Chapter
Part I Background Material
Chapter 1 Vibration of Single Degree of Freedom Systems
1.1 Setting up Equations of Motion for SDoF Systems
1.1.1 Example: Classical SDoF System
1.1.2 Example: Aircraft Control Surface
1.2 Free Vibration of SDoF Systems
1.2.1 Example: Aircraft Control Surface
1.3 Forced Vibration of SDoF Systems
1.4 Harmonic Forced Vibration – Frequency Response Functions
1.4.1 Response to Harmonic Excitation
1.4.2 Frequency Response Functions
1.4.3 Hysteretic (or Structural) Damping
1.5 Transient/Random Forced Vibration – Time Domain Solution
1.5.1 Analytical Approach
1.5.2 Principle of Superposition
1.5.3 Example: Single Cycle of Square Wave Excitation – Response Determined by Superposition
1.5.4 Convolution Approach
1.5.5 Direct Solution of Ordinary Differential Equations
1.5.6 Example: Single Cycle of Square Wave Excitation – Response Determined by Numerical Integration
1.6 Transient Forced Vibration – Frequency Domain Solution
1.6.1 Analytical Fourier Transform
1.6.2 Frequency Domain Response – Excitation Relationship
1.6.3 Example: Single Cycle of Square Wave Excitation – Response Determined via Fourier Transform
1.7 Random Forced Vibration – Frequency Domain Solution
Chapter 2 Vibration of Multiple Degree of Freedom Systems
2.1 Setting up Equations of Motion
2.2 Undamped Free Vibration
2.2.2 Eigenvalue Approach
2.2.3 Example: `Chain-like´ 2DoF System
2.3 Damped Free Vibration
2.3.1 Example: 2DoF `Chain-Like´ System with Proportional Damping
2.3.2 Example: 2DoF `Chain-Like´ System with Non-proportional Damping
2.4 Transformation to Modal Coordinates
2.4.2 Example: 2DoF `Chain-like´ System with Proportional Damping
2.4.3 Example: 2DoF `Chain-like´ System with Non-proportional Damping
2.4.4 Mode Shape Normalization
2.4.5 Meaning of Modal Coordinates
2.4.6 Dimensions of Modal Coordinates
2.4.6.1 Consistent Coordinates
2.4.6.2 Mixed Coordinates
2.4.7 Model Order Reduction
2.5 Two-DoF Rigid Aircraft in Heave and Pitch
2.7 Harmonic Forced Vibration
2.7.1 Equations in Physical Coordinates
2.7.2 Equations in Modal Coordinates
2.8 Transient/Random Forced Vibration – Time Domain Solution
2.8.1 Analytical Approach
2.8.2 Convolution Approach
2.8.3 Solution of Ordinary Differential Equations
2.9 Transient Forced Vibration – Frequency Domain Solution
2.10 Random Forced Vibration – Frequency Domain Solution
Chapter 3 Vibration of Continuous Systems – Assumed Shapes Approach
3.2 Modelling Continuous Systems
3.3 Elastic and Flexural Axes
3.4 Rayleigh–Ritz `Assumed Shapes´ Method
3.4.1 One-dimensional Systems
3.4.2 Two-dimensional Systems
3.4.3 Choice of Assumed Shapes
3.4.4 Normal Modes for a Continuous System
3.5 Generalized Equations of Motion – Basic Approach
3.5.1 Clamped–Free Member in Bending – Single Assumed Shape
3.5.2 Clamped–Free Member in Bending – Two Assumed Shapes
3.5.3 Clamped–Free Member in Torsion – One Assumed Shape
3.6 Generalized Equations of Motion – Matrix Approach
3.6.1 Representation of Deformation
3.6.3 Elastic Potential Energy
3.6.4 Incremental Work Done
3.6.5 Differentiation of Lagrange´s Equations in Matrix Form
3.7 Generating Whole Aircraft `Free–Free´ Modes from `Branch´ Modes
3.8 Whole Aircraft `Free–Free´ Modes
Chapter 4 Introduction to Steady Aerodynamics
4.1 The Standard Atmosphere
4.2 Effect of Air Speed on Aerodynamic Characteristics
