A Modern Course In Aeroelasticity

, by Dowell, E. H.; Cox, David; Curtiss, Howard C., Jr.; Edwards, John W.; Hall, Kenneth C.

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ISBN: 9781402027116 | 1402027117
Cover: Paperback
Copyright: 10/1/2004

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In this new edition, the fundamental material on classical linear aeroelasticity has been revised. Also new material has been added describing recent results on the research frontiers dealing with nonlinear aeroelasticity as well as major advances in the modelling of unsteady aerodynamic flows using the methods of computational fluid dynamics and reduced order modeling techniques. New chapters on aeroelasticity in turbomachinery and aeroelasticity and the latter chapters for a more advanced course, a graduate seminar or as a reference source for an entrée to the research literature.

Preface

xvii

Preface to the First Edition

xvii

Preface to the Second Edition

xix

Preface to the Third Edition

Preface to the Fourth Edition

xxi

Short Bibliography

xxiii

Introduction (Dowell)

(4)

Static Aeroelasticity (Dowell)

(48)

Typical Section Model of An Airfoil

(13)

Typical section model with control surface

(6)

Typical section model---nonlinear effects

(2)

One Dimensional Aeroelastic Model of Airfoils

(8)

Beam-rod representation of large aspect ratio wing

(4)

Eigenvalue and eigenfunction approach

(2)

Galerkin's method

(2)

Rolling of a Straight Wing

(15)

Integral equation of equilibrium

(1)

Derivation of equation of equilibrium

(1)

Calculation of Cαα

(1)

Sketch of function S(y1,η)

(2)

Aerodynamic forces (including spanwise induction)

(2)

Aeroelastic equations of equilibrium and lumped element solution method

(1)

Divergence

(1)

Reversal and rolling effectiveness

(3)

Integral equation eigenvalue problem and the experimental determination of influence functions

(4)

Two Dimensional Aeroelastic Model of Lifting Surfaces

(3)

Two dimensional structures---integral representation

(1)

Two dimensional aerodynamic surfaces---integral representation

(1)

Solution by matrix-lumped element approach

(1)

Other Physical Phenomena

(3)

Fluid flow through a flexible pipe

(3)

(Low speed) fluid flow over a flexible wall

(1)

Sweptwing Divergence

(6)

References for Chapter 2

(2)

Dynamic Aeroelasticity (Dowell)

(116)

Hamilton's Principle

(6)

Single particle

(2)

Many particles

(1)

Continuous body

(1)

Potential energy

(3)

Nonpotential forces

(1)

Lagrange's Equations

(4)

Example---typical section equations of motion

(3)

Dynamics of the Typical Section Model of An Airfoil

(23)

Sinusoidal motion

(3)

Periodic motion

(1)

Arbitrary motion

(6)

Random motion

(8)

Flutter - an introduction to dynamic aeroelastic instability

(4)

Quasi-steady, aerodynamic theory

(2)

Aerodynamic Forces

(10)

Aerodynamic theories available

(4)

General approximations

(1)

`Strip theory' approximation

(1)

`Quasisteady' approximation

(1)

Slender body or slender (low aspect ratio) wing approximation

(1)

Solutions to the Aeroelastic Equations of Motion

(6)

Time domain solutions

(2)

Frequency domain solutions

100

(3)

Representative Results and Computational Considerations

103

(25)

Time domain

103

(1)

Frequency domain

103

(2)

Flutter and gust response classification including parameter trends

105

(1)

Flutter

105

(16)

Gust response

121

(7)

Generalized Equations of Motion for Complex Structures

128

(28)

Lagrange's equations and modal methods (Rayleigh-Ritz)

128

(1)

Kinetic energy

129

(1)

Strain (potential elastic) energy

130

(3)

Examples

133

(1)

Torsional vibrations of a rod

133

(1)

Bending-torsional motion of a beam-rod

134

(1)

Natural frequencies and modes-eigenvalues and eigenvectors

135

(1)

Evaluation of generalized aerodynamic forces

136

(1)

Equations of motion and solution methods

137

(2)

Integral equations of equilibrium

139

(2)

Natural frequencies and modes

141

(2)

Proof of orthogonality

143

(1)

Forced motion including aerodynamic forces

144

(3)

Examples

147

(1)

Rigid wing undergoing translation responding to a gust

147

(6)

Wing undergoing translation and spanwise bending

153

(2)

Random gusts-solution in the frequency domain

155

(1)

Other Fluid-Structural Interaction Phenomena

156

(13)

Fluid flow through a flexible pipe: ``firehose'' flutter

156

(2)

(High speed) fluid flow over a flexible wall - a simple prototype for plate or panel flutter

158

(7)

References for Chapter 3

165

(4)

Nonsteady Aerodynamics (Dowell)

