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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
Phase plane for particle on rotating parabola      74
Phase plane for pendulum with linear damping      132
Phase plane for pendulum with quadratic damping      134—136
Phase plane for Rayleigh oscillator      131 142 145—146
Phase plane for simple pendulum      4 65
Phase plane for van der Pol equation      4. see also State plane
Phase, jump      37 588
Phase, jump, adjustment      395
Phase, jump, curve      166
Phase, jump, diagram      272
Phase, jump, modulation and amplitude      387
Phase, jump, of wave      585 see also Plane; Speed
Phase, jump, plane      1 42
Phase, jump, shift      166 346
pipe      269
Pipe, waves in      572
Piston      572
Piston, engine      269
Pitch      370—374 437
Planar motion      35 44 369 442 448 485
Plane, wave      37. See also Phase; State
plasma      107 587 601
Plasma, instability      156
Plate      31 192 267 379 387 500—519
Plate with material nonlinearity      445
Plate with orthotropy      501
Plate, forced      507—519
Plate, governing equations      501—507
Plate, layered      501
Plate, parametrically excited      268—269
Plate, rectangular      501
Plate, survey      444
Plate, waves in      608 see also Annular; Berger equations; Circular; Elliptic function; Laminated plate; Ring sector
Platform, drilling      374
Ply      502
Point: bifurcation      65 70 75
Point: degenerate      46
Point: equilibrium      2 43
Point: inflection      47 70
Point: Lagrange's      150
Point: libration      150
Point: noneiementary      46
Point: regular      109
Point: triangular      150 see also Singular point; Stationary process
Poiseuille flow      587
Poisson's ratio      502
Poisson's ratio, effect on Berger's hypothesis      504
Polar form      121
Positive damping      5 95
Postbuckling      506
Potential function      567 614.
Power lines, model for      604
power supply      see Energy source
Pressure perturbation      508
Prestressing      460
Primary resonance      163 217 366
Primary resonance for Duffing equation      7—9 163—174
Primary resonance for hinged-clamped beam      32 35 470—477
Primary resonance for hinged-hinged beam      461—462
Primary resonance for motion of missile      228
Primary resonance for multidegree-of-freedom systems      402—411 417—424
Primary resonance for plates      514—519
Primary resonance for system with quadratic and cubic nonlinearities      196—198
Primary resonance for van der Pol equation      19 204—209
Profile, wave      562
Progressive wave      571 607
Pulling-out, phenomenon      19 20 107
Pulling-out, phenomenon, frequency      20 208 209
Pulse excitation      162 455
pump      269
Quartz      367
Quasi-coordinate      372
Quasi-linear system      550
Quasi-linear, equation      546
Quasi-stationary process      8
Quenching      17 18 210 211 375
Radiation, damping      100—103 371
Radiation, damping, of waves      571 583
Rancher's method      241
Random      267 508 509
Rate dependence      555
Rayleigh equation      3 6 105 130 142 147 149
Rayleigh equation, parametricahy excited      342—343 see also van der Pol equation
Rayleigh — Taylor instability      156
rectangular      see Plate
Rectilinear      502
Reentry body      442 443.
Reflection      555 562 564 571
Regenerative element      382 392
Regular, point      109
Regulator      225
Relaxation      445
Relaxation, oscillation      6 131 142—246
Relief valve      535
Renormalization      555 556 602 603
resistor      103 349
Resonance: in shock tube      572 see also Combination resonance; Harmonic resonance;Internal resonance; Passage through resonance; Roll; Secondary resonance; Subharmonic resonance; Superharmonic resonance; Sweeping through resonance; Ultra-subharmonic resonance
Resonance: main      see Primary resonance
Resonance: principal      339
Response curve: for beams      447 484 485
Response curve: for parametrically excited multidegree-of-freedom systems      426 428 429
Response curve: for string      499 see also Frequency-response curve
Response, steady-state      7
Response, steady-state, nonstationary      11 see
Restraint: axial      460
Restraint: in-plane      504
Retarded time      564
Reynolds number      96 97
Riemann invariant      548 571 613
Right-running wave      see Simple wave
Rigidity      502
Ring      267 268 447
Ring, sector plate      508
Ring, survey of      444
Ritz — Gale'rkin method      417 445
Ritz — Gale'rkin method for membrane      505
Ritz — Kantorovich method      502
Rod: rocking on circular surface      85
Rod: sliding on smooth walls      78 see
Roll, resonance      228 370—374 437 442 443
Rotary      see Inertia
Rotating, parabola      72—76 78 351
Rotating, parabola, circle      41—42 79
Rotating, parabola, coordinate system      376
Rotating, parabola, frame      79
Rotating, parabola, inertia      448
Rotating, parabola, mass      228
Rotating, parabola, pendulum      64 350 see
Rotor      129 219 269 351
Rotor, dynamics      395
Rubber      546
Rudder      181
Saddle point      2 44 109 113 116 131 134 172 183 190 207 208 344 348 349
Saddle point for modulational instability      594 595
Sandwich      448 449
Sandwich, plate      501 508
Satellite      257 331 395 396
Saturation phenomenon      26 28 29 367 374 407 410 417 459
Saturation phenomenon in shell      534
Saturation phenomenon, nonexistence of      424
Sawblade      505
Sawtooth waveform      565 566
Scaling of damping      380. See also Ordering
Scattering      588
Schroedinger equation      37 584—588
Second-harmonic resonance      see Harmonic resonance
Secondary resonance      11 163 174 366 402 412 461
Secondary resonance of multidegrec-of-freedom systems      418 see
Secular terms      54 163 412
Secular terms in parametrically excited systems      306
