutions are worked out in detail for numerous examples and results are plotted and explanations are couched in physical terms. Contains an extensive bibliography.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1979

Количество страниц: 705

Добавлена в каталог: 14.05.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Kirchhoff's laws      104
Klein — Gordon equations      587 615
Korteweg — de Vries equation      608
Lagrange — Dirichlet theorem      47
Lagrange's equations: for double pendulum      262
Lagrange's equations: for nonideal system      228
Lagrange's equations: for particle on rotating parabola      72
Lagrange's equations: for ship motion      373
Lagrange's equations: for spherical pendulum      368
Lagrange's equations: for three-body problem      376—377
Lagrange's points      150 377
Lagrangian      424
Lagrangian, for plate      503 see also Lagrange's equations
Lagrangian, form of wave equation      611
Lagrangian, formulation      370
Laminated plates      502 507
Laminated plates, material      568
Lanchester-type dampers      130
Laser      107
Layered      501 506
Liapunov: function      172—174 272 273 284
Liapunov: method      172
Liapunov: stable in sense of      45
Liapunov: theorem      47
Libration point      150
Libration point of satellite      396
Lienard's method      117—119 126 147 156
Limit cycle      3 6 103 131 142 143 145 146 147 154 338 346
Limit cycle, caused by flutter      508
Limited power      see Nonideal energy source
Lindstedt — Poincare technique      54—56 66 67 94 293 304 445 617 994
Lindstedt — Poincare technique, applied to current-carrying conductor      71
Lindstedt — Poincare technique, applied to Hill's equation      295—299
Lindstedt — Poincare technique, applied to Hill's equation, with damping      300 301
Lindstedt — Poincare technique, applied to Mathieu equation      286—290
Lindstedt — Poincare technique, applied to membrane      505
Lindstedt — Poincare technique, applied to particle on rotating parabola      76
Lindstedt — Poincare technique, applied to simple pendulum      66—67
Linear damping      96 123 124 131—134 149 163
Linear damping, combined with Coulomb damping      152
Linear damping, combined with hysteretic damping      237
Linear damping, combined with negative damping      153
Linear damping, effect on frequency-response curves      167 178
Linear damping, effect on parametric combination resonance      320—321
Linear damping, effect on stability      300 320 341
Linear damping, large      156
Linear transformation      111
Linearization      see Equivalent linearization
Lipschitz function      108
Load      85
Load, axial      448
Load, displacement equations      502
Load, distributed      479
Load, eccentric      268
Load, impulsive      264 267
Load, moving      445 608
Load, periodic      343
Load, piecewise constant      267
Load, pulsating      545
Load, random      267 509
Load, repeated pulses      267
Load, short-duration      455 see also Buckling; Follower force
Lobe      567
Locking phenomenon      19 20 107 209
Locomotive      259
Longitudinal inertia      448 450—452 455 487
Longitudinal oscillations, coupling with transverse oscillation      450—452 455—460 488 533
Longitudinal waves      36 544—583 571 601
Longitudinal waves, effect of damping on      563
Longitudinal waves, simple      553—555
Losses of electric motor      225 563
Lossless, model      562
Lossless, model, medium      587
Lunar perigee      273
Machine, Q      107
Machinery      269
Main resonance      see Primary resonance
Mass, end      267
Mass, end, accelerating      486
Mass, end, concentrated      444 447
Mass, end, concentric, rigid      507
Mass, end, distributed      267 444
Mass, end, moving, particles      269
Matched asymptotic expansions      144
material      see Elastic; Hyperelastic; Nonlinear; Transmission
Material damping      100
Mathieu equation      20 22 259 274 277 309 352
Mathieu equation with linear damping      22 23 300
Mathieu equation with nonstationary excitation      302—304
Mathieu equation with quadratic damping      341
Mathieu equation, bounded solutions of      279
Mathieu equation, nonlinear      25 338 339
Mathieu equation, transition curves for      21 278 314
Mathieu equation, treated by Hill's determinant      284—286
Mathieu equation, treated by method, of multiple scales      290—295
Mathieu equation, treated by method, of strained parameters      286—290
Mathieu equation, unbounded solutions of      278
Matrix equation      446