169

(106)

Basic Fluid Dynamic Equations

169

(13)

Conservation of mass

170

(1)

Conservation of momentum

171

(1)

Irrotational flow, Kelvin's theorem and Bernoulli's equation

172

(2)

Derivation of a single equation for velocity potential

174

(1)

Small perturbation theory

175

(2)

Reduction to classical acoustics

177

(1)

Boundary conditions

178

(2)

Symmetry and anti-symmetry

180

(2)

Supersonic Flow

182

(19)

Two-dimensional flow

182

(1)

Simple harmonic motion of the airfoil

183

(2)

Discussion of inversion

185

(2)

Discussion of physical significance of the results

187

(2)

Gusts

189

(1)

Transient motion

190

(1)

Lift, due to airfoil motion

191

(1)

Lift, due to atmospheric gust

192

(3)

Three dimensional flow

195

(6)

Subsonic Flow

201

(31)

Derivation of the integral equation by transform methods and solution by collocation

201

(3)

An alternative determination of the Kernel Function using Green's Theorem

204

(3)

Incompressible, three-dimensional flow

207

(4)

Compressible, three-dimensional flow

211

(4)

Incompressible, two-dimensional flow

215

(3)

Simple harmonic motion of an airfoil

218

(6)

Transient motion

224

(5)

Evaluation of integrals

229

(3)

Representative Numerical Results

232

(6)

Transonic Flow

238

(37)

References for Chapter 4

270

(5)

Stall Flutter (Sisto)

275

(24)

Background

275

(1)

Analytical formulation

276

(2)

Stability and aerodynamic work

278

(1)

Bending stall flutter

279

(2)

Nonlinear mechanics description

281

(1)

Torsional stall flutter

282

(3)

General comments

285

(3)

Reduced order models

288

(1)

Computational stalled flow

289

(10)

References for Chapter 5

294

(5)

Aeroelasticity in Civil Engineering (Scanlan and Simiu)

299

(78)

Vortex-induced Oscillation

301

(13)

Vortex shedding

301

(4)

Modeling of vortex-induced oscillations

305

(1)

Coupled two-degree-of-freedom equations: wake oscillator models

306

(4)

Single-degree-of- freedom model of vortex-induced response

310

(4)

Galloping

314

(13)

Equation of motion of galloping bodies. The Glauert-Den Hartog necessary condition for galloping instability

314

(6)

Description of galloping motion

320

(1)

Chaotic galloping of two elastically coupled square bars

321

(1)

Wake galloping: physical description and analysis

321

(6)

Torsional Divergence

327

(1)

Flutter and Buffeting in the Presence of Aeroelastic Effects

328

(8)

Formulation and analytical solution of the two-dimensional bridge flutter problem in smooth flow

330

(4)

Bridge section response to excitation by turbulent wind in the presence of aeroelastic effects

334

(2)

Suspension-Span Bridges

336

(25)

Wind tunnel testing of suspended-span bridges

336

(2)

Torsional divergence analysis for a full bridge

338

(2)

Locked-in vortex-induced response

340

(10)

Flutter and buffeting of a full-span bridge

350

(10)

Reduction of bridge susceptibility to flutter

360

(1)

Tall Chimneys and Stacks, and Tall Buildings

361

(16)

Tall chimneys and stacks

361

(4)

Tall buildings

365

(2)

References for Chapter 6

367

(10)

Aeroelastic Response of Rotorcraft (Curtiss and Peters)

377

(76)

Blade Dynamics

379

(24)

Articulated, rigid blade motion

379

(11)

Elastic motion of hingeless blades

390

(13)

Stall Flutter

403

(6)

Rotor-Body Coupling

409

(24)

Unsteady Aerodynamics

433

(20)

Dynamic inflow

434

(6)

Frequency domain

440

(1)

Finite-state wake modelling

441

(3)

Summary

444

(1)

References for Chapter 7

444

(9)

Aeroelasticity in Turbomachines (Sisto)

453

(38)

Aeroelastic Environment in Turbomachines

454

(1)

The Compressor Performance Map

455

(5)

Blade Mode Shapes and Materials of Construction

460

(2)

Nonsteady Potential Flow in Cascades

462

(5)

Compressible Flow

467

(4)

Periodically Stalled Flow in Turbomachines

471

(4)

Stall Flutter in Turbomachines

475

(2)

Choking Flutter

477

(2)

Aeroelastic Eigenvalues

479

(2)

Recent Trends

481

(10)

References for Chapter 8

487

(4)

Modeling of Fluid-Structure Interaction (Dowell and Hall)

491

(50)

The Range Of Physical Models

491

(5)

The classical models

491

(3)

The distinction between linear and nonlinear models

494

(1)

Computational fluid dynamics models

495

(1)

