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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
Eigenvalue for clamped-free column      31 8
Eigenvalue for hinged-hinged beam      450
Eigenvalue for plate      511
Elastic systems      444
Elastic systems, bar      544
Elastic systems, nonlinear      444 501 521 560 563
Electronic oscillator      367. See also Circuit
Electrons in crystals      273
Ellipses      205 212 500
Elliptic function      65 75 86 158 369 382 384 385 401
Elliptic function for beam      460
Elliptic function for modulational stability      593
Elliptic function for waves      588
Elliptic function, equation      550
Elliptic function, integral      86
Elliptic function, membrane      274
Elliptic function, orbit      257
Elliptic function, plate      447
Elliptic function, three-body problem      331
Energy loss      563
Energy source      7 161 224
Energy, level      1 42 173
Energy, transfer of      30 422
Energy, transfer to lower modes      485 see also Continual exchange of energy
Engine      269
Entrainment      20 209
Envelope of waves      584
Envelope of, characteristics      555
Equal-area rule      567
Equidisplacement lines      507
Equilibrium, point      2 43 47
Equilibrium, point, stable      3
Equilibrium, point, unstable      3
Equivalent linearization      87 89 446
Eta function      369
Euler — Langrange, equations      503. See also Lagrange's
Euler, land      259
Euler, land, angles      371
Eulerian form of equations      613
Exchange      see Energy
Excitation      6
Excitation, combined external and parametric      339 356 358
Excitation, external      161 258
Excitation, hard      174 209
Excitation, ideal      224
Excitation, interaction with panel flutter      509
Excitation, Jacobi elliptic function      162 338
Excitation, large amplitude      162
Excitation, multi-harmonic      267
Excitation, nonideal      224 258 364
Excitation, nonstationary      162 219
Excitation, order of      163
Excitation, parametric      20 161
Excitation, pulse      162 501 514
Excitation, Shock      501
Excitation, soft      204
Excitation, step function      162 see also Load; Multifrequency
Excited, directly      468
Expansion, straightforward      50—54
Expansion, uniform      54—63
Experiment      449 460 472
Experiment for clamped-clamped beam      530
Experiment for disks      505
Experiment for plates      502
Experiment for shells      506
Experiment for strings      485 498
Experiment for waves in tube      572 575
Filament      see Cathode
Film, liquid      107
Finite differences      30 266 445 446
Finite differences for wave propagation      566
Finite elements      30 445 446 502
Flap      269
Flexural waves      505 571 601
Flexural, rigidity      502
Floquet solutions      274
Floquet theory      21 260 287 295
Floquet theory for Mathieu equation      284
Floquet theory for multidegree-of-freedom systems      279—283 313
Floquet theory for single-degree-of-freedom systems      273—279
Flow: effect on waves in ducts      603
Flow: equations of motion      61 3
Flow: Poiseuille      587 see also Gas; Supersonic flow
Fluid interface      379 587 614
Flutter      24 508 509. in
Focal point      116
Focus      3 116 131 134 172 183 190 207 208 344
Focusing, shock      572
Follower force      25 266 305 508
Follower force, effect on freefixed column      31 7—320
Force, follower      25
Force, multiharmonic      267
Fork, tuning      20 258
Form, drag      96
Form, polar      121 see also Jordan canonical form; Normal
Foundation      267
Foundation, beam on elastic      583—601
Foundation, plate on elastic      507 508
Fourier, series      120 136 220 284 295 612
Fourier, series, expansion      460
Fractional-harmonic pair      28 367 416 418
Frame structure      447
Frame, rotating      79 80
Frequency-response curve      172 462 464
Frequency-response curve , stationary      222
Frequency-response curve for combination resonance: of Duffing equation      186 187 194
Frequency-response curve for combination resonance: of hinged-clamped beam      483—485
Frequency-response curve for Duffing equation      8 166 167 177 178
Frequency-response curve for nonideal system      226 234
Frequency-response curve for parametrically excited Duffing equation      347
Frequency-response curve for parametrically excited multi-degree-of-freedom systems      428 429
Frequency-response curve for parametrically excited van der Pol oscillator      342—343
Frequency-response curve for primary resonance: of Duffing equation      167
