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Introduction to Aircraft Aeroelasticity and Loads

Book Description

Aircraft performance is influenced significantly both by aeroelastic phenomena, arising from the interaction of elastic, inertial and aerodynamic forces, and by load variations resulting from flight and ground manoeuvres and gust / turbulence encounters. There is a strong link between aeroelasticity and loads, and these topics have become increasingly integrated in recent years.

Introduction to Aircraft Aeroelasticity and Loads introduces the reader to the main principles involved in a wide range of aeroelasticity and loads topics. Divided into three sections, the book begins by reviewing the underlying disciplines of vibrations, aerodynamics, loads and control. It goes on to describe simplified models to illustrate aeroelastic behaviour and aircraft response before introducing more advanced methodologies. Finally, it explains how industrial certification requirements for aeroelasticity and loads may be met and relates these to the earlier theoretical approaches used.

  • Presents fundamentals of structural dynamics, aerodynamics, static and dynamic aeroelasticity, response and load calculations and testing techniques.

  • Covers performance issues related to aeroelasticity such as flutter, control effectiveness, divergence and redistribution of lift.

  • Includes up-to-date experimental methods and analysis.

  • Accompanied by a website with MatLAB and SIMULINK programs that relate to the models used.

Introduction to Aircraft Aeroelasticity and Loads enables the reader to understand the aeroelastic and loads principles and procedures employed in a modern aircraft design office. It will appeal to final year undergraduate and masters students as well as engineers who are new to the aerospace industry.

Note: The ebook version does not provide access to the companion files.