4.2.3 Inviscid/Viscous and Incompressible/Compressible Flows
4.3 Flows and Pressures Around a Symmetric Aerofoil
4.4 Forces on an Aerofoil
4.5 Variation of Lift for an Aerofoil at an Angle of Incidence
4.6 Pitching Moment Variation and the Aerodynamic Centre
4.7 Lift on a Three-dimensional Wing
4.7.2 Lift Curve Slope of a Three-dimensional Wing
4.7.3 Force and Moment Coefficients for a Three-dimensional Wing
4.7.4 Strip Theory for a Continuous Wing
4.7.5 Strip Theory for a Discretized Wing
4.8 Drag on a Three-dimensional Wing
Chapter 5 Introduction to Loads
5.1.1 Newton´s Laws of Motion for a Particle
5.1.2 Generalized Newton´s Laws of Motion for a Body
5.2 D´Alembert´s Principle – Inertia Forces and Couples
5.2.1 D´Alembert´s Principle for a Particle
5.2.2 Application of d´Alembert´s Principle to a Body
5.2.3 Extension to Distributed Inertia Forces
5.3 External Loads – Applied and Reactive
5.3.2 Reactive Loads (Reactions)
5.6 Internal Loads for a Continuous Member
5.6.1 Internal Loads for Uniformly Distributed Loading
5.6.1.1 `Exposing´ Internal Loads
5.6.1.2 Determining Internal Loads via Equilibrium of `Cut´ Sections
5.6.1.3 Other Boundary Conditions
5.6.2 Internal Loads for Non-uniformly Distributed Loading
5.6.2.1 Distributed Inertia Forces for a Continuous Member
5.6.2.2 Internal Loads for a Continuous Member under Non-uniform Loading
5.7 Internal Loads for a Discretized Member
5.7.1 Distributed Inertia Forces for a Discretized Member
5.7.2 Internal Loads for a Discretized Member
5.9 Obtaining Stresses from Internal Loads – Structural Members with Simple Load Paths
Chapter 6 Introduction to Control
6.1 Open and Closed Loop Systems
6.2.1 Solution of Differential Equations using Laplace Transforms
6.3 Modelling of Open and Closed Loop Systems using Laplace and Frequency Domains
6.4.2 Routh–Hurwitz Method
6.4.3 Frequency Domain Representation
6.4.3.2 Stability Analysis using Nyquist and Bode Plots
6.4.4 Time Domain Representation
6.4.4.1 State Space Representation
Part II Introduction to Aeroelasticity and Loads
Chapter 7 Static Aeroelasticity – Effect of Wing Flexibility on Lift Distribution and Divergence
7.1 Static Aeroelastic Behaviour of a Two-dimensional Rigid Aerofoil with a Torsional Spring Attachment
7.1.1.2 Further Iterations
7.1.2 Direct (Single Step) Approach
7.2 Static Aeroelastic Behaviour of a Fixed Root Flexible Wing
7.2.1 Twist and Divergence of the Fixed Root Flexible Wing
7.2.2 Variation of Lift Along the Fixed Root Flexible Wing
7.3 Effect of Trim on Static Aeroelastic Behaviour
7.3.1 Effect of Trim on the Divergence and Lift Distribution for a Simple Aircraft Model
7.3.2 Effect of Trim on the Variation of Lift along the Wing
7.3.3 Effect of Trim on the Wing and Tailplane Lift
7.4 Effect of Wing Sweep on Static Aeroelastic Behaviour
7.4.1 Effect of Wing Sweep on Effective Angle of Incidence
7.4.2 Effective Streamwise Angle of Incidence due to Bending/Twisting
7.4.3 Effect of Sweep Angle on Divergence Speed
Chapter 8 Static Aeroelasticity – Effect of Wing Flexibility on Control Effectiveness
8.1 Rolling Effectiveness of a Flexible Wing – Fixed Wing Root Case
8.1.1 Determination of Reversal Speed
8.1.2 Rolling Effectiveness – Rigid Fixed Wing Root Case
8.2 Rolling Effectiveness of a Flexible Wing – Steady Roll Case