Maxwell fluid      100
Mechanical-electrical system      261
Membrane      31 274 387
Membrane energy      503
Membrane, equations of      505
Membrane, spinning      542
Membrane, waves in      571 see also Disk
Merging of shocks      566
Method: collocation      50
Method: finite-element      50
Method: Galerkin      30 50—63 88 90
Method: geometrical      365
Method: iterative      50
Method: Krylov — Bogoliubov      62
Method: Krylov — Bogoliubov — Mitropolsky      6 2
Method: Lie series      62
Method: matched asymptotic expansions      144
Method: of equivalent linearization      87 89
Method: of harmonic balance      59—61 86 92
Method: of strained parameters      see Averaging; Isocline; Lindstedt-Poincare technique; Multiple scales; Renormalization
Midplane      see Stretching
Missile      227
Missile, flexible      269
Mixed boundary-and initial-value problem      552
Modal, solution      365 433
Modal, solution, damping      451 457 491
Modulation      107 387 394 395
Modulation, instability      593—595
Modulation, nonstationary      594
Modulation, stability      590—593
Modulus      583. See also Young's modulus
Moment, rolling      99
Moment, rolling, bending      501
Moment, rolling, of inertia      545
Moment, rolling, periodic      268
Moment, rolling, pitching      99
Moment, rolling, twisting      501
Momenta, generalized      400
Monochromatic waves      584 588—590 615 616
Motion, whirling or nonplanar      35
Motion, whirling or nonplanar, integral of      424
Motion, whirling or nonplanar, nonexistence of periodic      29 410 411
Motor      224 225
Multifrequency excitation      4 14 163 183—195 196 201 216 242—245 247—254 357 402
Multifrequency excitation of beam      460
Multifrequency excitation, parametric      359
Multimodal      460. See also Coupling of
Multiple scales, method of      56 120 121 132 138 270 445 446
Multiple scales, method of, applied to Mathieu equation      290—294
Multiple scales, method of, description      56—59
Multiple scales, method of, generalized      158 438 443 447 571
Multivalued      562 563 566 567 570 571.
Mutual inductance      see Circuit
Natural frequency: for clamped-clamped beams      530
Natural frequency: for hinged-clamped beam      469
Natural frequency: for hinged-hinged beam      460
Natural frequency: for plate      512
Natural system      72
Negative damping      4 95 103—107 129—131
Negative damping with hysteretic damping      236
Negative damping, mechanical system exhibiting      105
Negative dampingwith viscous damping      153 see also Rayleigh equation; van der Pol equation
Network, characteristic      551
Nodal pattern      441
Nodal pattern, point      113
Node      6 113—115 207 208 344
Nonautonomous      see Autonomous system
Nonconservative single-degree-of-freedom-system      3 95
Nondispersive waves      35 544 545.
Nonexistence, of periodic motions      26 29 410 411 460
Nonexistence, of periodic waves      576
Nonideal energy source      7 100 161 224
Nonideal energy source in missile motion      443
Nonideal energy source, effect on buckling of column      360
Nonideal energy source, nonideal system      224—234
Nonintegrable system      388
Nonlinear damping      96 97 123—125 134—136 154 155 235 238 246
Nonlinear damping for string      486
Nonlinear damping for systems with varying parameters      141
Nonlinear damping with Coulomb damping      152
Nonlinear damping with hysteretic damping      237
Nonlinear damping with viscous damping      153
Nonlinear damping, effect on parametric resonance      339 341 354 355 358
Nonlinear: coupling      see Internal resonance
Nonlinear: cubic      366 402 417
Nonlinear: due to large deformation      39 42
Nonlinear: geometric      30
Nonlinear: inertia      40—42
Nonlinear: material      40
Nonlinear: phenomena in nature      13 181
Nonlinear: quadratic      14 366
Nonlinear: sources of      30 39—42 444
Nonlinear: strongly      365 see also Elastic systems
Nonnatural system      72
Nonplanar motion      35 369 442
Nonplanar motion of beam      447—449 487
Nonplanar motion of string      485—500
Nonresonant excitations: of Duffing equation      174
Nonresonant excitations: of self-sustained systems      209
Nonstationary vibrations      11 136—142 158 162 185 202 219—224 438
Nonstationary vibrations, excitation      255 256
Nonstationary vibrations, modulation      594
Nonstationary vibrations, parametric excitation      302—304 see also Passage through resonance; Stationary process