Table of Contents

  1. Cover Page
  2. Title Page
  3. Copyright
  4. Dedication
  5. Contents
  6. Preface
  7. Series Preface
  8. Introduction
  9. Abbreviations
  10. Part I: Background Material
    1. 1: Vibration of Single Degree of Freedom Systems
      1. 1.1 SETTING UP EQUATIONS OF MOTION FOR SINGLE DoF SYSTEMS
      2. 1.2 FREE VIBRATION OF SINGLE DoF SYSTEMS
      3. 1.3 FORCED VIBRATION OF SINGLE DoF SYSTEMS
      4. 1.4 HARMONIC FORCED VIBRATION – FREQUENCY RESPONSE FUNCTIONS
      5. 1.5 TRANSIENT/RANDOM FORCED VIBRATION – TIME DOMAIN SOLUTION
      6. 1.6 TRANSIENT FORCED VIBRATION – FREQUENCY DOMAIN SOLUTION
      7. 1.7 RANDOM FORCED VIBRATION – FREQUENCY DOMAIN SOLUTION
      8. 1.8 EXAMPLES
    2. 2: Vibration of Multiple Degree of Freedom Systems
      1. 2.1 SETTING UP EQUATIONS OF MOTION
      2. 2.2 UNDAMPED FREE VIBRATION
      3. 2.3 DAMPED FREE VIBRATION
      4. 2.4 TRANSFORMATION TO MODAL COORDINATES
      5. 2.5 ‘FREE–FREE’ SYSTEMS
      6. 2.6 HARMONIC FORCED VIBRATION
      7. 2.7 TRANSIENT/RANDOM FORCED VIBRATION – TIME DOMAIN SOLUTION
      8. 2.8 TRANSIENT FORCED VIBRATION – FREQUENCY DOMAIN SOLUTION
      9. 2.9 RANDOM FORCED VIBRATION – FREQUENCY DOMAIN SOLUTION
      10. 2.10 EXAMPLES
    3. 3: Vibration of Continuous Systems – Assumed Shapes Approach
      1. 3.1 RAYLEIGH–RITZ ‘ASSUMED SHAPES’ METHOD
      2. 3.2 GENERALIZED EQUATIONS OF MOTION – BASIC APPROACH
      3. 3.3 GENERALIZED EQUATIONS OF MOTION – MATRIX APPROACH
      4. 3.4 GENERATING AIRCRAFT ‘FREE–FREE’ MODES FROM ‘BRANCH’ MODES
      5. 3.5 WHOLE AIRCRAFT ‘FREE–FREE’ MODES
      6. 3.6 EXAMPLES
    4. 4: Vibration of Continuous Systems – Discretization Approach
      1. 4.1 INTRODUCTION TO THE FINITE ELEMENT (FE) APPROACH
      2. 4.2 FORMULATION OF THE BEAM BENDING ELEMENT
      3. 4.3 ASSEMBLY AND SOLUTION FOR A STRUCTURE WITH BEAM ELEMENTS
      4. 4.4 TORSION ELEMENT
      5. 4.5 COMBINED BENDING/TORSION ELEMENT
      6. 4.6 COMMENTS ON MODELLING
      7. 4.7 EXAMPLES
    5. 5: Introduction to Steady Aerodynamics
      1. 5.1 THE STANDARD ATMOSPHERE
      2. 5.2 EFFECT OF AIR SPEED ON AERODYNAMIC CHARACTERISTICS
      3. 5.3 FLOWS AND PRESSURES AROUND A SYMMETRIC AEROFOIL
      4. 5.4 FORCES ON AN AEROFOIL
      5. 5.5 VARIATION OF LIFT FOR AN AEROFOIL AT AN ANGLE OF INCIDENCE
      6. 5.6 PITCHING MOMENT VARIATION AND THE AERODYNAMIC CENTRE
      7. 5.7 LIFT ON A THREE-DIMENSIONAL WING
      8. 5.8 DRAG ON A THREE-DIMENSIONAL WING
      9. 5.9 CONTROL SURFACES
      10. 5.10 SUPERSONIC AERODYNAMICS – PISTON THEORY
      11. 5.11 TRANSONIC FLOWS
      12. 5.12 EXAMPLES
    6. 6: Introduction to Loads
      1. 6.1 LAWS OF MOTION
      2. 6.2 D'ALEMBERT'S PRINCIPLE – INERTIA FORCES AND COUPLES
