Subject Index van der Pol equation. 1 self-excited vibration forced vibration. 1.2 vortex resonance vortex shedding Karman vortex

Transcription

1 1 self-excited vibration forced vibration 1.1 natural vibration conservative system parametric vibration non-autonomous system generalized coordinates elliptic integral homogeneous non-homogeneous primary resonance main resonance sub harmonic resonance super harmonic resonance combination frequency natural mode internal resonance combinational resonance Faraday, M. parametric resonance Mathieu s equation Strutt diagram Strutt, J. van der Pol van der Pol equation 1.2 vortex resonance vortex shedding Karman vortex nonconservative force positive definite stable equilibrium negative definite unstable equilibrium quasi-harmonic generalized dynamic system feedback closed loop Harkevich operator differential operator hybrid system Ritz-Galerkin method assumed-modes method 2 phase plane method point mapping method

2 3 Hurwitz criterion 3.5 quadratic form criterion 4 Hopf bifurcation theorem Lindstedt-Poincare method average method method of multiple scales 5 Nyquist stability criterion Popov stability criterion describing function method optimal control 6 chatter 6.3 hunting 7 nonholonomic constraint 8 fluid film force internal damping 9 flexible structure flutter cantilevered pipe classical flutter airfoil stall flutter fluid-elastic instability 10 time delay 2 phase diagram limit cycle hard excitation 2.1 Poincare, H. state space phase point phase path phase trajectory turning point center saddle characteristic equation coincident discriminant node focus spiral restoring force Rayleigh vibrator van der Pol vibrator Rayleigh equation van der Pol equation Taylor expansion nonsingular transformation attractor repellor index 2.6 soft excitation 391

3 2.7.2 relaxation vibration non-smooth Coulumb friction equilibrium zone Liénard construction continuum impulsive energy Poincare map hyperplane transversally open segment Bernoulli equation block diagram dead-zone sequential function Lamery diagram 3 stability algebraic criterion geometric criterion 3.1 Lyapunov, A. M eigenvalue problem characteristic equation characteristic value eigenvalue Routh, E. J. Routh problem Hurwitz, A. criterion of Liénard-Chipart Mihairov curve hodograph coprime 3.4 coefficient space parameter space subspace stable region boundary surface bifurcation node-saddle bifurcation Hopf-bifurcation Hopf, E Andronov, A. A. 3.5 holonomic system Lagrange s equation inertial force dissipative force gyroscopic force conservative force circulatory force quadratic form positive definite smooth function family trajectory 392

4 manifold singular point Lipschitz property topological chaotic non-degenerate eigenpair Hartman-Grobman theorem flow hyperbolic flow hyperbolic linear system invariant hyperbolic fixed point open subset open interval parameterization concomitant hyperbolicity center manifold theorem eigenspace invariant subspace invariant manifold stable manifold center manifold unstable manifold center subspace stable subspace unstable subspace 4.2 canonical form Poincare-Birkhoff normal form Poincare-Androvov-Hopf theorem 4.3 secular term fundamental frequency periodicity trivial solution 4.4 Krylov, N. M. Bogoliubov, N. N. 4.5 Sturrock, P. A. Nayfeh, A. H differential operator 5 transfer function frequency domain frequency criterion optimal algorithm input response output controller controlled object error input command control effect desired output reference input component proportional component amplification coefficient inertial component time constant oscillatory component 393

5 damping ratio integral component differential component time delay component delay time Laplace transformation rational fraction signal channel feedback channel forward channel polynomial 5.2 Nyquist criterion Nyquist, H. pole frequency response Lurie, A. I. Postnikov, V. I. absolute stability Popov, V. M Popov Theorems modified frequency response 5.4 Goldfarb, L. S. Kochenburger, R. K describing function on-off nonlinearity hysteresis saturation nonlinearity 5.5 quadratic optimal control pole allocation optimal control performance index Lagrange multiplier Euler s equation Riccati differential equation Kalman, E. Riccati algebraic matrix equation optimal control law optimal output control 6 constitutive law friction instability Leonardo da Vinci Amontons, G. Coulomb, C. A. kinetic friction Coulomb friction law static friction Stribeck curve Karnopp, D. Newton s law momentum stick-slip motion 6.2 Dudley, B. R. Swift, H. W non-smooth 394