Nonuniform      see Heterogeneity; Secular terms; Small divisor
Nonuniformity      557. See also Secular terms; Small divisor
Norm of vectors      108
Normal solutions      21 274 277
Normal solutions for Mathieu equation      284
Normal solutions, form      275 276
Normal solutions, mode      365 433 445
Normalized      see Renormalization
Numerical methods      30 365 445
Numerical methods, disadvantages of      412
Numerical-perturbation methods      30 445 447
Nutational motion      442
Oblate earth      396
Oil drilling platforms      374
Optics      587 601
Optimal linearization      see Equivalent linearization
optimize      88
Orbit      257 331 376 396
Ordering of damping, excitation, and nonlinearity      164 196 198 204 229 388 402 418 452 453 455
Orthotrophy      501 502 507
Out of plane      see Nonplanar motion
Oval      447
Overtone      see Higher-harmonic resonances; Superharmonic resonance
pair      see Fractional-harmonic pair
Panel      472 501
Panel, curved      506
Panel, flutter      509
parabola      167
Parabola, arch      268
Parabola, exercise with variable spin      351
Parabola, particle on a rotating      72—76 78
Parabolic equations, coupled      595—599. See also Schroedinger equation
Parameter, slowly varying      140
Parameterized      577 610
Parametric excitation      161 406
Parametric excitation in electrical-mechanical systems      261 349
Parametric excitation in hinged-clamped column      424
Parametric excitation in hinged-hinged beam      528
Parametric excitation in multidegree-of-freedom-systems      279
Parametric excitation in pendulums      260 262 350 351
Parametric excitation in strings      489 524
Parametric excitation in swinging spring      360
Parametric excitation of plates      508
Parametric excitation, combined with external excitation      356 357 358
Parametric excitation, high frequency      302
Parametric excitation, multifrequency      359
Parametric excitation, nonideal      360
Parametric excitation, nonlinear      353 355
Parametric excitation, nonstationary      302—304
Parametric resonance      20—26 258—264 374
Parametric resonance in gyroscopic systems      331—338
Parametric resonance in multidegree-of-freedom nonlinear systems      359 424—430
Parametric resonance in rotary motions      269
Parametric resonance in swinging spring      360 436
Parametric resonance in systems with distinct frequencies      23 304—321
Parametric resonance in systems with repeated frequencies      321—331 359
Parametric resonance, analyzed by method of harmonic balance      352
Parametric resonance, caused by multifrequency excitation      359
Parametric resonance, effect of linear damping on      22 267—268 300 301 320
Parametric resonance, effect of nonlinearities on      268 338—348
Parametric resonance, effect of other nonlinear damping      354 355
Parametric resonance, effect of quadratic damping      341
Parametric resonance, Parametric resonance, nonstationary      302—304
Parametric resonance, principal      258 259 300
Parametric resonance, single-degree-of-freedom-systerns      283—304 355
Passage through resonance      219—223
Peak, rounded      565
Pendulum: attached to rotating base      350
Pendulum: attached to spring      432 434
Pendulum: attached to wheels      82 83 431
Pendulum: centripetal      387 388
Pendulum: clock      155
Pendulum: compound      305
Pendulum: coupled      395
Pendulum: double      262 305 358 387 430
Pendulum: equation      609
Pendulum: forced      239
Pendulum: gyroscopic      261 338
Pendulum: inelastic collision      82
Pendulum: inverted      302
Pendulum: on rotating frame      79 80
Pendulum: parametrically excited      20 21 260 262 338 349
Pendulum: phase plane      65
Pendulum: rod      82 430 431
Pendulum: rotating or spinning      64
Pendulum: spring      26—27 261 369—370 432 436
Pendulum: with bilinear hysteresis      261
Pendulum: with dashpot      150
Pendulum: with linear damping      131—134 149
Pendulum: with quadratic damping      134—136 149
Pendulum: with rusty hinge      149
Pendulum: with slowly varying parameters      140
Pendulum: with varying length      351 see also Spherical pendulum
Period      46
Periodic motion, for multidegree-of-freedom-systems      417. See also Non-existence of periodic motion
Phase plane      1 42—49 108—119 423
Phase plane for Coulomb damping      126 127
Phase plane for current-carrying conductor      69 70
Phase plane for modulational instability      594 595
1 2 3 4 5
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