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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
Absorber, vibration      370 387
Accelerating mass      486
Acoustic, field      509
Acoustic, geometrical method of      555 570
Acoustic, waves      614
Adjustment of frequencies      472 475 479 482
Adjustment of frequencies for plate      519
Aerodynamics      98—100
Aeroelastic systems      269
Airplane      181
Airstream      508 601
Analog, simulation      266 306
Analog, simulation, dynamic: of Berger's equations      504
Analog, simulation, dynamic: of von Karman's equations      503
Analytic method      445
Analytic method of characteristics      555 556 571 582 609
Analytic method, advantages of      411
Analytical techniques      see Method
Andronov and Witt, method of      206
Angle of attack      98 99 443
Angle ply      502
Anisotropic      502 508
Annular, plate      502 508
Anode      see Circuit
Aperiodic      221
Arc discharge      107
arch      267 268 447
Area, equal, rule      507
Artificial satellite      see Satellite
Aspect ratio      504
Asymmetries      442
Atmosphere      228 443 568
Attenuation      563 564 566
Attitude stability, satellite      331
Attraction      see Domain
Autonomous system      165 175 179 270 340 417
Autonomous system, equations      229
Autoparametric resonance      269 406.
Averaging, methods of      62 63 121—122 137 138 270 309 311 369 445 555
Averaging, methods of, for coupling of modes in strings      417
Averaging, methods of, for multi-degree-of-freedom systems      417
Averaging, methods of, for nonideal systems      229—231
Averaging, methods of, for parametrically excited systems      354 424
Averaging, methods of, for strongly nonlinear problems      157
Averaging, methods of, for waves in bars      571 575 607
Axial      448 455
Axial, prestressing      460
Axial, restraint      460
Axle      82
Backbone curve      167
Ballooning motion      see Nonplanar motion
Band      269
bar      35 36
Bar, curved      268
Bar, finite      571—583
Bar, longitudinal waves along      544
Bar, nonlinear elastic      521
Bar, nonuniform      519
Bar, rotating      448
Bar, waves along      544—583
Basin      568
Beam      30 192 224 387 447—485
Beam on elastic foundation      35—38 445
Beam with varying properties      447. See also Column
Beam, buckled      433 447
Beam, cantilever      448
Beam, clamped-clamped      530—533
Beam, curved      449
Beam, dynamic buckling of      24
Beam, equations of motion      448
Beam, hinged-clamped      32—35 420 469—485 529
Beam, hinged-hinged      452—455 460—468 525—529
Beam, longitudinal inertia      445 455—460
Beam, longitudinal-transverse coupling      450—452 455—460
Beam, nonlinear clastic      444
Beam, nonuniform      447
Beam, parametrically excited      24 449
Beam, plane bending of      267
Beam, supported by springs      432
Beam, survey of      444
Bearing      107 129 331
Beating, heart      6
Beating, heart, phenomenon      18 209 223 224
Belt      269
Benard cells      156
Bending      192
Bending energy      503
Bending instability      268
Bending moment      501
Berger's equations      504 507 541—542
Bessel functions      240
Betatron      379
Bifurcation      65 70 75 158 494
Bisector rule      568
Blade      219
Block waves      273
Block, sliding      434
Boom sonic      568
Boundary conditions: axial restraint      460
Boundary conditions: nonlinear      445
Boundary conditions: spring      453
Boundary conditions: time-dependent      454
Boundary conditions: varying      258
Boundary-value, problem      446 551 552.
Breaking distance      562 563 571
Bubble, pulsating      100
Buckled beam      433 447 460
Buckling, dynamic      24 84 305
Buckling, dynamic, load      259 267
Buckling, dynamic, of column by nonideal energy source      360
Buckling, dynamic, of free-fixed column      317—320
Buckling, dynamic, post      506
Burgers' equation      37 562 607
Burgers' equation, exact solution of      608
Canonical form      547 550 551
Canonical form, system      174 284
Canonical form, variables      369 see also Jordan canonical form
cantilever      448
Capacitor      see Circuit
Capillary-gravity waves      601
CART      434
Catastrophe      170 171
Cathode      see Circuit
Cauchy problem      551
Center      2 45 116 207 208 349
Center for modulational instability      594
Characteristic, exponents      21 276 278 314 550 551
Characteristic, exponents, determination of      283 284
Characteristic, exponents, for Mathieu equation      285 see also Hill's equations
Characteristics      577
Characteristics, analytic method of      555 609
Characteristics, exact, of wave equation      612
Characteristics, for $n^{th}$-order system      550—551
Characteristics, for second-order system      546—550
Characteristics, of motor      225 229 283 284
Characteristics, significance of      551—553
Chattering      107
Chinchilla      367
Circle, particle on rotating      41—42 79
Circle, ring      447
Circuit, electrical      103—105 261 262 338 349
Circuit, electrical, consisting of two oscillators      374
Circular, plate      502 507—519 536—542
Classification of singular points      110—117
Classification of waves      544
Clock pendulum      155
Closed trajectory      45 49
Cnoidal waves      593
Cochlear      397
col      2 44
column      379
Column of fluid      587 611
Column with hysteresis      100
Column, buckled      443 447
Column, dynamic stability of      24 264—268 317—320
Column, imperfect      267
Column, parametrically excited      23 24 259 305 317—320 343 360
Column, stability of      460
Column, thin-walled      267
Column, variable cross section      267 see also Beam
Combination resonance      26 28 219 242 366 367 374 469
Combination resonance, destabilizing effects of viscosity on      24 268 320—321 338
Combination resonance, difference      366
Combination resonance, for Duffing equation      15 183—187 192—195
Combination resonance, for gyroscopic systems      336—338
Combination resonance, for hinged-clamped beam      480—485
Combination resonance, for hinged-hinged beam      467—468
Combination resonance, for parametric-ally excited systems      23 430
Combination resonance, for sound waves in ducts      362
Combination resonance, for systems with quadratic nonlinearities      201—203 438 440
Combination resonance, for van der Pol oscillator      216—219
Combination resonance, in machinery      269
Combination resonance, in shafts      269 396
Combination resonance, in two-degree-of-freedom systems      414—417 434 437 438
Combination resonance, in waveguides      363
Combination resonance, summed      366
Combination resonance, with repeated frequencies      325—328
Commensurable frequencies      17 186 189 192 194 203 210 218 219 366 379 394 519
Commensurable frequencies in hinged-hinged beam      461
Commensurable frequencies, destabilizing effect on gyroscopic systems      402
Compatability equations      505
Composite      445 see
Concavity      546
Conductor, current-carrying      67—71
Coning      158
Conlinua      444
Conservative single-degree-of-freedom system      1 39
Consistency condition      549
Constitutive relation      545 548
Constitutive relation for viscoelastic material      563 564
Constraint, nonlinear      445 535
Continual exchange of energy      27 366 367 370 385 394 410 411 460
Continuous systems      30 444
Control      275 231.
