chapter 1 introduction 1.1 main features of self-excited vibration 1.1.1 natural vibration in conservative systems 1.1.2 forced vibration under periodic excitations 1.1.3 parametric vibration 1.1.4 self-excited vibration 1.2 conversion between forced vibration and self-excitedvibration 1.3 excitation mechanisms of self-excited vibration 1.3.1 energy mechanism 1.3.2 feedback mechanism 1.4 a classification of self-excited vibration systems 1.4.1 discrete system 1.4.2 continuous system 1.4.3 hybrid system 1.5 outline of the book references chapter 2 geometrical method 2.1 structure of phase plane 2.2 phase diagrams of conservative systems 2.2.1 phase diagram of a simple pendulum 2.2.2 phase diagram of a conservative system 2.3 phase diagrams of nonconservative systems 2.3.1 phase diagram of damped linear vibrator 2.3.2 phase diagram of damped nonlinear vibrator 2.4 classification of equilibrium points of dynamic systems 2.4.1 linear approximation at equilibrium point 2.4.2 classification of equilibrium points 2.4.3 transition between types of equilibrium points 2.5 the existence of limit cycle of an autonomous system 2.5.1 the index of a closed curve with respect to vectorfield 2.5.2 theorems about the index of equilibrium point 2.5.3 the index of equilibrium point and limit cycle 2.5.4 the existence of a limit cycle 2.6 soft excitation and hard excitation of self-excitedvibration 2.6.1 definition of stability of limit cycle 2.6.2 companion relations 2.6.3 soft excitation and hard excitation 2.7 self-excited vibration in strongly nonlinear systems 2.7.1 waveforms of self-excited vibration 2.7.2 relaxation vibration 2.7.3 self-excited vibration in a non-smooth dynamicsystem. 2.8 mapping method and its application 2.8.1 poincare map 2.8.2 piecewise linear system 2.8.3 application of the mapping method references chapter 3 stability methods 3.1 stability of equilibrium position 3.1.1 equilibrium position of autonomous system 3.1.2 first approximation equation of a nonlinear autonomoussystem 3.1.3 definition of stability of equilibrium position 3.1.4 first approximation theorem of stability of equilibriumposition 3.2 an algebraic criterion for stability of equilibriumposition 3.2.1 eigenvalues of linear ordinary differential equations 3.2.2 distribution of eigenvalues of a asymptotic stablesystem 3.2.3 hurwitz criterion 3.3 a geometric criterion for stability of equilibriumposition 3.3.1 hodograph of complex vector d(ico) 3.3.2 argument of hodograph of complex vector d(ico) 3.3.3 geometric criterion for stability of equilibriumposition 3.3.4 coefficient condition corresponding to the second type ofcritical stability 3.4 parameter condition for stability of equilibriumposition 3.4.1 stable region in coefficient space 3.4.2 stable region in parameter space 3.4.3 parameter perturbation on the boundaries of stableregion. 3.5 a quadratic form criterion for stability of equilibriumposition 3.5.1 linear equations of motion of holonomic system 3.5.2 quadratic form of eigenvectors of a holonomic system 3.5.3 quadratic form criterion for a holonomic system 3.5.4 influence of circulatory force on stability of equilibriumposition references chapter 4 quantitative methods 4.1 center manifold 4.1.1 concept of flow 4.1.2 hartman-grobman theorem 4.1.3 center manifold theorem 4.1.4 equation of center manifold 4.2 hopf bifurcation method 4.2.1 poincare-birkhoffnormal form 4.2.2 poincare-andronov-hopfbifurcation theorem 4.2.3 hopf bifurcation method 4.3 lindstedt-poincare method 4.3.1 formulation of equations 4.3.2 periodic solution of the van der poi equation 4.4 an averaging method of second-order autonomous system 4.4.1 formulation of equations 4.4.2 periodic solution of rayleigh equation 4.5 method of multiple scales for a second-order autonomoussystem 4.5.1 formulation of equation system 4.5.2 formulation of periodic solution 4.5.3 periodic solution of van der pol equation references chapter 5 analysis method for closed-loop system 5.1 mathematical model in frequency