8.2.1 Determination of Reversal Speed for Steady Roll Case
8.2.2 Lift Distribution for the Steady Roll Case
8.3 Effect of Spanwise Position of the Control Surface
8.4 Full Aircraft Model – Control Effectiveness
8.5 Effect of Trim on Reversal Speed
Chapter 9 Introduction to Unsteady Aerodynamics
9.1 Quasi-steady Aerodynamics
9.2 Unsteady Aerodynamics related to Motion
9.2.1 Instantaneous Change in Angle of Incidence – Wagner Function
9.2.2 Harmonic Motion – Convolution using the Wagner Function
9.2.3 Harmonic Motion using the Theodorsen Function
9.3 Aerodynamic Lift and Moment for an Aerofoil Oscillating Harmonically in Heave and Pitch
9.4 Oscillatory Aerodynamic Derivatives
9.5 Aerodynamic Damping and Stiffness
9.6 Approximation of Unsteady Aerodynamic Terms
9.7 Unsteady Aerodynamics related to Gusts
9.7.1 Lift due to a Sharp-Edged Gust – Küssner Function
9.7.2 Lift due to a Sinusoidal Gust – Sears Function
Chapter 10 Dynamic Aeroelasticity – Flutter
10.1 Simplified Unsteady Aerodynamic Model
10.2 Binary Aeroelastic Model
10.2.1 Aeroelastic Equations of Motion
10.3 General Form of the Aeroelastic Equations
10.4 Eigenvalue Solution of the Flutter Equations
10.5 Aeroelastic Behaviour of the Binary Model
10.5.1 Zero Aerodynamic Damping
10.5.2 Aerodynamic Damping with Quasi-steady Aerodynamics
10.5.3 Aerodynamic Damping with Unsteady Aerodynamics
10.5.4 Illustration of Phasing for Flutter
10.5.5 Soft and Hard Flutter
10.5.6 Inclusion of Structural Damping
10.5.7 Effect of Changes in Position of the Elastic and Mass Axes
10.5.8 Effect of Spacing between Wind-off Frequencies
10.6 Aeroelastic Behaviour of a Multiple Mode System
10.7 Flutter Speed Prediction for Binary Systems
10.8 Divergence of Dynamic Aeroelastic Systems
10.9 Inclusion of Unsteady Reduced Frequency Effects
10.9.1 Frequency Matching: `k´ Method
10.9.2 Frequency Matching: `p–k´ Method
10.9.3 Comparison of Results for `k´ and `p–k´ Methods
10.10 Control Surface Flutter
10.11 Whole Aircraft Model – Inclusion of Rigid Body Modes
10.11.1 Binary Aeroelastic Model with Free–Free Heave Motion
10.11.2 Relevance of Rigid Body Motions to Loads
10.12 Flutter in the Transonic Regime
10.13 Effect of Non-Linearities – Limit Cycle Oscillations
Chapter 11 Aeroservoelasticity
11.1 Mathematical Modelling of a Simple Aeroelastic System with a Control Surface
11.2 Inclusion of Gust Terms
11.3 Implementation of a Control System
11.4 Determination of Closed Loop System Stability
11.5 Gust Response of the Closed Loop System
11.6 Inclusion of Control Law Frequency Dependency in Stability Calculations
11.7 Response Determination via the Frequency Domain
11.8 State Space Modelling
Chapter 12 Equilibrium Manoeuvres
12.1 Equilibrium Manoeuvre – Rigid Aircraft under Normal Acceleration
12.1.1 Steady Level Flight
12.1.2 Accelerated Flight Manoeuvre – Load Factor
12.1.3 Steady Climb/Descent
12.1.4 Steady Pull-Up and Push-Down
12.1.5 Example: Steady Pull-up
12.1.7 Example: Steady Banked Turn
12.3 Equilibrium Manoeuvre – Rigid Aircraft Pitching
12.3.1 Inertial Axes System
12.3.2 Determination of External Forces to Balance the Aircraft
12.3.3 Thrust and Drag In-line
12.3.4 Example: Thrust and Drag In-line
12.3.5 Thrust and Drag Out-of-line
12.3.6 Example: Thrust and Drag Out-of-line
12.3.7 Determination of Balanced Condition – Thrust/Drag In-line
