自激振动 理论、范例及研究方法 英文PDF|Epub|txt|kindle电子书版本下载

自激振动 理论、范例及研究方法 英文PDF格式电子书版下载

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Chapter 1 Introduction1

1.1 Main Features of Self-Excited Vibration1

1.1.1 Natural Vibration in Conservative Systems1

1.1.2 Forced Vibration under Periodic Excitations3

1.1.3 Parametric Vibration6

1.1.4 Self-Excited Vibration9

1.2 Conversion between Forced Vibration and Self-Excited Vibration12

1.3 Excitation Mechanisms of Self-Excited Vibration13

1.3.1 Energy Mechanism13

1.3.2 Feedback Mechanism15

1.4 A Classification of Self-Excited Vibration Systems16

1.4.1 Discrete System17

1.4.2 Continuous System17

1.4.3 Hybrid System18

1.5 Outline ofthe Book18

References20

Chapter 2 Geometrical Method21

2.1 Structure of Phase Plane21

2.2 Phase Diagrams of Conservative Systems23

2.2.1 Phase Diagram of a Simple Pendulum23

2.2.2 Phase Diagram of a Conservative System24

2.3 Phase Diagrams of Nonconservative Systems25

2.3.1 Phase Diagram of Damped Linear Vibrator25

2.3.2 Phase Diagram of Damped Nonlinear Vibrator28

2.4 Classification of Equilibrium Points of Dynamic Systems32

2.4.1 Linear Approximation at Equilibrium Point32

2.4.2 Classification of Equilibrium Points33

2.4.3 Transition between Types of Equilibrium Points35

2.5 The Existence of Limit Cycle of an Autonomous System36

2.5.1 The Index of a Closed Curve with Respect to Vector Field36

2.5.2 Theorems about the Index of Equilibrium Point39

2.5.3 The Index of Equilibrium Point and Limit Cycle39

2.5.4 The Existence of a Limit Cycle40

2.6 Soft Excitation and Hard Excitation of Self-Excited Vibration42

2.6.1 Definition of Stability of Limit Cycle43

2.6.2 Companion Relations43

2.6.3 Soft Excitation and Hard Excitation45

2.7 Self-Excited Vibration in Strongly Nonlinear Systems46

2.7.1 Waveforms of Self-Excited Vibration46

2.7.2 Relaxation Vibration47

2.7.3 Self-Excited Vibration in a Non-Smooth Dynamic System49

2.8 Mapping Method and its Application52

2.8.1 Poincare Map52

2.8.2 Piecewise Linear System55

2.8.3 Application of the Mapping Method56

References58

Chapter 3 Stability Methods59

3.1 Stability of Equilibrium Position59

3.1.1 Equilibrium Position of Autonomous System59

3.1.2 First Approximation Equation of a Nonlinear Autonomous System60

3.1.3 Definition of Stability of Equilibrium Position60

3.1.4 First Approximation Theorem of Stability of Equilibrium Position61

3.2 An Algebraic Criterion for Stability of Equilibrium Position62

3.2.1 Eigenvalues of Linear Ordinary Differential Equations62

3.2.2 Distribution of Eigenvalues of a Asymptotic Stable System63

3.2.3 Hurwitz criterion63

3.3 A Geometric Criterion for Stabilitv of Equilibrium Position65

3.3.1 Hodograph of Complex VectorD(iω)65

3.3.2 Argument of Hodograph of Complex Vector D(iω)66

3.3.3 Geometric Criterion for Stability of Equilibrium Position67

3.3.4 Coefficient Condition corresponding to the Second Type of Critical Stability68

3.4 Parameter Condition for Stability of Equilibrium Position70

3.4.1 Stable Region in Coefficient Space70

3.4.2 Stable Region in Parameter Space71

3.4.3 Parameter Perturbation on the Boundaries of Stable Region73

3.5 A Quadratic Form Criterion for Stability of Equilibrium Position75

3.5.1 Linear Equations of Morion of Holonomic System75

