A modern course in aeroelasticity

Preface to the Sixth Edition
Preface to the Fifth Edition
Preface to the Fourth Edition
Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
Contents
Contributors
Short Bibliography
	Books
	Survey articles
	Journals
Introduction
Static Aeroelasticity
	1 Typical Section Model of an Airfoil
		1.1 Typical Section Model with Control Surface
		1.2 Typical Section Model—Nonlinear Effects
	2 One Dimensional Aeroelastic Model of Airfoils
		2.1 Beam-Rod Representation of Large Aspect Ratio Wing
		2.2 Eigenvalue and Eigenfunction Approach
		2.3 Galerkin's Method
	3 Rolling of a Straight Wing
		3.1 Integral Equation of Equilibrium
		3.2 Derivation of Equation of Equilibrium
		3.3 Calculation of Cαα
		3.4 Sketch of Function S (y1, η)
		3.5 Aerodynamic Forces (Including Spanwise Induction)
		3.6 Aeroelastic Equations of Equilibrium and Lumped Element Solution Method
		3.7 Divergence
		3.8 Reversal and Rolling Effectiveness
		3.9 Integral Equation Eigenvalue Problem and the Experimental Determination of Influence Functions
	4 Two Dimensional Aeroelastic Model of Lifting Surfaces
		4.1 Two Dimensional Structures—Integral Representation
		4.2 Two Dimensional Aerodynamic Surfaces—Integral Representation
		4.3 Solution by Matrix-Lumped Element Approach
	5 Other Physical Phenomena
		5.1 Fluid Flow Through A Flexible Pipe
		5.2 (Low Speed) Fluid Flow Over A Flexible Wall
	6 Sweptwing Divergence
	References
Dynamic Aeroelasticity
	1 Hamilton's Principle
		1.1 Single Particle
		1.2 Many Particles
		1.3 Continuous Body
		1.4 Potential Energy
		1.5 Nonpotential Forces
	2 Lagrange's Equations
		2.1 Example—Typical Section Equations of Motion
	3 Dynamics of the Typical Section Model of An Airfoil
		3.1 Sinusoidal Motion
		3.2 Periodic Motion
		3.3 Arbitrary Motion
		3.4 Random Motion
		3.5 Flutter—An Introduction to Dynamic Aeroelastic Instability
		3.6 Quasi-Steady, Aerodynamic Theory
	4 Aerodynamic Forces for Airfoils-An Introduction and Summary
		4.1 Aerodynamic Theories Available
		4.2 General Approximations
		4.3 Slender Body or Slender (Low Aspect Ratio) Wing Approximation
	5 Solutions to the Aeroelastic Equations of Motion
		5.1 Time Domain Solutions
		5.2 Frequency Domain Solutions
	6 Representative Results and Computational  Considerations
		6.1 Time Domain
		6.2 Frequency Domain
		6.3 Flutter and Gust Response Classification Including Parameter Trends
		6.4 Gust Response
	7 Generalized Equations of Motion for Complex Structures
		7.1 Lagrange's Equations and Modal Methods (Rayleigh–Ritz)
		7.2 Kinetic Energy
		7.3 Strain (Potential Elastic) Energy
		7.4 Natural Frequencies and Modes-Eigenvalues and Eigenvectors
		7.5 Evaluation of Generalized Aerodynamic Forces
		7.6 Equations of Motion and Solution Methods
		7.7 Integral Equations of Equilibrium
		7.8 Natural Frequencies and Modes
		7.9 Forced Motion Including Aerodynamic Forces
	8 Other Fluid-Structural Interaction Phenomena
		8.1 Fluid Flow Through a Flexible Pipe: ``Firehose'' Flutter
		8.2 (High Speed) Fluid Flow Over a Flexible Wall—A Simple Prototype for Plate or Panel Flutter
	References
Nonsteady Aerodynamics of Lifting and Non-lifting Surfaces
	1 Basic Fluid Dynamic Equations
		1.1 Conservation of Mass
		1.2 Conservation of Momentum
		1.3 Irrotational Flow, Kelvin's Theorem and Bernoulli's Equation
		1.4 Derivation of a Single Equation for Velocity Potential
		1.5 Small Perturbation Theory
