Mechanical Instability by Krysinski, Tomasz -- Read -- Imperial Library of Trantor

Index

Cover Title Copyright Foreword Preface Chapter 1: Notions of Instability

1.1. Introduction

1.1.1. Lyapunov’s Direct Method 1.1.2. Lyapunov’s Indirect Method

1.2. Comparison of Notions of Resonance and Instability

1.2.1. Notion of Resonance

1.2.1.1. Behavior Before Resonance 1.2.1.2. Behavior at Eigenfrequency 1.2.1.3. Behavior Beyond Resonant Frequency 1.2.1.4. Typical Blade Forced Response

1.2.2. Notion of Instability

1.3. Instability Due to Self-Sustained Excitation

1.3.1. Multiple-Degree-of-Freedom Systems

1.3.1.1. Use of a Time Approach or State System

1.3.1.1.1. Method of Poles 1.3.1.1.2. FPM (Force Phasing Matrix) Method

1.3.1.2. Use of Transfer Functions

1.3.1.2.1. Routh (or Routh-Hurwitz) Algebraic Criterion 1.3.1.2.2. Graphical Nyquist Criterion 1.3.1.2.3. Graphical Black Criterion

1.3.1.3. Energy Consideration

1.3.1.3.1. Lejeune-Dirichlet’s Theorem 1.3.1.3.2. Typical Application

1.3.2. Single-Degree-of-Freedom System

1.3.2.1. Non-Oscillatory Instability

1.3.2.1.1. Definition of a Stability Criterion 1.3.2.1.2. Special Case: Without Damping 1.3.2.1.3. Typical Illustration

1.3.2.2. Oscillatory Instability

1.3.2.2.1. Definition of a Stability Criterion 1.3.2.2.2. Typical Illustration

1.3.2.3. Stability Analysis by Phase Diagram

1.4. Parametric Instability

1.4.1. General Case 1.4.2. Mathieu’s Equation 1.4.3. Typical Application

1.4.3.1. Equation Setting

1.5. Summary of Methods Used to Ensure or Increase the Stability of a System

1.5.1. Notion of Degrees of Stability

1.5.1.1. Pole Location Method 1.5.1.2. Graphical Criterion: Stability Margin

1.5.1.2.1. Illustration of Instability and Effect of Phase Shift 1.5.1.2.2. Analysis of Stability Margins in Nyquist Plane 1.5.1.2.3. Analysis of Stability Margins through Bode Diagram

1.5.2. Main Corrector Systems

1.5.2.1. Architecture of Robust State Feedback Correctors 1.5.2.2. Several Types of Corrector

1.5.2.2.1. Proportional Corrector (P) 1.5.2.2.2. Proportional-Integral Corrector (PI) 1.5.2.2.3. Proportional-Derivative Corrector (PD) 1.5.2.2.4. Proportional-Integral-Derivative Corrector (PID)

1.5.2.3. Corrector Performance

1.5.2.3.1. Accuracy 1.5.2.3.2. Accuracy 1.5.2.3.3. Rapidity or Response Time 1.5.2.3.4. Exceedance 1.5.2.3.5. Summary of Static Gain on Performance

Chapter 2: Rotor/Structure Coupling: Examples of Ground Resonance and Air Resonance

2.1. Introduction to Ground Resonance 2.2. Ground Resonance Modeling

2.2.1. Minimum Degree-of-Freedom Model

2.2.1.1. Definition of Degrees of Freedom

2.2.1.1.1. Lag Motion 2.2.1.1.2. Lateral Motion and Longitudinal Motion

2.2.1.2. Setting Up Equations

2.2.1.2.1. Kinetic Energy

Adapter Contribution Landing Gear Contribution

2.2.1.2.2. Equations of motion 2.2.1.2.3. Coleman Transformation

Collective Lag Motion δ0(t) Motion at δ1c Motion at δ1s Motion at δcp

2.2.2. Stability Criteria 2.2.3. Energy Analysis

2.3. Active Control of Ground Resonance

2.3.1. Active Control Algorithm

2.3.1.1. Physical Principles Involved 2.3.1.2. Knowledge Model Equations

2.3.1.2.1. Effect Through Pitch/Flap/Lag Coupling 2.3.1.2.2. Effect of Flapping on Roll

2.3.1.3. Method Retained

2.3.1.3.1. Method Based on Two Parameters 2.3.1.3.2. Method Based on One Measured Parameter

2.3.2. Performance Indicators 2.3.3. Implementation of Active Control

2.3.3.1. Simulation and Ground Tests 2.3.3.2. Tests on Helicopter

2.4. Air Resonance

2.4.1. Phenomenon Description 2.4.2. Modeling and Setting Up Equations

2.4.2.1. Parameterization 2.4.2.2. Setting Up Equations 2.4.2.3. Mode and Stability Analysis

2.4.3. Active Control of Air Resonance

Chapter 3: Torsional System: Instability of Closed-Loop Systems

3.1. Introduction 3.2. Governing Principle

3.2.1. History and Sizing of Flyball Governor 3.2.2. Simple Mathematical Sizing Criterion 3.2.3. Physical Analysis of Criterion and Effect of Parameters