3.5.2 Quadratic Form of Eigenvectors of a Holonornic System76

3.5.3 Quadratic Form Criterion for a Holonomic System78

3.5.4 Influence of Circulatory Force on Stability of Equilibrium Position78

References79

Chapter 4 Quantitative Methods80

4.1 Center Manifold80

4.1.1 Concept of Flow80

4.1.2 Hartrnan-Grobman Theorem82

4.1.3 Center Manifold Theorem83

4.1.4 Equation of Center Manifold85

4.2 Hopf Bifurcation Method87

4.2.1 Poincare-Birkhoff Normal Form87

4.2.2 Poincare-Andronov-Hopf Bifurcation Theorem91

4.2.3 Hopf Bifurcation Method94

4.3 Lindstedt-Poincare Method96

4.3.1 Formulation of Equations96

4.3.2 Periodic Solution of the van der Pol Equation98

4.4 An Averaging Method of Second-Order Autonomous System100

4.4.1 Formulation of Equations100

4.4.2 Periodic Solution of Rayleigh Equation102

4.5 Method of Multiple Scales for a Second-Order Autonomous System103

4.5.1 Formulation of Equation System103

4.5.2 Formulation of Periodic Solution104

4.5.3 Periodic Solution of van der Pol Equation105

References107

Chapter 5 Analysis Method for Closed-Loop System108

5.1 Mathematical Model in Frequency Domain108

5.1.1 Concepts Related to the Closed-Loop System108

5.1.2 Typical Components110

5.1.3 Laplace Transformation111

5.1.4 Transfer Function112

5.1.5 Block Diagram of Closed-Loop Systems113

5.2 Nyquist Criterion114

5.2.1 Frequency Response114

5.2.2 Nyquist Criterion116

5.2.3 Application of Nyquist Criterion118

5.3 A Frequency Criterion for Absolute Stability of a Nonlinear Closed-Loop System121

5.3.1 Absolute Stability121

5.3.2 Block Diagram Model of Nonlinear Closed-Loop Systems122

5.3.3 Popov Theorems123

5.3.4 Application of Popov Theorem125

5.4 Describing Function Method127

5.4.1 Basic Principle127

5.4.2 Describing Function128

5.4.3 Amplitude and Frequency of Self-Excited Vibration130

5.4.4 Stability of Self-Excited Vibration131

5.4.5 Application ofDescribing Function Method131

5.5 Quadratic Optimal Control133

5.5.1 Quadratic Optimal State Control134

5.5.2 Optimal Output Control136

5.5.3 Application of Quadratic Optimal Control137

References139

Chapter 6 Stick-Slip Vibration140

6.1 Mathematical Description of Friction Force140

6.1.1 Physical Background of Friction Force141

6.1.2 Three Kinds of Mathematical Description of Friction Force141

6.2 Stick-Slip Motion145

6.2.1 A Simple Model for Studying Stick-S1ip Motion145

6.2.2 Non-Smooth Limit Cycle Caused by Friction147

6.2.3 First Type of Excitation Efiects for Stick-Slip Motion148

6.3 Hunting in Flexible Transmission Devices148

6.3.1 A Mechanical Model and its Equation of Motion149

6.3.2 Phase Path Equations in Various Stages of Hunting Motion151

6.3.3 Topological Structure of the Phase Diagram153

6.3.4 Critical Parameter Equation for the Occurrence of Hunting156

6.4 Asymmetric Dynamic Coupling Causedby Friction Force159

6.4.1 Mechanical Model and Equations of Motion159

6.4.2 Stability of Constant Velocity Motion of Dynamic System161

6.4.3 Second Type of Excitation Effect for Stick-Slip Motion164

References166

Chapter 7 Dynamic Shimmy of Front Wheel167

7.1 Physical Background of Tire Force167

7.1.1 Tire Force168

7.1.2 Cornering Force169

7.1.3 Analytical Description of Cornering Force170