12.3.8 Determination of Balanced Condition – Thrust/Drag Out-of-line
12.3.9 Aerodynamic Derivatives
12.3.10 Static Stability (Stick Fixed)
12.3.11 Example: Steady Equilibrium Manoeuvre – Rigid Aircraft Pitching
12.4 Equilibrium Manoeuvre – Flexible Aircraft Pitching
12.4.1 Definition of the Flexible Aircraft with Unswept Wings
12.4.2 Definition of the Flexible Mode Shape
12.4.3 Expressions for Displacement and Angles over the Aircraft
12.4.7 Incremental Work Done Terms
12.4.8 Aerodynamic Derivatives – Rigid Body and Flexible
12.4.9 Equations of Motion for Flexible Aircraft Pitching
12.4.10 General Form of Equilibrium Manoeuvre Equations
12.4.11 Values for the Flexible Mode Parameters
12.4.12 Lift Distribution and Deformed Shape in the Manoeuvre
12.4.13 Example: Equilibrium Manoeuvre – Flexible Aircraft Pitching
12.4.13.1 Fuselage Bending Mode
12.4.13.2 Wing Bending Mode
12.4.13.3 Wing Twist Mode
12.4.14 Summary of Flexible Effects in an Equilibrium Pitching Manoeuvre for an Unswept Wing
12.4.15 Consideration of Flexible Swept Wing Effects on an Equilibrium Pitching Manoeuvre
12.4.15.1 Effects of a Flexible Swept Wing on Incidence
12.4.15.2 Effects of a Flexible Swept Wing on Equilibrium Manoeuvre
12.5 Representation of the Flight Control System (FCS)
Chapter 13 Dynamic Manoeuvres
13.3 Axes Transformations
13.3.1 Transformation in 2D
13.3.2 Transformation in 3D
13.4 Velocity and Acceleration Components for Moving Axes in 2D
13.4.1 Position Coordinates for Fixed and Moving Axes Frames in 2D
13.4.2 Differentiation with Respect to Time
13.4.3 Velocity Components for Fixed and Moving Axes in 2D
13.4.4 Acceleration Components for Fixed and Moving Axes in 2D
13.5 Flight Mechanics Equations of Motion for a Rigid Symmetric Aircraft in 2D
13.5.1 Non-linear Equations for Longitudinal Motion
13.5.2 Non-linear Equations for Combined Longitudinal/Lateral Motion in 3D
13.5.3 Linearized Equations of Motion in 3D
13.6 Representation of Disturbing Forces and Moments
13.6.2 Propulsion (or Power) Term
13.6.3 Gravitational Term
13.7 Modelling the Flexible Aircraft
13.7.1 Mean Axes Reference Frame
13.7.2 Definition of Flexible Deformation
13.7.3 Accelerations in 2D including Flexible Effects
13.7.4 Equations of Motion including Flexible Effects – Motion of Axes
13.7.5 Equations of Motion including Flexible Effects – Modal Motion
13.7.6 Full Flight Mechanics Equations with Flexible Modes
13.8 Solution of Flight Mechanics Equations for the Rigid Aircraft
13.8.1 Solving the Longitudinal Non-linear Equations of Motion
13.8.2 Dynamic Stability Modes
13.9 Dynamic Manoeuvre – Rigid Aircraft in Longitudinal Motion
13.9.1 Flight Mechanics Equations of Motion – Rigid Aircraft in Pitch
13.9.2 Aerodynamic Stability Derivatives in Heave/Pitch
13.9.3 Solution of the Flight Mechanics Equations – Rigid Aircraft
13.9.4 Pitch Rate per Elevator Transfer Function
13.9.5 Short Period Motion
13.9.7 Conversion to Earth Axes Motion
13.9.8 Example: Rigid Aircraft in Heave/Pitch
13.10 Dynamic Manoeuvre – Flexible Aircraft Heave/Pitch
13.10.1 Flight Mechanics Equations of Motion – Flexible Aircraft in Pitch
13.10.2 Aerodynamic Derivatives for Flexible Aircraft
13.10.3 Pitch Rate per Elevator Transfer Function
13.10.4 Elevator Effectiveness
13.10.4.1 Fuselage Bending Mode
13.10.4.2 Wing Bending Mode