6 6.3.1 friction drop logarithmic spiral 6.4 Gallina, P. Giobagononi, M asymmetric dynamic couple 7 dynamic shimmy tire force cornering force nonholonomic constraint D-decomposition anisotropic continuum constraint force d Alembert s principle cornering force slip angle tractive force lateral force normal force overturning moment rolling resistance moment alignment moment Brouheit, M. G. Point contact theory Stretch spring theory von Schlippe, B. Collins, R Brouheit, M. G. slip law Greidanus, J. H. Keldish, M. B nonholonomic constraint kingpin axis mechanical trail pneumatic trail freeplay Grossman, D. T. Gordan, J. T Neimark, Y. I. D-decomposition 8 internal damping aerodynamic cross coupling torsional coupling fluid film force rotor whirl planar whirl oil film force labyrinth seal force work fluid force certrifugal force synchronous whirl nonsynchronous whirl whirl frequency Jeffcott, H. H. mass unbalance supersynchronous whirl subsynchronous whirl nonsynchronous whirl 395

7 cone whirl Rankine, W. A. Jeffcott rotor hydrodynamic pressure film pressure converging wedge off-center diverging wedge Reynolds, O. Reynolds equation Newtonian fluid laminar mass conservation impermeable incompressible fluid adherence condition Gümbel condition cavitated bearing Sommerfeld s number Stodola, A. cross-coupled average circumferential velocity ratio eccentricity secondary flow oil whirl oil whip Muszynska, A. Muszynska model Poore, A. B. Hollis, P. Taylor, D. L. Deepak, J. C. Noah, S. T Lund, J. W. half-speed whirl Guo, Z. L. Kirk, R. G. Crandall, S. H. Wang, J. K. Khonsari, M. M spectrum cascade processional Ritz method finite element method hysteresis Hook s law constitutive law 9 Strouhal, V. vortex-induced vibration flutter random vibration vortex resonance airfoil galloping bluff section cross flow 9.1 Rayleigh, Lord von Karman vortex shedding bluff cylinder 396

8 stagnation pressure Reynolds numbers Lienhard, J. H. subcritical supercritical Jackson, C. P. Navier-Stokes equations Karman vortex street Strouhal number Jackson, C. P. Mach number turbulence spectrum frequency lock-in submultiple Bishop, R. E. Hassan, A. Y. Hartlen, R. T. Currie, I. G. Liénard s equation Skop, A. Griffin, O. M. lift coefficient internal resonance Scalan, R. H. Goswami, I. fluctuation shear layer taper ratio included angle 9.2 fluid-conveying Bourrieres, F. J. eigenvalue problem transverse deflection modulus bending moment tension Gregory, R. W. Paidousis, M. P Rousselet, J. Herrmann, G. slenderness friction factor self-adjoint transcendental open system Coriolis force Holmes, P. J. divergence instability Chen, S. S. 9.3 torsion plunge Lanchester, F. W. classical flutter stall flutter galloping elastic axis leading edge chordwise chord length bending rigidity the torsional rigidity quasi-steady assumption moment coefficient Joukowsky s theorem semispan lift coefficient Galerkin method 397

9 9.3.3 aerodynamic center velocity circulation circulation Lee, B. H. K. Liu, L. Chung, K. W. Sheta, E. F elastic center Maxwell s theorem reciprocity aerodynamic center midchord line plunge pitch 9.4 aeroelastic instability angle of attack lateral force coefficient attack angle Parkinson, G. V. Smith, J. D. reduced velocity dissipative force 9.5 cylinder arrays turbulent excitation acoustic excitation fluid-elastic instability added mass fluid stiffness force cross flow reduced velocity Price, S. J. Paidousis, M. P dissipative coefficient 10.2 position control command half-plane 10.4 hydraulic actuator compressibility generalized negative damping phase lag Fourier analysis frequency spectrum phase crossover feedback channel forward channel minimal model motive force vibrating body exciting body dynamic damper 398

10 wake oscillator parameter estimation grey box identification Minis, I. E. frequency domain Cochard, A Hamilton s principle undisturbed motion principal axes virtual work generalized coordinates elliptic integral configuration space stationary piezoelectric sensor actuator layer strain-energy Kirchhoff quadrilateral element Kirchhoff technique interpolation function McIver, D. B. open boundary closed boundary open volume closed volume 11.5 discretization assumed modes method finite element method lumped parameter method Euler-beam theory flexural stiffness Holzer s method Myklestad s method trial functions distribution function free end Dirac function mode function orthogonality Rayleigh-Ritz method global function local function admissible function 11.6 active control passive control Hu, H. Y. Hu, M. L. ultrasonic motor Theodorsen s aerodynamic force robust controller 399