	2 Supersonic Flow
		2.1 Two-Dimensional Flow
		2.2 Simple Harmonic Motion of the Airfoil
		2.3 Discussion of Inversion
		2.4 Discussion of Physical Significance of the Results
		2.5 Gusts
		2.6 Transient Motion
		2.7 Lift, Due to Airfoil Motion
		2.8 Lift, Due to Atmospheric Gust
		2.9 Three Dimensional Flow
	3 Subsonic Flow
		3.1 Derivation of the Integral Equation by Transform Methods and Solution by Collocation
		3.2 An Alternative Determination of the Kernel Function Using Green's Theorem
		3.3 Incompressible, Three-Dimensional Flow
		3.4 Compressible, Three-Dimensional Flow
		3.5 Incompressible, Two-Dimensional Flow
	4 Representative Numerical Results
	5 Transonic Flow
	6 Concluding Remarks
	References
Stall Flutter
	1 Background
	2 Analytical Formulation
	3 Stability and Aerodynamic Work
	4 Bending Stall Flutter
	5 Nonlinear Mechanics Description
	6 Torsional Stall Flutter
	7 General Comments
	8 Reduced Order Models
	9 Computational Stalled Flow
	References
Aeroelasticity in Civil Engineering
	1 Fundamentals
		1.1 Vortex-Induced Oscillation
		1.2 Galloping
		1.3 Torsional Divergence
		1.4 Flutter and Buffeting in the Presence of Aeroelastic Effects
	2 Applications
		2.1 Suspension-Span Bridges
		2.2 Tall Chimneys and Stacks, and Tall Buildings
	References
Aeroelastic Response of Rotorcraft
	1 Blade Dynamics
		1.1 Articulated, Rigid Blade Motion
		1.2 Elastic Motion of Hingeless Blades
	2 Stall Flutter
	3 Rotor-Body Coupling
	4 Unsteady Aerodynamics
		4.1 Dynamic Inflow
		4.2 Frequency Domain
		4.3 Finite-State Wake Modelling
	5 Summary
	References
Aeroelasticity in Turbomachines
	1 Aeroelastic Environment in Turbomachines
	2 The Compressor Performance Map
	3 Blade Mode Shapes and Materials of Construction
	4 Nonsteady Potential Flow in Cascades
	5 Compressible Flow
	6 Periodically Stalled Flow in Turbomachines
	7 Stall Flutter in Turbomachines
	8 Choking Flutter
	9 Aeroelastic Eigenvalues
	10 Recent Trends
	References
Modeling of Fluid-Structure Interaction
	1 The Range of Physical Models
		1.1 The Classical Models
		1.2 The Distinction Between Linear and Nonlinear Models
		1.3 Computational Fluid Dynamics Models
		1.4 The Computational Challenge of Fluid Structure Interaction Modeling
	2 Time-Linearized Models
		2.1 Classical Aerodynamic Theory
		2.2 Classical Hydrodynamic Stability Theory
		2.3 Parallel Shear Flow with An Inviscid Dynamic Perturbation
		2.4 General Time-Linearized Analysis
		2.5 Some Numerical Examples
	3 Nonlinear Dynamical Models
		3.1 Harmonic Balance Method
		3.2 System Identification Methods
		3.3 Nonlinear Reduced-Order Models
		3.4 Reduced-Order Models
		3.5 Constructing Reduced Order Models
		3.6 Linear and Nonlinear Fluid Models
		3.7 Eigenmode Computational Methodology
		3.8 Proper Orthogonal Decomposition Modes
		3.9 Balanced Modes
		3.10 Synergy Among the Modal Methods
		3.11 Input/Output Models
		3.12 Structural, Aerodynamic, and Aeroelastic Modes
		3.13 Representative Results
	4 Concluding Remarks and Directions for Future Research
	References
Experimental Aeroelasticity
	1 Review of Structural Dynamics Experiments
	2 Wind Tunnel Experiments
		2.1 Sub-critical Flutter Testing
		2.2 Approaching the Flutter Boundary
		2.3 Safety Devices
		2.4 Research Tests Versus Clearance Tests
		2.5 Scaling Laws
	3 Flight Experiments
		3.1 Approaching the Flutter Boundary
		3.2 Excitation
		3.3 Examples of Recent Flight Flutter Test Programs
