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