Frequency-response curve for primary resonance: of hinged-clamped beam      473 474 476 477
Frequency-response curve for primary resonance: of plate      518
Frequency-response curve for primary resonance: of string      495 498 499
Frequency-response curve for primary resonance: of van der Pol oscillators      189 206
Frequency-response curve for simultaneous resonance of Duffing equation      189 191 192 194
Frequency-response curve for string      534 535
Frequency-response curve for subharmonic resonance: of Duffing equation      182
Frequency-response curve for subharmonic resonance: of van der Pol oscillator      216
Frequency-response curve for superharmonic resonance: of Duffing equation      178
Frequency-response curve for superharmonic resonance: of hinged-clamped beam      480
Frequency-response curve for superharmonic resonance: of van der Pol oscillator      213 see also Response curve
Frequency-response curve, nonstationary      222 223
Frequency-response equation      8
Frequency-response equation for combination resonance of: Duffing equation      18 193 242
Frequency-response equation for combination resonance of: van der Pol oscillator      218
Frequency-response equation for hysteretic damping      236 237
Frequency-response equation for primary resonance of: Duffing equation      9 12 17 165 234 235
Frequency-response equation for primary resonance of: of hinged-clamped beam      32
Frequency-response equation for primary resonance of: of hinged-hinged beam      462
Frequency-response equation for primary resonance of: van der Pol equation      19 205
Frequency-response equation for string      495 534
Frequency-response equation for subharmonic resonance: of Duffing equation      180
Frequency-response equation for subharmonic resonance:of van der Pol oscillator      215
Frequency-response equation for superharmonic resonance: of Duffing equation      176 271
Frequency-response equation for superharmonic resonance: of hinged-hinged beam      464
Frequency-response equation for superharmonic resonance: of van der Pol equation      21 2
Frequency-response equation, comparison of stationary and nonstationary      11
Frequency: adjustment      472
Frequency: amplitude relationship      54 56
Frequency: demultiplication      181
Frequency: shift      588 see also Natural frequency; Subharmonic resonance
Friction: dry      95 96
Friction: dynamic or kinetic coefficient of      95
Friction: internal      445
Friction: linear force      96
Friction: Newton force      96
Friction: static coefficient of      95
Function, potential energy      369
Function, potential energy, general      48—49
Function, potential energy, having inflection point      46—48
Function, potential energy, having maximum      44 45
Function, potential energy, having minimum      45 46
Function, potential energy, monotonic      43 44
Functional equations      578 579
Fundamental, set of solutions      274 275 280 283
Fundamental, set of solutions, matrix      280 283
Fundamental, set of solutions, mode      421
Galerkin procedure      30 88 90 259 266 270 417 445 447
Gamma function      92 354
Gas, flow      486
Gas, flow, column      575
Gas, flow, filled tube      572 611
Gears      269
Generalized      see Multiple scales
Geometrical acoustics      555
Geometrical methods      365
Geometrical methods, acoustic      570 see also Isocline; Phase plane; State plane
Graphical construction of integral curves      see Isocline; Lienard's method
Gravity, gradient      396
Gravity, gradient, capillary      601
Grid voltage      see Circuit
Group velocity      35 586 598
Gyration, radius of      448 449
Gyroscope      396
Gyroscopic systems      27 144 378
Gyroscopic systems, free oscillations of      395—402
Gyroscopic systems, nonlinear, systems      366
Gyroscopic systems, parametrically excited      304 331—338
Gyroscopic systems, pendulum      261
Hamilton's principle      72 503
Hamilton's principle, equations      400
Hamiltonian      27 174 284 424
Hamiltonian for gyroscopic system      400
Hamiltonian, formulation      378
hard      see Excitation; Spring
Hardening      see String; Work
Harmonic balance, method of      59—61 86 92 241 242 270 272 352 445—447
Harmonic balance, method of, for Duffing equation      352
Harmonic balance, method of, for multi-degree-of-freedom systems      417
Harmonic balance, method of, for string      486
Harmonic resonance      37 38 584 596 598
Harmonic resonance in duct      614
Harmonic resonance, second      150 601
Harmonic, higher      56. See also Fractional harmonic pair; Resonance
Heat equation      608