7.1.4 Linear Model for Cornering Force172

7.2 Point Contact Theory174

7.2.1 Classification of Point Contact Theory174

7.2.2 Nonholonomic Constraint176

7.2.3 Potential Energy of a Rolling Tire177

7.3 Dynamic Shimmy of Front Wheel179

7.3.1 Isolated Front Wheel Model179

7.3.2 Stability of Front Wheel under Steady Rolling181

7.3.3 Stable Regions in Parameter Plane182

7.3.4 Influence of System Parameters on Dynamic Shimmy of Front Wheel183

7.4 Dynamic Shimmy of Front Wheel Coupled with Vehicle184

7.4.1 A Simplified Model of a Front Wheel System184

7.4.2 Mathematical Model of the Front Wheel System185

7.4.3 Stability of Steady Rolling of the Front Wheel System187

7.4.4 Prevention of Dynamic Shimmy in Design Stage189

References190

Chapter 8 Rotor Whirl191

8.1 Mechanical Model of Rotor in Planar Whirl191

8.1.1 Classification of rotor whirls192

8.1.2 Mechanical Model of Whirling Rotor193

8.2 Fluid-Film Force195

8.2.1 Operating Mechanism of Hydrodynamic Bearings195

8.2.2 Reynolds' Equation196

8.2.3 Pressure Distribution on Journal Surface199

8.2.4 Linearized Fluid Film Force202

8.2.5 Concentrated Parameter Model of Fluid Film Force204

8.2.6 Linear Expressions of Seal Force207

8.3 Oil Whirl and Oil Whip208

8.3.1 Hopf Bifurcation leading to Oil Whirl of Rotor208

8.3.2 Threshold Speed and Whirl Frequency212

8.3.3 Influence of Shaft Elasticity on the Oil Whirl of Rotor215

8.3.4 Influence of Extemal Damping on Oil Whirl218

8.3.5 Oil Whip222

8.4 Internal Damping in Deformed Rotation Shaft226

8.4.1 Physical Background of Internal Force of Rotation Shaft226

8.4.2 Analytical Expression of Internal Force of Rotation Shaft227

8.4.3 Three Components of Internal Force of Rotation Shaft231

8.5 Rotor Whirl Excited by Internal Damping232

8.5.1 A Simple Model of Internal Damping Force of Deformed Rotating Shaft232

8.5.2 Synchronous Whirl of Rotor with Unbalance233

8.5.3 Supersynchronous Whirl236

8.6 Cause and Prevention of Rotor Whirl237

8.6.1 Structure of Equation of Motion238

8.6.2 Common Causes of Two Kinds of Rotor Whirls239

8.6.3 Preventing the Rotor from Whirling239

References240

Chapter 9 Self-Excited Vibrations from Interaction of Structures and Fluid243

9.1 Vortex Resonance in Flexible Structures243

9.1.1 Vortex Shedding244

9.1.2 Predominate Frequency246

9.1.3 Wake Oscillator Model249

9.1.4 Amplitude Prediction253

9.1.5 Reduction of Vortex Resonance254

9.2 Flutter in Cantilevered Pipe Conveying Fluid255

9.2.1 Linear Mathematical Model255

9.2.2 Critical Parameter Condition258

9.2.3 Hopf Bifurcation and Critical Flow Velocity261

9.2.4 Excitation Mechanism and Prevention of Flutter265

9.3 Classical Flutter in Two-Dimensional Airfoil268

9.3.1 A Continuous Model of Long Wing268

9.3.2 Critical Flow Velocity of Classical Flutter270

9.3.3 Excitation Mechanism of Classical Flutter273

9.3.4 Influence of Parameters of the Wing on Critical Speed of Classical Flutter274

9.4 Stall Flutter in Flexible Structure277

9.4.1 Aerodynamic Forces Exciting Stall Flutter278

9.4.2 A Mathematical Model of Galloping in the Flexible Structure281

9.4.3 Critical Speed and Hysteresis Phenomenon of Galloping282

9.4.4 Some Features of Stall Flutter and its Prevention Schemes286

9.5 Fluid-Elastic Instability in Array of Circular Cylinders288