	4 The Role of Experimentation and Theory in Design
	References
Nonlinear Aeroelasticity
	1 Introduction
	2 Generic Nonlinear Aeroelastic Behavior
	3 Flight Experience with Nonlinear Aeroelastic Effects
		3.1 Nonlinear Aerodynamic Effects
		3.2 Freeplay
		3.3 Geometric Structural Nonlinearities
	4 Physical Sources of Nonlinearities
	5 Efficient Computation of Unsteady Aerodynamic Forces: Linear and Nonlinear
	6 Correlations of Experiment/Theory and Theory/Theory
		6.1 Aerodynamic Forces
	7 Flutter Boundaries in Transonic Flow
		7.1 AGARD 445.6 Wing
		7.2 HSCT Rigid and Flexible Semispan Models
		7.3 Benchmark Active Control Technology (BACT) Model
		7.4 Isogai Case a Model
	8 Limit Cycle Oscillations
		8.1 Airfoils with Stiffness Nonlinearities
		8.2 Nonlinear Internal Resonance Behavior
		8.3 Delta Wings with Geometrical Plate Nonlinearities
		8.4 Very High Aspect Ratio Wings with Both Structural and Aerodynamic Nonlinearities
		8.5 Nonlinear Structural Damping
		8.6 Large Shock Motions and Flow Separation
		8.7 Abrupt Wing Stall
		8.8 Uncertainty Due to Nonlinearity
	9 Concluding Remarks
	References
Aeroelastic Control
	1 Introduction
	2 Linear System Theory
		2.1 System Interconnections
		2.2 Controllability and Observability
	3 Aeroelasticity: Aerodynamic Feedback
		3.1 Development of a Typical Section Model
		3.2 Aerodynamic Model, 2D
		3.3 Balanced Model Reduction
		3.4 Combined Aeroelastic Model
		3.5 Development of a Delta Wing Model
		3.6 Transducer Effects
		3.7 Aerodynamic Model, 3D
		3.8 Coupled System
	4 Open-Loop Design Considerations
		4.1 Optimization Strategy
		4.2 Optimization Results
	5 Control Law Design
		5.1 Control of the Typical Section Model
		5.2 Control of the Delta Wing Model
	6 Parameter Varying Models
		6.1 Linear Matrix Inequalities
		6.2 LMI Controller Specifications
		6.3 An LMI Design for the Typical Section
	7 Experimental Results
		7.1 Typical Section  Experiment
		7.2 LPV System Identification
		7.3 Closed-Loop Results
		7.4 Delta Wing Experiment
	8 Closing Comments on Aeroelastic Control
	References
Modern Analysis for Complex and Nonlinear Unsteady Flows in Turbomachinery
	1 Linearized Analysis of Unsteady Flows
	2 Analysis of Unsteady Flows in Multistage Machines
	3 The Harmonic Balance Method for Nonlinear Unsteady Aerodynamics
	4 Conclusions
	References
Some Recent Advances in Nonlinear Aeroelasticity
	1 Introduction
	2 Motivation and Goals
	3 Current Examples of Recent Advances
		3.1 Transonic and Subsonic Panel Flutter
		3.2 Freeplay Induced Flutter and Limit Cycle Oscillations
		3.3 Reduced Order Modeling of Unsteady Aerodynamics
	4 Transonic Flutter and LCO of Lifting Surfaces
		4.1 Generic Nonlinear Aeroelastic Behavior
		4.2 Flight Experience with Nonlinear Aeroelastic Effects
		4.3 Physical Sources of Nonlinearities
		4.4 Efficient and Accurate Computation of Unsteady Aerodynamic Forces: Linear and Nonlinear
		4.5 Experimental/Theoretical Correlations
	5 Aerodynamic LCO: Buffet, AWS and NSV
	6 Concluding Remarks
	References
Aeroelastic Models Design/Experiment and Correlation with New Theory
	1 Introduction
	2 Experimental Models for Measuring Flutter/Limit Cycle Oscillation (LCO) Response to Evaluate A Nonlinear Structural Theory
		2.1 High Altitude Long Endurance Models (Nonlinear Beam Structural Theory and ONERA Aerodynamic Model)
		2.2 Flapping Flag and Yawed Plate Models (Nonlinear Inextensible Beam and Plate Theory)