3.2.3.1. 1st Case: Before Resonance 3.2.3.2. 2nd Case: After Resonance

3.3. Industrial Cases

3.3.1. Case of Airplane With Variable-Setting Angle Propeller Rotor

3.3.1.1. Propeller Pitch Governing Principle 3.3.1.2. Overspeed Configuration 3.3.1.3. Underspeed Configuration

3.3.2. Case of Tiltrotor Aircraft 3.3.3. Case of Helicopter

3.3.3.1. Engine Technologies and Comparison

3.3.3.1.1 Coupled Turbine 3.3.3.1.2. Free Turbine

3.3.3.2. Governing System Operation for a Free Turbine

3.3.3.2.1. Proportional Governor 3.3.3.2.2. Pitch Control Anticipator

3.3.3.3. Theoretical Study and Stability Criterion

3.3.3.3.1. Governed System Modeling and Eigenfrequencies 3.3.3.3.2. Interaction With Governing 3.3.3.3.3. Stability Criterion

3.3.3.4. Practical Example of Helicopter

Chapter 4: Self-Sustaining Instability for Rotating Shafts

4.1. Introduction to Self-Sustaining Instability 4.2. Modeling of Effect of Internal Damping on Rotating Systems

4.2.1. Instability Origins 4.2.2. Highlighting Instability

4.2.2.1. Force Due to Internal Damping

4.2.2.1.1. Structural Damping

4.2.2.2. Effect of Shaft Material Damping 4.2.2.3. Effect of Stress Variation Frequency

4.2.2.3.1. Small ω 4.2.2.3.2. Great ω

4.2.2.4. Conclusion

4.2.3. Stability Criterion for a Flexible Shaft

4.2.3.1. Setting Up Equations

4.2.3.1.1. Kinetic Energy 4.2.3.1.2. Potential Function 4.2.3.1.3. Internal Damping 4.2.3.1.4. External Damping 4.2.3.1.5. Equations of motion

4.2.3.2. Definition of a Stability Criterion 4.2.3.3. Case of a Drive Shaft

4.2.3.3.1. Stability Criterion Special Features 4.2.3.3.2. Simplified Example

4.2.3.4. Dynamic Shaft Adaptation, Example of a Turbine

4.2.3.4.1. Calculation of Instability Critical Speed on First Bending Mode 4.2.3.4.2. Positioning of Rigid Modes

Chapter 5: Fluid-Structure Interaction

5.1. Introduction

5.1.1. Fluid-Structure Interaction Issues 5.1.2. Instability and Energy Analysis 5.1.3. Brief Description of Flutter

5.1.3.1. Static Divergence 5.1.3.2. Conventional Flutter 5.1.3.3. Stall Flutter 5.1.3.4. Whirl Flutter 5.1.3.5. Servoelasticy-Type Instabilities

5.2. Flutter of an Airfoil in an Airstream

5.2.1. Setting Up Equations 5.2.2. Industrial Examples

5.2.2.1. Overhead Power Line Galloping

5.2.2.1.1. Theoretical Study 5.2.2.1.2. Numerical Application

5.2.2.2. Stabilizers: Helicopter Empennage 5.2.2.3. Bridge Decks

5.2.2.3.1. Introduction to Bridge Issues 5.2.2.3.2. Bridge Excitation Related to Pedestrians 5.2.2.3.3. Stability Control Methods 5.2.2.3.4. Study of Bridge Instability With Bridge/Wind Coupling

Numerical Application

5.2.2.4. Blade Flutter

5.2.2.4.1. Example of Pitch-Lag Flutter on Helicopter 5.2.2.4.2. Example of Pitch-Flag Flutter 5.2.2.4.3. Flutter With Participation of a Servomechanism

5.3. Whirl Flutter

5.3.1. Introduction to Convertible Aircraft Case 5.3.2. Enhanced Convertible Aircraft Rotor Reed’s Modeling - Stability

5.3.2.1. Presentation 5.3.2.2. Mockup Design

5.3.2.2.1. Displacement of Rotor Center 5.3.2.2.2. Damping Change Versus Speed V 5.3.2.2.3. Mode Change Versus Speed V 5.3.2.2.4. Variation of Torsional Stiffness 5.3.2.2.5. Effect of Blade Moment of Inertia 5.3.2.2.6. Effect of Connection K 5.3.2.2.7. Effect of Flapping Stiffness 5.3.2.2.8. Conclusion

5.3.3. Whirl Flutter Active Control: Case of Tilt Rotor

5.3.3.1. Scope 5.3.3.2. Active Control Algorithms

5.3.3.2.1. Single-Variable Control 5.3.3.2.2. LQG/LTR Control 5.3.3.2.3. Generalized Predictive Control

Active Control Algorithms

Bibliography Index

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