自激振动

出版时间：2011-4  出版社：清华大学  作者：丁文镜  页数：399  

内容概要

　　本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。
　　本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。

作者简介

丁文镜，was the Director of the Dynamics and VibrationDivision of the Engineering Mechanics Department of Tsinghua University, China.

书籍目录

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
　　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 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
　　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 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
　　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 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
　　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 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
　　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 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
　　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 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
　　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 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
　　references
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
　　references
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
　　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 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
references
subject index

章节摘录

版权页：插图：To demonstrate the conversion between forced vibration and self-excited vibration,let us consider a simple example here.  It is known that the vortex resonance is an important technical problem. Whena fluid flow crosses a cylindrical structure, the wake behind the structure is nolonger regular but distinct vortices of the pattern shown in Fig.1.will be foundin it. The vortices are alternately clockwise and anticlockwise. They are shed fromthe cylinder in a perfect regular manner, and are associated with an alternatingside-wise force. The vortex shedding on alternate sides of the cylinder causes aharmonically varying force on the cylinder in a direction perpendicular to that ofthe stream.The vortices come off with a natural frequency. This phenomenon hasbeen studied experimentally and it has been found that the frequency has a definiterelation with both the diameter of the cylinder and the velocity of the stream.

编辑推荐

《自激振动:理论、范例及研究方法(英文图书)》：Based on a systematic understanding of its theoretical foundations,Self-Excited Vibration Theory, Paradigms, and Research Methods of fersa method for analyzing any type of self-excited vibration （SEV）.Aftersummarizing the research results of various SEV phenomenon, includingchatter, shimmy, rotor whirl, flutter, gallop, and SEV of man-made controlsystems, the author constructs a general constitutive mechanism of SEV,as well as a common research program and detailed analysis technique.All of these will help the reader independently analyze any new SEVphenomena.

用户评论 (总计3条)

•   专业经典工具书
•   很好的书，尤其是阐述车轨共振的机理，能量法和反馈法
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