		2.3 Free-to Roll Fuselage Flutter Model (Symmetric and Anti-symmetric Flutter/LCO Theory)
	3 Experimental Models for Measuring Flutter/LCO Response to Evaluate Nonlinear Freeplay Theory
		3.1 Airfoil Section with Control Surface Freeplay
		3.2 All-Movable Tail Model with Freeplay
	4 Experimental Models for Measuring Aerodynamic Response Phenomenon in Buffeting Flow
		4.1 An Oscillating Airfoil Section Model in Buffeting Flow
		4.2 An Airfoil with and without Freeplay Control Surface in Buffeting Flow
	5 Design of A Gust Generator and Gust Responses to Linear and Nonlinear Structural Models
		5.1 Structural Design of RSC Gust Generator and Measurement of Gust Angles
		5.2 Verification of Design Principle of RSC Gust Generator
		5.3 Gust Responses for High-Aspect-Ratio Wing
	6 Aero-Electromechanical Interaction: Theoretical and Experimental Correlation of Energy Harvesting
		6.1 Experimental Model and Measurement System
		6.2 Theoretical/Experimental Correlations
	7 Conclusions
	References
Fluid/Structural/Thermal/Dynamics Interaction (FSTDI) in Hypersonic Flow
	1 An Introduction and Overview
		1.1 Two Disciplines Interaction
		1.2 Three Disciplines (FSD) Interaction
		1.3 Four Disciplines (FSTD) Interaction
		1.4 Distinction Between a Plate with All Fixed (Clamped) Edges and a Cantilevered Plate (Clamped on One Edge Only)
	2 Correlations of Theory and Experiment
		2.1 Introduction
		2.2 Physical Phenomena of Interest
		2.3 Key Parameters for Experiments and Theory
		2.4 Representative Correlations of Theory and Experiment
		2.5 Summary of the State of the Art Based upon Correlations of Theory and Experiment and Opportunities to Advance the State of the Art
	3 Current Experimental Programs and Complementary Computational Results
		3.1 Air Force Research Laboratory (SM Spottswood, R Perez, T Berberniss) with Computational Support from Duke University (M Freydin, EH Dowell)
		3.2 University of New South Wales (A Neely and G Currao) with Computational Support from Duke University (M Freydin, K McHugh and EH Dowell)
		3.3 Sandia (K Caspers) with Supporting Computations from the Duke Team
		3.4 North Carolina State University (V Narayanaswamy) with Computational and Experimental Support from Duke University (M Freydin, D Levin, EH Dowell)
		3.5 University of Maryland (S Laurence, T Whalen) and NASA Langley Research Center (G Buck) with Computational Support from Duke University (M Freydin, EH Dowell)
	4 Computational Models and Methods
		4.1 Computational Models (Fluids)
		4.2 Computational Models (Structures)
		4.3 Computational Models (Thermal)
	5 Concluding Remarks on the State of the Art and Prospects for Future Work
	References
Appendix A A Primer for Structural Response to Random Pressure Fluctuations
A.1 Introduction
A.2 Excitation-Response Relation For The Structure
A.3 Sharp Resonance or Low Damping Approximation
Appendix B Some Example Problems
B.1 For Chapter ``Static Aeroelasticity''
B.2 For Sect.3.1
B.3 For Sect.3.3
B.4 For Sect.3.6
B.5 For Sect.4.1
Appendix C Shock Wave Boundary Layer Interaction in Hypersonic Flow—A Fluid Structures Thermal Dynamics Interaction (FSTDI) Perspective
C.1 Shock Wave Boundary Layer Interaction in Hypersonic Flow—A Brief Review of the Literature and a Proposed Research Approach
C.2 Proposed Approach
C.2.1 Flat Plate with a Leading Edge Followed by a Ramp
C.2.2 Computational Protocol
C.2.3 Expected Outcomes
Index