自激振动 : 理论、范例及研究方法

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-excited vibration

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

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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 vector field

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-excited vibration

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 dynamic system.

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

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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 autonomous system

3.1.3 definition of stability of equilibrium position

3.1.4 first approximation theorem of stability of equilibrium position

3.2 an algebraic criterion for stability of equilibrium position

3.2.1 eigenvalues of linear ordinary differential equations

3.2.2 distribution of eigenvalues of a asymptotic stable system

3.2.3 hurwitz criterion

3.3 a geometric criterion for stability of equilibrium position

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 equilibrium position

3.3.4 coefficient condition corresponding to the second type of critical stability

3.4 parameter condition for stability of equilibrium position

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 stable region.

3.5 a quadratic form criterion for stability of equilibrium position

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 equilibrium position

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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 autonomous system

4.5.1 formulation of equation system

4.5.2 formulation of periodic solution

4.5.3 periodic solution of van der pol equation

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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 nonlinear closed-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

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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 friction force

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-slip motion

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 of hunting

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 dynamic system

6.4.3 second type of excitation effect for stick-slip motion

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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 front wheel

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

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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 of rotor

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 rotation shaft

8.4.2 analytical expression of internal force of rotation shaft

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 deformed rotating 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

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chapter 9 self-excited vibrations from interaction of structures and 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 of classical 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 flexible structure

9.4.3 critical speed and hysteresis phenomenon of galloping

9.4.4 some features of stall flutter and its prevention schemes

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 circular cylinders

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-elastic instability

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chapter 10 self-excited oscillations in feedback control system

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 temperature derivation

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 hysteresis nonlinearity

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 and dead-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 control system

10.4.3 linearized mathematical model

10.4.4 equilibrium stability of hydraulic position control system

10.4.5 amplitude and frequency of self-excited vibration

10.4.6 influence of dead-zone on motion ofhydraulic position control system

10.4.7 influence of hysteresis and dead-zone on motion of hydraulic position control system

10.5 a nonlinear control system under velocity feedback with time delay

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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 of continuum

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 distributed parameter 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

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subject index

《自激振动：理论、范例及研究方法（英文图书）》试图揭示一切自激振动共同的形成机制，同时建立分析研究它的统一程序，从而形成这门横向分支学科的理论体系。全书共分11章，全面论述自激振动及其系统的本质特征；介绍分析研究自激振动数学模型应用的各种数学方法；介绍工程中典型的和重要的自激振动——从建立数学模型开始，通过分析研究，揭示其成因和影响因素，并指出有效的控制方法；通过归纳分析许多具体自激振动现象的实践经验，总结出自激振动现象的共同的成因机制和统一的建模分析程序。《自激振动：理论、范例及研究方法（英文图书）》可作为力学教师和相关专业研究生的教学和科研参考书，也可作为各类工程（如航天航空、军工、机械、车辆、化工、土建）技术人员的研究参考书。