      3. 6.3 EXTERNALLY APPLIED/REACTIVE LOADS
      4. 6.4 FREE BODY DIAGRAMS
      5. 6.5 INTERNAL LOADS
      6. 6.6 INTERNAL LOADS FOR CONTINUOUS REPRESENTATION OF A STRUCTURE
      7. 6.7 INTERNAL LOADS FOR DISCRETIZED REPRESENTATION OF A STRUCTURE
      8. 6.8 INTERCOMPONENT LOADS
      9. 6.9 OBTAINING STRESSES FROM INTERNAL LOADS – STRUCTURAL MEMBERS WITH SIMPLE LOAD PATHS
      10. 6.10 EXAMPLES
    7. 7: Introduction to Control
      1. 7.1 OPEN AND CLOSED LOOP SYSTEMS
      2. 7.2 LAPLACE TRANSFORMS
      3. 7.3 MODELLING OF OPEN AND CLOSED LOOP SYSTEMS USING LAPLACE AND FREQUENCY DOMAINS
      4. 7.4 STABILITY OF SYSTEMS
      5. 7.5 PID CONTROL
      6. 7.6 EXAMPLES
  11. Part II: Introduction to Aeroelasticity and Loads
    1. 8: Static Aeroelasticity – Effect of Wing Flexibility on Lift Distribution and Divergence
      1. 8.1 STATIC AEROELASTIC BEHAVIOUR OF A TWO-DIMENSIONAL RIGID AEROFOIL WITH SPRING ATTACHMENT
      2. 8.2 STATIC AEROELASTIC BEHAVIOUR OF A FIXED ROOT FLEXIBLE WING
      3. 8.3 EFFECT OF TRIM ON STATIC AEROELASTIC BEHAVIOUR
      4. 8.4 EFFECT OF WING SWEEP ON STATIC AEROELASTIC BEHAVIOUR
      5. 8.5 EXAMPLES
    2. 9: Static Aeroelasticity – Effect of Wing Flexibility on Control Effectiveness
      1. 9.1 ROLLING EFFECTIVENESS OF A FLEXIBLE WING – THE STEADY ROLL CASE
      2. 9.2 ROLLING EFFECTIVENESS OF A FLEXIBLE WING – THE FIXED WING ROOT CASE
      3. 9.3 EFFECT OF SPANWISE POSITION OF THE CONTROL SURFACE
      4. 9.4 FULL AIRCRAFT MODEL – CONTROL EFFECTIVENESS
      5. 9.5 EFFECT OF TRIM ON REVERSAL SPEED
      6. 9.6 EXAMPLES
    3. 10: Introduction to Unsteady Aerodynamics
      1. 10.1 QUASI-STEADY AERODYNAMICS
      2. 10.2 UNSTEADY AERODYNAMICS
      3. 10.3 AERODYNAMIC LIFT AND MOMENT FOR A HARMONICALLY OSCILLATING AEROFOIL
      4. 10.4 OSCILLATORY AERODYNAMIC DERIVATIVES
      5. 10.5 AERODYNAMIC DAMPING AND STIFFNESS
      6. 10.6 UNSTEADY AERODYNAMICS RELATED TO GUSTS
      7. 10.7 EXAMPLES
    4. 11: Dynamic Aeroelasticity – Flutter
      1. 11.1 SIMPLIFIED UNSTEADY AERODYNAMIC MODEL
      2. 11.2 BINARY AEROELASTIC MODEL
      3. 11.3 GENERAL FORM OF THE AEROELASTIC EQUATIONS
      4. 11.4 EIGENVALUE SOLUTION OF FLUTTER EQUATIONS
      5. 11.5 AEROELASTIC BEHAVIOUR OF THE BINARY MODEL
      6. 11.6 AEROELASTIC BEHAVIOUR OF A FLEXIBLE WING
      7. 11.7 AEROELASTIC BEHAVIOUR OF A MULTIPLE MODE SYSTEM
      8. 11.8 FLUTTER SPEED PREDICTION FOR BINARY SYSTEMS
      9. 11.9 FLUTTER CONIC
      10. 11.10 DIVERGENCE OF AEROELASTIC SYSTEMS
      11. 11.11 INCLUSION OF UNSTEADY REDUCED FREQUENCY EFFECTS
      12. 11.12 CONTROL SURFACE FLUTTER
      13. 11.13 WHOLE AIRCRAFT MODEL – INCLUSION OF RIGID BODY MODES