domain 5.1.1 concepts related to the closed-loop system 5.1.2 typical components 5.1.3 laplace transformation 5.1.4 transfer function 5.1.5 block diagram of closed-loop systems 5.2 nyquist criterion 5.2.1 frequency response 5.2.2 nyquist criterion 5.2.3 application of nyquist criterion 5.3 a frequency criterion for absolute stability of a nonlinearclosed-loop system 5.3.1 absolute stability 5.3.2 block diagram model of nonlinear closed-loop systems 5.3.3 popov theorems 5.3.4 application of popov theorem 5.4 describing function method 5.4.1 basic principle 5.4.2 describing function 5.4.3 amplitude and frequency of self-excited vibration 5.4.4 stability of self-excited vibration 5.4.5 application of describing function method 5.5 quadratic optimal control 5.5.1 quadratic optimal state control 5.5.2 optimal output control 5.5.3 application of quadratic optimal control references chapter 6 stick-slip vibration 6.1 mathematical description of friction force 6.1.1 physical background of friction force 6.1.2 three kinds of mathematical description of frictionforce 6.2 stick-slip motion 6.2.1 a simple model for studying stick-slip motion 6.2.2 non-smooth limit cycle caused by friction 6.2.3 first type of excitation effects for stick-slipmotion 6.3 hunting in flexible transmission devices 6.3.1 a mechanical model and its equation of motion 6.3.2 phase path equations in various stages of hunting motion 6.3.3 topological structure of the phase diagram 6.3.4 critical parameter equation for the occurrence ofhunting 6.4 asymmetric dynamic coupling caused by friction force 6.4.1 mechanical model and equations of motion 6.4.2 stability of constant velocity motion of dynamicsystem 6.4.3 second type of excitation effect for stick-slipmotion references chapter 7 dynamie shimmy of front wheel 7.1 physical background of tire force 7.1.1 tire force 7.1.2 cornering force 7.1.3 analytical description of cornering force 7.1.4 linear model for cornering force 7.2 point contact theory 7.2.1 classification of point contact theory 7.2.2 nonholonomic constraint 7.2.3 potential energy of a rolling tire 7.3 dynamic shimmy of front wheel 7.3.1 isolated front wheel model 7.3.2 stability of front wheel under steady rolling 7.3.3 stable regions in parameter plane 7.3.4 influence of system parameters on dynamic shimmy of frontwheel 7.4 dynamic shimmy of front wheel coupled with vehicle 7.4.1 a simplified model of a front wheel system 7.4.2 mathematical model of the front wheel system 7.4.3 stability of steady rolling of the front wheel system 7.4.4 prevention of dynamic shimmy in design stage references chapter 8 rotor whirl 8.1 mechanical model of rotor in planar whiff 8.1.1 classification of rotor whirls 8.1.2 mechanical model of whirling rotor 8.2 fluid-film force 8.2.1 operating mechanism of hydrodynamic bearings 8.2.2 reynolds' equation 8.2.3 pressure distribution on journal surface 8.2.4 linearized fluid film force 8.2.5 concentrated parameter model of fluid film force 8.2.6 linear expressions of seal force 8.3 oil whirl and oil whip 8.3.1 hopfbifurcation leading to oil whirl of rotor 8.3.2 threshold speed and whiff frequency 8.3.3 influence of shaft elasticity on the oil whirl ofrotor 8.3.4 influence of external damping on oil whirl 8.3.5 oil whip 8.4 internal damping in deformed rotation shaft 8.4.1 physical background of internal force of rotationshaft 8.4.2 analytical expression of internal force of rotationshaft 8.4.3 three components of internal force of rotation shaft 8.5 rotor whirl excited by internal damping 8.5.1 a simple model of internal damping force of deformedrotating shaft 8.5.2 synchronous whirl of rotor with unbalance 8.5.3 supersynchronous whirl 8.6 cause and prevention of rotor whirl 8.6.1 structure of equation of motion 8.6.2 common causes of two kinds of rotor whirls 8.6.3 preventing the rotor from whirling references chapter 9 self-excited vibrations from interaction of structuresand fluid 9.1 vortex resonance in flexible structures 9.1.1 vortex