Secular terms, elimination of      55 58 120 132 135 136 291—293
Self modulation      593
Self-exciting system      see Self-sustaining system
Self-sustaining system      6 17 107 203—219
Self-sustaining system, oscillator      130
Self-sustaining system, two coupled oscillators      374 439
Self-sustaining system, waves in pipe      572 see also Rayleigh equation; Negative damping; van der Pol equation
Separatrices      2 44 146 594
Shaft      106 219 225 269 331 379
Shaft, Crank      259
Shaft, nonlinear clastic      444
Shaft, rotating      305 396 433
Shallow, arch      447
Shear, transverse      448 500
Shear, transverse, modulus      502
Shear, transverse, perturbation      508
Shear, transverse, wave      571
Shell      31 267 379
Shell, equations of motion      506—507
Shell, influtter      509
Shell, layered      501
Shell, nonlinear elastic      444
Shell, parametrically excited      269
Shell, survey of      444
Shift, frequency      588
Shift, frequency, wavenumber      589
Ship motion      28 370—374 379
Ship motion, multifrequency excitation of      7 43 438
Shock formation      see Breaking distance
Shock, wave      36 555
Shock, wave, condition formation      562 563 575
Shock, wave, delay      583
Shock, wave, excitation      501
Shock, wave, fitting      546 564—568
Shock, wave, in tube      572
Shock, wave, like      608
Shock, wave, structure      564
Shooting technique      446
sigma      369
Similar matrices      111
Simple wave      36 546 553—555 614
Simple wave, solution by multiple scales      555—571
Simultaneous resonance      14 24 184 185 202 217 243—245 247—254
Simultaneous resonance for Duffing equation      188—192
Simultaneous resonance for hinged-hinged beam      465—467
Simultaneous resonance for parametrically excited systems      267 309 314—317
Sine — Gordon equation      609
Single-valued      562
Singular point      43 109—117 146 165 269 344 405
Singular point, classification of      110—117
Singular point, degenerate or nonelementary      46 214
Singular point, of higher order      111 see also Center; Classification of Singular points; Focus; Nodal point; Saddle point; Stability of
Singularly perturbed system      144
Sinusoidal wave      560 561
Skew      502 507 508
Slenderness ratio      450 457
slope      see Infinite slope
Slot      486
Slowly varying      445 447.
Small divisor      163 174 306 312
Snap-through instability      269
soft      see Excitation; Spring
Soil      546
Solitary      601. See also Soliton
Soliton      37 588 590—592 594 595
Solvability condition      120 334 362 364 380 403 409
Solvability condition for gyroscopic systems      398
Solvability condition for longitudinal waves      558 567
Sommerfeld effect      227
Sonic boom      568
Sound waves      566 see also Speed of
Sound, pressure level      367
Source, energy      7 100 161.
Spacecraft      442
Spacelike      553
Speed, state      109
Speed, state, angular      230
Speed, state, critical      219
Speed, state, of propagation      560 564
Speed, state, of rotor      225
Speed, state, of sound      488 553 556 571
Speed, state, phase      544 545 596
Speed, state, shock      564
Speed, state, wave      544
Spherical pendulum      261 368—369 387 441
Spherical pendulum with moving support      261 369 439
Spin      136 158 370 442.
Spring      8 81 85 92
Spring for relief valve      535
Spring support      453
Spring, hard      40 163 167—169 462 494 516
Spring, helical      445
Spring, nonanalytic force      238
Spring, nonlinear      40 77 387 396
Spring, soft      40 163 167—169
Spring, supporting beam      432
Spring, swinging      26 261 369—370
Stability: dynamic      85
Stability: in sense of Liapunov      45
Stability: nonlinear      152
Stability: of compressed column      460
Stability: of conservative systems      47
Stability: of gyroscopic systems      401
Stability: of primary resonances: of system with quadratic non.      405
Stability: of primary resonances: string      495—500
Stability: of primary resonances: van der Pol oscillator      206—209
Stability: of response of nonideal system      233—234
Stability: of steady-state motion      171 172 273—279 418
Stability: of superharmonic response of van der Pol oscillator      213 214
Stability: regions of      278 301 319 345 423
Stability: static      84
standing waves      544 572
Standing waves, nonexistence of      576
State      108—110
State plane      166 405
State plane for Coulomb damping      126 127
State plane for Duffing equation      10 108 173 182
State plane for parametrically excited duffing equation      348
State plane for simultaneous resonance of Duffing equation      190
State plane for subharmonic resonance of Duffing equation      182 see
State, space      108
State, speed      109
Static stability      84
Stationary process      8 162
Stationary process, point      271 417
Stationary process, quasi-      8
Stationary process, waves      506 584 590 599—601 see
Steady streaming      see Drift
Steady-state response      7 65 271 382 404 416.
Steepening      561 563 570
Step-function excitation      162
Stokes flow      96
Straightforward expansion: for Duffing equation      51—54
Straightforward expansion: for simple waves      556—557 602 603
strain      444 446 447 501 503 560
Strain in bar      545
Strain, compatability of      505
Strain, initial      505
Strained, parameters, coordinates      555 556.
Stratification      555 568
Streamfunction      567
Stress      444 447 501 504
Stress in bar      545
Stress, function      505
Stress, initial      505
Stress, strain relation      546 555
Stretching, of midplane      16 51 192 195 268 343 387 444 448
Stretching, of midplane, of beam      447
Stretching, of midplane, of plate      508
Stretching, of midplane, of string      350
1 2 3 4 5
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