      14. 11.14 FLUTTER IN THE TRANSONIC REGIME
      15. 11.15 FLUTTER IN THE SUPERSONIC REGIME – WING AND PANEL FLUTTER
      16. 11.16 EFFECT OF NONLINEARITIES – LIMIT CYCLE OSCILLATIONS
      17. 11.17 EXAMPLES
    5. 12: Aeroservoelasticity
      1. 12.1 MATHEMATICAL MODELLING OF A SIMPLE AEROELASTIC SYSTEM WITH A CONTROL SURFACE
      2. 12.2 INCLUSION OF GUST TERMS
      3. 12.3 IMPLEMENTATION OF A CONTROL SYSTEM
      4. 12.4 DETERMINATION OF CLOSED LOOP SYSTEM STABILITY
      5. 12.5 GUST RESPONSE OF THE CLOSED LOOP SYSTEM
      6. 12.6 INCLUSION OF CONTROL LAW FREQUENCY DEPENDENCY IN STABILITY CALCULATIONS
      7. 12.7 RESPONSE DETERMINATION VIA THE FREQUENCY DOMAIN
      8. 12.8 STATE SPACE MODELLING
      9. 12.9 EXAMPLES
    6. 13: Equilibrium Manoeuvres
      1. 13.1 EQUILIBRIUM MANOEUVRE – RIGID AIRCRAFT UNDER NORMAL ACCELERATION
      2. 13.2 MANOEUVRE ENVELOPE
      3. 13.3 EQUILIBRIUM MANOEUVRE – RIGID AIRCRAFT PITCHING
      4. 13.4 EQUILIBRIUM MANOEUVRE – FLEXIBLE AIRCRAFT PITCHING
      5. 13.5 FLEXIBLE CORRECTIONS TO RIGID AIRCRAFT PITCHING DERIVATIVES
      6. 13.6 EQUILIBRIUM MANOEUVRES – AIRCRAFT ROLLING AND YAWING
      7. 13.7 REPRESENTATION OF THE FLIGHT CONTROL SYSTEM (FCS)
      8. 13.8 EXAMPLES
    7. 14: Flight Mechanics Model for Dynamic Manoeuvres
      1. 14.1 AIRCRAFT AXES
      2. 14.2 MOTION VARIABLES
      3. 14.3 AXES TRANSFORMATIONS
      4. 14.4 VELOCITY AND ACCELERATION COMPONENTS FOR MOVING AXES
      5. 14.5 FLIGHT MECHANICS EQUATIONS OF MOTION FOR A RIGID AIRCRAFT
      6. 14.6 REPRESENTATION OF DISTURBING FORCES AND MOMENTS
      7. 14.7 EQUATIONS FOR FLEXIBLE AIRCRAFT IN LONGITUDINAL MOTION
      8. 14.8 SOLUTION OF FLIGHT MECHANICS EQUATIONS
      9. 14.9 FLIGHT CONTROL SYSTEM (FCS)
    8. 15: Dynamic Manoeuvres
      1. 15.1 DYNAMIC MANOEUVRE – RIGID AIRCRAFT HEAVE/PITCH DUE TO ELEVATOR INPUT
      2. 15.2 DYNAMIC MANOEUVRE – FLEXIBLE AIRCRAFT HEAVE/PITCH DUE TO ELEVATOR INPUT
      3. 15.3 GENERAL FORM OF LONGITUDINAL EQUATIONS
      4. 15.4 DYNAMIC MANOEUVRE – RIGID AIRCRAFT ROLL DUE TO AILERON INPUT
      5. 15.5 DYNAMIC MANOEUVRE – FLEXIBLE AIRCRAFT ROLL DUE TO AILERON INPUT
      6. 15.6 FLEXIBLE CORRECTIONS TO FLIGHT MECHANICS EQUATIONS
      7. 15.7 REPRESENTATION OF THE FLIGHT CONTROL SYSTEM (FCS)
      8. 15.8 EXAMPLES
    9. 16: Gust and Turbulence Encounters
      1. 16.1 GUSTS AND TURBULENCE
      2. 16.2 GUST RESPONSE IN THE TIME DOMAIN
      3. 16.3 TIME DOMAIN GUST RESPONSE – RIGID AIRCRAFT IN HEAVE
      4. 16.4 TIME DOMAIN GUST RESPONSE – RIGID AIRCRAFT IN HEAVE/PITCH
      5. 16.5 TIME DOMAIN GUST RESPONSE – FLEXIBLE AIRCRAFT
      6. 16.6 GENERAL FORM OF EQUATIONS IN THE TIME DOMAIN