13.10.4.3 Wing Torsion Mode
13.10.5 Short Period/Flexible Modes
13.10.6 Example: Flexible Aircraft in Heave/Pitch
13.10.6.1 Fuselage Bending Mode
13.10.6.2 Wing Bending Mode
13.10.6.3 Wing Torsion Mode
13.11 General Form of Longitudinal Equations
13.12 Dynamic Manoeuvre for Rigid Aircraft in Lateral Motion
13.12.1 Fully Coupled Equations
13.12.2 Uncoupled Equation in Roll
13.13 Bookcase Manoeuvres for Rigid Aircraft in Lateral Motion
13.13.1 Roll Bookcase Analyses
13.13.1.1 Steady Roll Rate
13.13.1.2 Maximum Roll Acceleration
13.13.2 Yaw Bookcase Analyses
13.13.2.1 Abrupt Application of Rudder
13.13.2.2 Steady Sideslip
13.14 Flight Control System (FCS)
13.15 Representation of the Flight Control System (FCS)
Chapter 14 Gust and Turbulence Encounters
14.1 Gusts and Turbulence
14.2 Gust Response in the Time Domain
14.2.1 Definition of Discrete Gusts
14.2.1.1 `Sharp-edged´ Gust
14.3 Time Domain Gust Response – Rigid Aircraft in Heave
14.3.1 Gust Response of Rigid Aircraft in Heave using Quasi-Steady Aerodynamics
14.3.3 Unsteady Aerodynamic Effects in the Time Domain
14.3.4 Gust Response of Rigid Aircraft in Heave using Unsteady Aerodynamics
14.3.4.1 Gust-dependent Lift
14.3.4.2 Response-dependent Lift
14.3.4.3 Equation of Motion
14.3.4.4 Gust Alleviation Factor
14.4 Time Domain Gust Response – Rigid Aircraft in Heave/Pitch
14.4.1 Gust Penetration Effect
14.4.2 Equations of Motion – Rigid Aircraft including Tailplane Effect
14.4.3 Example: Gust Response in the Time Domain for a Rigid Aircraft with Tailplane Effects
14.4.3.2 Sharp-edged Gust
14.5 Time Domain Gust Response – Flexible Aircraft
14.5.1 Equations of Motion – Flexible Aircraft
14.5.2 Example: Gust Response in the Time Domain for a Flexible Aircraft
14.6 General Form of Equations in the Time Domain
14.7 Turbulence Response in the Frequency Domain
14.7.1 Definition of Continuous Turbulence
14.7.2 Definition of a Harmonic Gust Velocity Component
14.7.3 FRFs for Response per Harmonic Gust Velocity
14.7.4 PSD of Response to Continuous Turbulence
14.8 Frequency Domain Turbulence Response – Rigid Aircraft in Heave
14.8.1 FRF for Rigid Aircraft Response in Heave per Harmonic Gust Velocity – Quasi-Steady Aerodynamics
14.8.2 Unsteady Aerodynamic Effects in the Frequency Domain
14.8.3 FRF for Rigid Aircraft Response in Heave per Harmonic Gust Velocity – Unsteady Aerodynamics
14.8.4 Example: Turbulence Response in the Frequency Domain for a Rigid Aircraft in Heave with Quasi-Steady Aerodynamics
14.8.5 Example: Turbulence Response in the Frequency Domain for a Rigid Aircraft in Heave with Unsteady Aerodynamics
14.9 Frequency Domain Turbulence Response – Rigid Aircraft in Heave/Pitch
14.9.1 FRF for Rigid Aircraft Response in Heave/Pitch per Harmonic Gust Velocity
14.9.2 Example: Turbulence Response in the Frequency Domain for a Rigid Aircraft in Heave/Pitch
14.10 Frequency Domain Turbulence Response – Flexible Aircraft
14.10.1 FRF for Flexible Aircraft Response in Heave/Pitch per Harmonic Gust Velocity
14.10.2 Example: Turbulence Response in the Frequency Domain for a Flexible Aircraft
14.11 General Form of Equations in the Frequency Domain
14.12 Representation of the Flight Control System (FCS)
Chapter 15 Ground Manoeuvres
15.1.1 Oleo-pneumatic Shock Absorber
15.1.2 Wheel and Tyre Assembly