shedding 9.1.2 predominate frequency 9.1.3 wake oscillator model 9.1.4 amplitude prediction 9.1.5 reduction of vortex resonance 9.2 flutter in cantilevered pipe conveying fluid 9.2.1 linear mathematical model 9.2.2 critical parameter condition 9.2.3 hopfbifurcation and critical flow velocity 9.2.4 excitation mechanism and prevention of flutter 9.3 classical flutter in two-dimensional airfoil 9.3.1 a continuous model of long wing 9.3.2 critical flow velocity of classical flutter 9.3.3 excitation mechanism of classical flutter 9.3.4 influence of parameters of the wing on critical speed ofclassical flutter 9.4 stall flutter in flexible structure 9.4.1 aerodynamic forces exciting stall flutter 9.4.2 a mathematical model of galloping in the flexiblestructure 9.4.3 critical speed and hysteresis phenomenon of galloping 9.4.4 some features of stall flutter and its preventionschemes 9.5 fluid-elastic instability in array of circular cylinders 9.5.1 fluid-elastic instability 9.5.2 fluid forces depending on motion of circularcylinders 9.5.3 analysis of flow-induced vibration 9.5.4 approximate expressions of critical flow velocity 9.5.5 prediction and prevention of fluid-elasticinstability references chapter 10 self-excited oscillations in feedback controlsystem 10.1 heating control system 10.1.1 operating principle of the heating control system 10.1.2 mathematical model of the heating control system 10.1.3 time history of temperature variation 10.1.4 stable limit cycle irrphase plane 10.1.5 amplitude and' frequency of room temperaturederivation 10.1.6 an excitation mechanism of self-excited oscillation 10.2 electrical position control system with hysteresis 10.2.1 principle diagram 10.2.2 equations of position control system with hysteresisnonlinearity 10.2.3 phase diagram and point mapping 10.2.4 existence of limit cycle 10.2.5 critical parameter condition 10.3 electrical position control system with hysteresis anddead-zone 10.3.1 equation of motion 10.3.2 phase diagram and point mapping 10.3.3 existence and stability of limit cycle 10.3.4 critical parameter condition 10.4 hydraulic position control system 10.4.1 schematic diagram of a hydraulic actuator 10.4.2 equations of motion of hydraulic position controlsystem 10.4.3 linearized mathematical model 10.4.4 equilibrium stability of hydraulic position controlsystem 10.4.5 amplitude and frequency of self-excited vibration 10.4.6 influence of dead-zone on motion ofhydraulic positioncontrol system 10.4.7 influence of hysteresis and dead-zone on motion ofhydraulic position control system 10.5 a nonlinear control system under velocity feedback with timedelay references chapter 11 modeling and control 11.1 excitation mechanism of self-excited oscillation 11.1.1 an explanation about energy mechanism 11.1.2 an explanation about feedback mechanism 11.1.3 joining of energy and feedback mechanisms 11.2 determine the extent of a mechanical model 11.2.1 minimal model and principle block diagram 11.2.2 first type of extended model 11.2.3 second type of extended model 11.3 mathematical description of motive force 11.3.1 integrate the differential equations of motion ofcontinuum 11.3.2 use of the nonholonomic constraint equations 11.3.3 establishing equivalent model of the motive force 11.3.4 construct the equivalent oscillator of motive force 11.3.5 identification of grey box model 11.3.6 constructing an empiric formula of the motive force 11.4 establish equations of motion of mechanical systems 11.4.1 application of lagrange's equation of motion 11.4.2 application of hamilton's principle 11.4.3 hamilton's principle for open systems 11.5 discretization of mathematical model of a distributedparameter system 11.5.1 lumped parameter method 11.5.2 assumed-modes method 11.5.3 finite element method 11.6 active control for suppressing self-excited vibration 11.6.1 active control of flexible rotor 11.6.2 active control of an airfoil section with flutter references subject index
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