      7. 16.7 TURBULENCE RESPONSE IN THE FREQUENCY DOMAIN
      8. 16.8 FREQUENCY DOMAIN TURBULENCE RESPONSE – RIGID AIRCRAFT IN HEAVE
      9. 16.9 FREQUENCY DOMAIN TURBULENCE RESPONSE – RIGID AIRCRAFT IN HEAVE/PITCH
      10. 16.10 FREQUENCY DOMAIN TURBULENCE RESPONSE – FLEXIBLE AIRCRAFT
      11. 16.11 GENERAL FORM OF EQUATIONS IN THE FREQUENCY DOMAIN
      12. 16.12 REPRESENTATION OF THE FLIGHT CONTROL SYSTEM (FCS)
      13. 16.13 EXAMPLES
    10. 17: Ground Manoeuvres
      1. 17.1 LANDING GEAR
      2. 17.2 TAXI, TAKE-OFF AND LANDING ROLL
      3. 17.3 LANDING
      4. 17.4 BRAKING
      5. 17.5 ‘SPIN-UP’ AND ‘SPRING-BACK’ CONDITION
      6. 17.6 TURNING
      7. 17.7 SHIMMY
      8. 17.8 REPRESENTATION OF THE FLIGHT CONTROL SYSTEM (FCS)
      9. 17.9 EXAMPLES
    11. 18: Aircraft Internal Loads
      1. 18.1 LIMIT AND ULTIMATE LOADS
      2. 18.2 INTERNAL LOADS FOR AN AIRCRAFT
      3. 18.3 GENERAL INTERNAL LOADS EXPRESSIONS – CONTINUOUS WING
      4. 18.4 EFFECT OF WING-MOUNTED ENGINES/LANDING GEAR
      5. 18.5 INTERNAL LOADS – CONTINUOUS FLEXIBLE WING
      6. 18.6 GENERAL INTERNAL LOADS EXPRESSIONS – DISCRETIZED WING
      7. 18.7 INTERNAL LOADS – DISCRETIZED FUSELAGE
      8. 18.8 INTERNAL LOADS – CONTINUOUS TURBULENCE ENCOUNTER
      9. 18.9 LOADS GENERATION AND SORTING TO YIELD CRITICAL CASES
      10. 18.10 AIRCRAFT DIMENSIONING CASES
      11. 18.11 STRESSES FROM INTERNAL LOADS – COMPLEX LOAD PATHS
      12. 18.12 EXAMPLES
    12. 19: Potential Flow Aerodynamics
      1. 19.1 ELEMENTS OF INVISCID, INCOMPRESSIBLE FLOW ANALYSIS
      2. 19.2 INCLUSION OF VORTICITY
      3. 19.3 NUMERICAL STEADY AERODYNAMIC MODELLING OF THIN TWO-DIMENSIONAL AEROFOILS
      4. 19.4 STEADY AERODYNAMIC MODELLING OF THREE-DIMENSIONAL WINGS USING A PANEL METHOD
      5. 19.5 UNSTEADY AERODYNAMIC MODELLING OF WINGS UNDERGOING HARMONIC MOTION
      6. 19.6 AICS IN MODAL SPACE
      7. 19.7 EXAMPLES
    13. 20: Coupling of Structural and Aerodynamic Computational Models
      1. 20.1 MATHEMATICAL MODELLING – STATIC AEROELASTIC CASE
      2. 20.2 2D COUPLED STATIC AEROELASTIC MODEL – PITCH
      3. 20.3 2D COUPLED STATIC AEROELASTIC MODEL – HEAVE/PITCH
      4. 20.4 3D COUPLED STATIC AEROELASTIC MODEL
      5. 20.5 MATHEMATICAL MODELLING – DYNAMIC AEROELASTIC RESPONSE
      6. 20.6 2D COUPLED DYNAMIC AEROELASTIC MODEL – BENDING/TORSION
      7. 20.7 3D FLUTTER ANALYSIS
      8. 20.8 INCLUSION OF FREQUENCY DEPENDENT AERODYNAMICS FOR STATE-SPACE MODELLING – RATIONAL FRACTION APPROXIMATION
  12. Part III: Introduction to Industrial Practice
    1. 21: Aircraft Design and Certification
      1. 21.1 AEROELASTICS AND LOADS IN THE AIRCRAFT DESIGN PROCESS
      2. 21.2 AIRCRAFT CERTIFICATION PROCESS