15.1.3 Determinate and Statically Indeterminate Landing Gear Layouts
15.1.4 Determinate and Statically Indeterminate Landing Gear Attachments
15.2 Taxi, Take-Off and Landing Roll
15.2.2 Rigid Aircraft Taxiing
15.2.3 Example of Rigid Aircraft Taxiing
15.2.4 Flexible Aircraft Taxiing
15.2.4.1 Flexible Airframe Equations
15.2.4.2 Landing Gear Equations – Linear
15.2.4.3 Landing Gear Equations – Non-linear
15.2.5 Example of Flexible Aircraft Taxiing
15.3.1 Rigid Aircraft Landing – Non-linear Shock Absorber but No Tyre
15.3.2 Rigid Aircraft Landing – Non-linear Shock Absorber with Tyre
15.3.3 Flexible Aircraft Landing
15.3.4 Friction Forces at the Tyre-to-runway Interface
15.3.5 `Spin-up´ and `Spring-back´ Conditions
15.3.6 Bookcase Landing Calculations
15.4.1 Bookcase Braked Roll
15.4.2 Rational Braked Roll
15.7 Representation of the Flight Control System (FCS)
Chapter 16 Aircraft Internal Loads
16.1 Limit and Ultimate Loads
16.2 Internal Loads for an Aircraft
16.2.1 Internal Loads for a Wing
16.2.2 Internal Loads for a Fuselage
16.3 General Internal Loads Expressions – Continuous Wing
16.3.1 General Expression for Internal Loads
16.3.2 Example: Equilibrium Manoeuvre – Continuous Wing
16.4 Effect of Wing-mounted Engines and Landing Gear
16.5 Internal Loads – Continuous Flexible Wing
16.5.1 Steady and Incremental Loads
16.5.2 Internal Loads in an Equilibrium Manoeuvre
16.5.2.1 Inertia Force per Unit Span
16.5.2.2 Aerodynamic Force per Unit Span
16.5.2.3 Internal Loads in an Equilibrium Manoeuvre
16.5.3 Internal Loads in a Dynamic Manoeuvre/Gust Encounter
16.5.3.1 Inertia Force per Unit Span
16.5.3.2 Aerodynamic Force per Unit Span
16.5.3.3 Internal Loads in a Gust Encounter
16.5.4 Example: Internal Loads during a `1-Cosine´ Gust Encounter
16.5.4.1 Steady Loads experienced Prior to the Gust Encounter
16.5.4.2 Incremental Loads in the Gust Encounter
16.5.5 Form of Internal Loads for a Continuous Wing Representation
16.6 General Internal Loads Expressions – Discretized Wing
16.6.1 Wing Discretization
16.6.2 General Expression for Internal Loads – Discretized Wing
16.6.3 Example: Equilibrium Manoeuvre – Discretized Wing
16.6.4 Form of Internal Loads for a Discretized Wing Representation
16.7 Internal Loads – Discretized Fuselage
16.7.1 Separating Wing and Fuselage Components
16.7.2 Discretized Fuselage Components
16.7.3 Example: Equilibrium Manoeuvre – Discretized Fuselage
16.7.4 Internal Loads for General Manoeuvres and Gusts
16.8 Internal Loads – Continuous Turbulence Encounter
16.9 Loads Generation and Sorting to yield Critical Cases
16.9.1 One-dimensional Load Envelopes
16.9.2 Two-dimensional Load Envelopes
16.10 Aircraft Dimensioning Cases
16.11 Stresses derived from Internal Loads – Complex Load Paths
Chapter 17 Vibration of Continuous Systems – Finite Element Approach
17.1 Introduction to the Finite Element Approach
17.2 Formulation of the Beam Bending Element
17.2.1 Stiffness and Mass Matrices for a Uniform Beam Element
17.2.1.1 Element Shape Functions
17.2.1.2 Element Equation of Motion
17.2.1.3 Consistent and Lumped Mass Models
17.2.1.4 Kinematically Equivalent Nodal Forces
17.3 Assembly and Solution for a Beam Structure
17.3.1 Element and Structure Notation
17.3.2 Element and Structure Displacements – Imposing Compatibility
17.3.3 Assembly of the Global Stiffness Matrix – Imposing Equilibrium