9.5.1 Fluid-Elastic Instability289

9.5.2 Fluid Forces Depending on Motion of Circular Cylinders290

9.5.3 Analysis of Flow-Induced Vibration292

9.5.4 Approximate Expressions of Critical Flow Velocity294

9.5.5 Prediction and Prevention of Fluid-Elastic Instability298

References299

Chapter 10 Self-Excited Oscillations in Feedback Control System302

10.1 Heating Control System303

10.1.1 Operating Principle of the Heating Control System303

10.1.2 Mathematical Model of the Heating Control System303

10.1.3 Time History of Temperature Variation305

10.1.4 Stable Limit Cycle in Phase Plane306

10.1.5 Amplitude and Frequency of Room Temperature Derivation307

10.1.6 An Excitation Mechanism of Self-Excited Oscillation308

10.2 Electrical Position Control System with Hysteresis308

10.2.1 Principle Diagram308

10.2.2 Equations of Position Control System with Hysteresis Nonlinearity310

10.2.3 Phase Diagram and Point Mapping311

10.2.4 Existence of Limit Cycle313

10.2.5 Critical Parameter Condition314

10.3 Electrical Position Control System with Hysteresis and Dead-Zone315

10.3.1 Equation of Motion315

10.3.2 Phase Diagram and Point Mapping316

10.3.3 Existence and Stability of Limit Cycle318

10.3.4 Critical Parameter Condition321

10.4 Hydraulic Position Control System322

10.4.1 Schematic Diagram of a Hydraulic Actuator322

10.4.2 Equations of Motion of Hydraulic Position Control System323

10.4.3 Linearized Mathematical Model325

10.4.4 Equilibrium Stability of Hydraulic Position Control System327

10.4.5 Amplitude and Frequency of Self-Excited Vibration328

10.4.6 Influence of Dead-Zone on Motion of Hydraulic Position Control System330

10.4.7 Influence of Hysteresis and Dead-Zone on Motion of Hydraulic Position Control System334

10.5 A Nonlinear Control System under Velocity Feedback with Time Delay338

References344

Chapter 11 Modeling and Control345

11.1 Excitation Mechanism of Self-Excited Oscillation346

11.1.1 An Explanation about Energy Mechanism346

11.1.2 An Explanation about Feedback Mechanism347

11.1.3 Joining of Energy and Feedback Mechanisms349

11.2 Determine the Extent of a Mechanical Model350

11.2.1 Minimal Model and Principle Block Diagram351

11.2.2 First Type of Extended Model352

11.2.3 Second Type of Extended Model355

11.3 Mathematical Description of Motive Force358

11.3.1 Integrate the Differential Equations of Motion of Continuum358

11.3.2 Use of the Nonholonomic Constraint Equations359

11.3.3 Establishing Equivalent Model of the Motive Force360

11.3.4 Construct the Equivalent Oscillator of Motive Force361

11.3.5 Identification of Grey Box Model362

11.3.6 Constructing an Empiric Formula of the Motive Force363

11.4 Establish Equations of Morion of Mechanical Systems365

11.4.1 Application of Lagrange's Equation of Motion365

11.4.2 Application of Hamilton's Principle368

11.4.3 Hamilton's Principle for Open Systems372

11.5 Discretization of Mathematical Model of a Distributed Parameter System374

11.5.1 Lumped Parameter Method374

11.5.2 Assumed-Modes Method376

11.5.3 Finite Element Method379

11.6 Active Control for Suppressing Self-Excited Vibration380

11.6.1 Active Control of Flexible Rotor381

11.6.2 Active Control of an Airfoil Section with Flutter384

References387

Subject Index390