    2. 22: Aeroelasticity and Loads Models
      1. 22.1 STRUCTURAL MODEL
      2. 22.2 AERODYNAMIC MODEL
      3. 22.3 FLIGHT CONTROL SYSTEM
      4. 22.4 OTHER MODEL ISSUES
      5. 22.5 LOADS TRANSFORMATIONS
    3. 23: Static Aeroelasticity and Flutter
      1. 23.1 STATIC AEROELASTICITY
      2. 23.2 FLUTTER
    4. 24: Flight Manoeuvre and Gust/Turbulence Loads
      1. 24.1 EVALUATION OF INTERNAL LOADS
      2. 24.2 EQUILIBRIUM/BALANCED FLIGHT MANOEUVRES
      3. 24.3 DYNAMIC FLIGHT MANOEUVRES
      4. 24.4 GUSTS AND TURBULENCE
    5. 25: Ground Manoeuvre Loads
      1. 25.1 AIRCRAFT/LANDING GEAR MODELS FOR GROUND MANOEUVRES
      2. 25.2 LANDING GEAR/AIRFRAME INTERFACE
      3. 25.3 GROUND MANOEUVRES – LANDING
      4. 25.4 GROUND MANOEUVRES – GROUND HANDLING
      5. 25.5 LOADS PROCESSING
    6. 26: Testing Relevant to Aeroelasticity and Loads
      1. 26.1 INTRODUCTION
      2. 26.2 WIND TUNNEL TESTS
      3. 26.3 GROUND VIBRATION TEST
      4. 26.4 STRUCTURAL COUPLING TEST
      5. 26.5 FLIGHT SIMULATOR TEST
      6. 26.6 STRUCTURAL TESTS
      7. 26.7 FLIGHT FLUTTER TEST
      8. 26.8 FLIGHT LOADS VALIDATION
  13. Appendices
    1. A: Aircraft Rigid Body Modes
      1. A.1 RIGID BODY TRANSLATION MODES
      2. A.2 RIGID BODY ROTATION MODES
    2. B: Table of Longitudinal Aerodynamic Derivatives
    3. C: Aircraft Symmetric Flexible Modes
      1. C.1 AIRCRAFT MODEL
      2. C.2 SYMMETRIC FREE–FREE FLEXIBLE MODE
    4. D: Model Condensation
      1. D.1 INTRODUCTION
      2. D.2 STATIC CONDENSATION
      3. D.3 DYNAMIC CONDENSATION – GUYAN REDUCTION
      4. D.4 STATIC CONDENSATION FOR AEROELASTIC MODELS
      5. D.5 MODAL CONDENSATION
      6. D.6 MODAL REDUCTION
    5. E: Aerodynamic Derivatives in Body Fixed Axes
      1. E.1 LONGITUDINAL DERIVATIVE Z W
      2. E.2 LATERAL DERIVATIVES L P , L ξ
    6. F: Aircraft Antisymmetric Flexible Modes
      1. F.1 AIRCRAFT MODEL
      2. F.2 ANTISYMMETRIC FREE–FREE FLEXIBLE MODES
  14. References
  15. Index
  16. G: MTLAB/SIMULINK Programs for Vibration
    1. G.1 FORCED RESPONSE OF AN SDoF SYSTEM
    2. G.2 MODAL SOLUTION FOR AN MDoF SYSTEM
    3. G.3 FINITE ELEMENT SOLUTION
  17. H: MATLAB/SIMULINK Programs for Flutter
    1. H.1 DYNAMIC AEROELASTIC CALCULATIONS
    2. H.2 AEROSERVOELASTIC SYSTEM
  18. I: MATLAB/SIMULINK Programs for Flight/Ground Manoeuvres and Gust/Turbulence Encounters
    1. I.1 RIGID AIRCRAFT DATA
    2. I.2 FLEXIBLE AIRCRAFT DATA
    3. I.3 FLIGHT CASE DATA
    4. I.4 AERODYNAMIC DERIVATIVE CALCULATION
    5. I.5 EQUILIBRIUM MANOEUVRES
    6. I.6 DYNAMIC MANOEUVRES
    7. I.7 GUST RESPONSE IN THE TIME DOMAIN
    8. I.8 GUST RESPONSE IN THE FREQUENCY DOMAIN
    9. I.9 GROUND MANOEUVRES