17.3.4 Matrix Equation for the Assembled Structure
17.3.5 Solution Process for the Assembled Structure
17.3.5.1 Static Loading Analysis: Two Elements
17.3.5.2 Normal Modes Analysis: Two Elements
17.3.5.3 Normal Modes Analysis – Effect of Increasing the Number of Elements
17.5 Combined Bending/Torsion Element
17.6 Concentrated Mass Element
17.8.1 Rigid Body Element with an Infinite Constraint
17.8.2 Rigid Body Element with an Interpolation Constraint
17.10 Comments on Modelling
17.10.1 `Beam-like´ Representation of Slender Members in Aircraft
17.10.2 `Box-like´ Representation of Slender Members in Aircraft
Chapter 18 Potential Flow Aerodynamics
18.1 Components of Inviscid, Incompressible Flow Analysis
18.1.2 Point Source and Point Sink
18.1.5 Source–Sink Pair in a Uniform Flow (Rankine Oval)
18.1.6 Doublet in a Uniform Flow
18.2 Inclusion of Vorticity
18.2.2 Flow past a Cylinder with a Vortex at the Centre
18.3 Numerical Steady Aerodynamic Modelling of Thin Two-dimensional Aerofoils
18.3.1 Aerofoil Flow Modelled using a Single Element
18.3.2 Aerofoil Flow Modelled using Two Elements
18.4 Steady Aerodynamic Modelling of Three-Dimensional Wings using a Panel Method
18.4.1 Vortex Filaments and the Biot–Savart Law
18.4.2 Finite Span Wing – Modelled with a Single Horseshoe Vortex
18.4.3 Finite Span Wing – Modelled with a Vortex Lattice
18.5 Unsteady Aerodynamic Modelling of Wings undergoing Harmonic Motion
18.5.1 Harmonic Motion of a Two-dimensional Aerofoil
18.5.2 Harmonic Motion of a Three-Dimensional Wing
18.6 Aerodynamic Influence Coefficients in Modal Space
18.6.1 Heave Displacement
18.6.3 Flexible Mode Motion
18.6.4 Summary of Steady Aerodynamic Terms
18.6.5 Unsteady Aerodynamics
18.6.6 Gust-dependent Terms
Chapter 19 Coupling of Structural and Aerodynamic Computational Models
19.1 Mathematical Modelling – Static Aeroelastic Case
19.2 2D Coupled Static Aeroelastic Model – Pitch
19.3 2D Coupled Static Aeroelastic Model – Heave/Pitch
19.4 3D Coupled Static Aeroelastic Model
19.4.3 Transformation of Aerodynamic Forces to Structural Model
19.4.4 Assembly of Aeroelastic Model
19.5 Mathematical Modelling – Dynamic Aeroelastic Response
19.6 2D Coupled Dynamic Aeroelastic Model – Bending/Torsion
19.8 Inclusion of Frequency Dependent Aerodynamics for State–Space Modelling – Rational Function Approximation
Part III Introduction to Industrial Practice
Chapter 20 Aircraft Design and Certification
20.1 Aeroelastics and Loads in the Aircraft Design Process
20.2 Aircraft Certification Process
20.2.1 Certification Authorities
20.2.2 Certification Requirements
20.2.4 Bookcase and Rational Load Cases
20.2.5 Limit and Ultimate Loads
20.2.6 Fatigue and Damage Tolerance
Chapter 21 Aeroelasticity and Loads Models
21.1.3 Structural Model 1 – `Stick´ Representation
21.1.4 Structural Models – `Box-Like´ Representation
21.1.4.1 Structural Model 2 – Concentrated Mass attached to a Condensed FE Model
21.1.4.2 Structural Model 3 – Concentrated Mass attached to a `Box-Like´ FE Model
21.1.7 Rigid Aircraft Model
21.2.1 Aerodynamic Model for Flight Mechanics
21.2.2 Aerodynamic Model for Aeroelastics and Gusts
21.3 Flight Control System
21.5 Loads Transformations
Chapter 22 Static Aeroelasticity and Flutter
22.1 Static Aeroelasticity
22.1.1 Aircraft Model for Static Aeroelasticity