Helical      445
Hereditary damping      501
Heterogeneity      546 555
Heterogeneity in infinite bar      568—571 576—583
Higher-harmonic resonances      1 75
Hill's equation      22 259 273 277 287
Hill's equation with viscous damping      300 301
Hill's equation, coupled, equations      305
Hill's equation, determinant      22 284 331
Hill's equation, determinant, for Mathieu equation      284—286
Hill's equation, method      290
Hill's equation, treated by Lindstedt — Poincare technique      295—299
hole      592
Holonomic constraint      72 73
Honeycomb      448 472
Hookcan material      502 503
Hyperbolic equations      546—555
Hyperbolic equations, definition of      548 550
Hyperelastic      506
Hysteresis      40
Hysteretic damping      97—100 127—129
Hysteretic damping, bilinear      98 100 261 339
Hysteretic damping, effect of parametric resonance      339
Hysteretic damping, forced response of system with      235—237
Hysteretic damping, foundation      227
Hysteretic damping, hardening      98
Hysteretic damping, pointed, loop      100
Hysteretic damping, softening      98
Ideal      see Nonideal
impact      82 83
Inductance      see Circuit
Inertia, nonlinear      40—42
Inertia, nonlinear, added      371—373
Inertia, nonlinear, for membrane      505
Inertia, nonlinear, in-plane      504 506
Inertia, nonlinear, moments of      432 443 448 545 583
Inertia, nonlinear, rotary      448 500
Inertia, nonlinear, tensor      372 see also Longitudinal inertia
Infinite slope      562 563
Inflection point      46 47 70
Influence, domain of      552
Initial, conditions      9 50 51—53 56 170—173 181 183 190 206 551
Initial, conditions, strain      505
Initial, conditions, stress      505
Initial, conditions, value problem      551 552
Instability: bending-torsional      268
Instability: caused by internal resonance      402
Instability: caused by nonconservative forces      100
Instability: caused by viscosity      24
Instability: dynamic      259
Instability: of steady-state solution      410 see also Parametric resonance
Instability: regions for Mathieu equations      277—278
Instability: snap-through      269
Integral: curve      42 113 118 423
Integral: elliptic      64 75 86
Integral: Jacobi      73
Integral: of motion      173 174 424
Integrodifferential equations      487
Interaction, modal      447
Interaction, of waves      571—583
Interaction, wave-wave      584 see also Harmonic resonance; Internal resonance
Internal resonance      26 31 268 366 367 412 430—433 447 468 472 514
Internal resonance for hinged-clamped beams      469 471 475
Internal resonance for membrane      505
Internal resonance for plate      512
Internal resonance for ship motion      373 374
Internal resonance for swinging spring      360
Internal resonance for three-body problem      150—378
Internal resonance in bar      522
Internal resonance in clamped-clamped beans      530
Internal resonance in coupling of longitudinal and transverse oscillations of beam      456 458
Internal resonance in string      488 523
Internal resonance in systems, with cubic nonlinearities      390—395
Internal resonance in systems, with quadratic nonlinearities      379—387 404—417
Internal resonance, absence of      461
Internal resonance, effect on gyroscopic systems      398—402
Internal resonance, effect on parametrically excited systems      424—430
Internal resonance, to accelerate dissipation      396
Invariant, of middle surface      503
Invariant, of middle surface, second      504 see also Riemann invariant
Inverse scattering      588
Isentropic      611 612 613
Isocline, method of      117 118
Isolation, dynamic vibration      387
Isothermal atmosphere      568
Isotropic      501
Jacobi integral      73
Jacobian elliptic function      see Elliptic function
Jerky, oscillation      see Relaxation
Jordan canonical form      24 112—115 272 275 280 281 304
Jump phenomenon      8 167—171 181
Jump phenomenon in combination resonance of Duffing equation      186 194
Jump phenomenon in nonideal system      227
Jump phenomenon in parametric resonance: of Duffing equation      348
Jump phenomenon in parametric resonance: of two-degree-of-freedom systems      426
Jump phenomenon in primary resonance of Duffing equation      168—171
Jump phenomenon in string      485 498—500
Jump phenomenon in superharmonic resonance of Duffing equation      177
Jump phenomenon in two-degree-of-freedom systems      407 409
Jump rope      see Nonplanar motion
Kelvin solid      100
kinetic energy      1 42
1 2 3 4 5
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