Convergence      388
Coordinate      372
Coulomb damper      97
Coulomb damping      95 97 106 125—127 149 234 246
Coulomb damping, combined with viscous damping      152
Coupling, nonlinear      366 373 386 394 421 447
Coupling, nonlinear, coefficients      461 469
Coupling, nonlinear, of longitudinal and transverse oscillations      440—452 455—460
Coupling, nonlinear, of modes      460 468
Crankshaft      259
Critical speed      219
Critical speed, passage through      227
Critical speed, viscous coefficient      563
Critical speed, wavenumber      37 616
Cross ply      502
Crystal      273
Cumulative      563 583
Current-carrying conductory      67—71
Current-carrying conductory, bifurcation values for      70
Current-carrying conductory, phase planes for      69 70
Curvature, large      444
Curve: backbone      167
Curve: closed      45 46 48 49 143
Curve: frequency-response      166
Curve: of constant energy      42
Curve: phase      166
Curve: stationary      222 see also Integral
Curved, beam      449
Curved, plate      509
Cusp      46 70 170
Cutout, plate with      507
CYCLE      see Limit cycle
Cylinder: containing fluid      506
Cylinder: restrained by a spring      93
Cylinder: rolling on circular surface      78 351 434 435
Damper      130 396
Damper, Lanchester-type      130. See also Coulomb damper
Damping      163
Damping from experiment      163
Damping, analytic form      97
Damping, dry friction      3
Damping, effect on parametric resonance      267—269 300 301 320 341
Damping, force      96 97
Damping, influence on response of Duffing equation      167 168
Damping, internal      331 396
Damping, mechanisms      95—107
Damping, modal      481 520
Damping, models      449
Damping, positive      95
Damping, sinusoidal function of velocity      240 see also Coulomb damping; Form drag;
Decay rate      566
Decay rate into solitions      595
Decay rate of shock      566
Decay rate, effect of internal resonance      386
Deep      see Water
Deflection, waves      571. See also Beam; Disc; Membrane; Plate; Ring; Shell; String
Deformable body      444 445
Degenerate point      47 70
Delayed, amplitude limiting      147
Delayed, shock formation      583
Delta function      467
Demultiplication of frequency      181. See also Subharmonic resonance
Dependence rate      555
Dependence, domain of      552 553
Derivative-expansion method      571. See also Multiple scales
Determinacy, domain of      552
Determinant      496 497.
Detuning      8
Detuning parameter      8 163 175 178 179 185 188 199 230 291 293 308
Dielectric      598
DIP      592
Dirac, delta function      467
Directly excited      468 471
Dirichlet      see Lagrange
Disc      444
Discontinuous, derivatives      549. See also Shock
Disk      92
Disk spinning      441 505 506
dispersion relation      544 545 585 586 596 615
Dispersive waves      35 544 545.
Dissipation, effect on waves      565 566 583
Dissipation, function      373 555
Dissipation, internal      563 see also Damping
Distortion, nonlinear      560 561 571 572 574 605.
Divergence      508
Divisor      see Small divisor
Domain, of attraction      10 172 173
Domain, of dependence      552 553
Drag force      96
Drag-out phenomenon      219
Drift      3 49 56 198 200
Drilling      374
Dry friction      see Coulomb damping
Dual-spin satellite      331 396
Duct      361 587 603 614
Duffing equation      9 10 162—195 352 516 531
Duffing equation, coupled      396
Duffing equation, parametrically-excited      343—348
Duffing equation, response to multifrequency excitation      16
Duffing equation, state plane      10
Dumbbell satellite      396
Dynamic, stability      184 259 260 264—269
Dynamic, stability, pressure      508 see also Buckling
Ears      367
Eigenvalue      23 111 11 1 234 274 275 280 283 344
Eigenvalue for beams      453
1 2 3 4 5
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