22.1.2 Control Effectiveness and Reversal
22.1.3 `Jig Shape´ – Flexible Deformation and Effect on Loads Distribution
22.1.4 Correction of Rigid Body Aerodynamics for Flexible Effects
22.2.1 Aircraft Model for Flutter
22.2.2 Flutter Boundary – Normal and Failure Conditions
22.2.3 Flutter Calculations
22.2.4 Aeroservoelastic Calculations
22.2.5 Non-linear Aeroelastic Behaviour
Chapter 23 Flight Manoeuvre and Gust/Turbulence Loads
23.1 Evaluation of Internal Loads
23.2 Equilibrium/Balanced Flight Manoeuvres
23.2.1 Aircraft Model for Equilibrium Manoeuvres
23.2.2 Equilibrium Flight Manoeuvres – Pitching
23.2.3 Equilibrium Flight Manoeuvres – Rolling
23.2.4 Equilibrium Flight Manoeuvres – Yawing
23.3 Dynamic Flight Manoeuvres
23.3.1 Aircraft Model for Dynamic Manoeuvres
23.3.2 Dynamic Manoeuvres – Pitching
23.3.3 Dynamic Manoeuvres – Rolling
23.3.4 Dynamic Manoeuvres – Yawing
23.3.5 Engine Failure Cases
23.4 Gusts and Turbulence
23.4.1 Aircraft Model for Gusts and Turbulence
23.4.2 Discrete Gust Loads
23.4.3 Continuous Turbulence Loads
23.4.4 Handling Aircraft with Non-linearities
Chaper 24 Ground Manoeuvre Loads
24.1 Aircraft/Landing Gear Models for Ground Manoeuvres
24.2 Landing Gear/Airframe Interface
24.3 Ground Manoeuvres – Landing
24.4 Ground Manoeuvres – Ground Handling
24.4.1 Taxi, Take-off and Roll Case
24.4.2 Braked Roll, Turning and Other Ground Handling Cases
24.5.2 Obtaining Stresses from Internal Loads
Chapter 25 Testing Relevant to Aeroelasticity and Loads
25.3 Ground Vibration Test
25.4 Structural Coupling Test
25.5 Flight Simulator Test
25.8 Flight Loads Validation
A Aircraft Rigid Body Modes
A.1 Rigid Body Translation Modes
A.2 Rigid Body Rotation Modes
B Table of Longitudinal Aerodynamic Derivatives
C Aircraft Symmetric Flexible Modes
C.2 Symmetric Free–Free Flexible Mode
C.2.1 Description of the Flexible Mode Shape
C.2.2 Conditions for Orthogonality with Rigid Body Modes
C.2.3 Wing Deformation Shapes
C.2.4 Mode with Fuselage Bending Dominant
C.2.5 Mode with Wing Bending Dominant
C.2.6 Mode with Wing Twist Dominant
C.2.7 Modal Mass Values for the Flexible Aircraft
C.2.8.1 Fuselage Bending Dominant
C.2.8.2 Wing Bending Dominant
C.2.8.3 Wing Torsion Dominant
D.3 Dynamic Condensation – Guyan Reduction
D.4 Static Condensation for Aeroelastic Models
E Aerodynamic Derivatives in Body Fixed Axes
E.1 Longitudinal Derivative Zw
E.1.2 Derivative for Normal Force due to Normal Velocity Perturbation
E.2 Lateral Derivatives Lp, Lξ
E.2.1 Rolling Moment Derivative due to the Roll Rate
E.2.2 Rolling Moment Derivative due to Aileron
F MATLAB/SIMULINK Programs for Vibration
F.1 Forced Response of an SDoF System
F.1.1 Superposition (Essentially Convolution)
F.1.2 Numerical Integration
F.2 Modal Solution for an MDoF System
F.3 Finite Element Solution
G MATLAB/SIMULINK Programs for Flutter
G.1 Dynamic Aeroelastic Calculations
G.2 Aeroservoelastic System
H MATLAB/SIMULINK Programs for Flight/Ground Manoeuvres and Gust/Turbulence Encounters
H.2 Flexible Aircraft Data
H.4 Aerodynamic Derivative Calculation
H.5 Equilibrium Manoeuvres
H.6 Equilibrium Manoeuvres
H.8 Gust Response in the Time Domain
H.9 Gust Response in the Frequency Domain
Introduction to Aircraft Aeroelasticity and Loads
( Aerospace Series )
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