The computational challenge of fluid structure interaction modeling

495

(1)

Time-Linearized Models

496

(4)

Classical aerodynamic theory

496

(1)

Classical hydrodynamic stability theory

497

(1)

Parallel shear flow with an inviscid dynamic perturbation

497

(1)

General time-linearized analysis

498

(2)

Some numerical examples

500

(1)

Nonlinear Dynamical Models

500

(24)

Harmonic balance method

503

(1)

System identification methods

503

(1)

Nonlinear reduced-order models

504

(1)

Reduced-order models

504

(1)

Constructing reduced order models

505

(1)

Linear and nonlinear fluid models

506

(1)

Eigenmode computational methodology

507

(1)

Proper orthogonal decomposition modes

508

(1)

Balanced modes

509

(1)

Synergy among the modal methods

509

(1)

Input/output models

509

(2)

Structural, aerodynamic, and aeroelastic modes

511

(1)

Representative results

512

(1)

The effects of spatial discretization and a finite computational domain

512

(4)

The effects of mach number and steady angle of attack: subsonic and transonic flows

516

(5)

The effects of viscosity

521

(1)

Nonlinear aeroelastic reduced-order models

522

(2)

Concluding Remarks

524

(17)

References for Chapter 9

529

(9)

Appendix: Singular-Value Decomposition, Proper Orthogonal Decomposition, & Balanced Modes

538

(3)

Experimental Aeroelasticity (Dowell)

541

(10)

Review of Structural Dynamics Experiments

541

(2)

Wind Tunnel Experiments

543

(2)

Sub-critical flutter testing

543

(1)

Approaching the flutter boundary

544

(1)

Safety devices

544

(1)

Research tests vs. clearance tests

544

(1)

Scaling laws

544

(1)

Flight Experiments

545

(1)

Approaching the flutter boundary

545

(1)

When is flight flutter testing required?

545

(1)

Excitation

545

(1)

Examples of recent flight flutter test programs

546

(1)

The Role of Experimentation and Theory in Design

546

(5)

References for Chapter 10

548

(3)

Nonlinear Aeroelasticity (Dowell, Edwards and Strganac)

551

(60)

Introduction

551

(1)

Generic Nonlinear Aeroelastic Behavior

552

(2)

Flight Experience with Nonlinear Aeroelastic Effects

554

(3)

Nonlinear aerodynamic effects

556

(1)

Freeplay

556

(1)

Geometric structural nonlinearities

557

(1)

Physical Sources of Nonlinearities

557

(1)

Efficient Computation of Unsteady Aerodynamic Forces: Linear and Nonlinear

558

(2)

Correlations of Experiment/Theory and Theory/Theory

560

(6)

Aerodynamic forces

560

(6)

Flutter Boundaries in Transonic Flow

566

(7)

Limit Cycle Oscillations

573

(38)

Airfoils with stiffness nonlinearities

573

(2)

Nonlinear internal resonance behavior

575

(2)

Delta wings with geometrical plate nonlinearities

577

(1)

Very high aspect ratio wings with both structural and aerodynamic nonlinearities

578

(3)

Nonlinear structural damping

581

(1)

Large shock motions and flow separation

581

(13)

Abrupt wing stall

594

(1)

Uncertainty due to nonlinearity

595

(3)

References for Chapter 11

598

(13)

Aeroelastic Control (Clark and Cox)

611

(64)

Introduction

611

(1)

Linear System Theory

612

(5)

System interconnections

612

(3)

Controllability and observability

615

(2)

Aeroelasticity: Aerodynamic Feedback

617

(19)

Development of a typical section model

617

(2)

Aerodynamic model, 2D

619

(3)

Balanced model reduction

622

(1)

Combined aeroelastic model

623

(4)

Development of a delta wing model

627

(3)

Transducer effects

630

(3)

Aerodynamic model, 3D

633

(1)

Coupled system

634

(2)

Open-Loop Design Considerations

636

(6)

HSVs and the modal model

637

(1)

Optimization strategy

638

(3)

Optimization results

641

(1)

Control Law Design

642

(5)

Control of the typical section model

644

(3)

Control of the delta wing model

647

(1)

Parameter Varying Models

647

(7)

Linear matrix inequalities

648

(1)

LMI controller specifications

649

(3)

An LMI design for the typical section

652

(2)

Experimental Results

654

(13)

Typical section experiment

655

(1)

LPV system identification

656

(2)

Closed-loop results

658

(6)

Delta wing experiment

664

(3)

Closing Comments

667

(8)

References for Chapter 12

669

(6)

Modern Analysis for Complex and Nonlinear Unsteady Flows in Turbomachinery (Hall)

675

(29)

Linearized Analysis of Unsteady Flows

676

(7)

Analysis of Unsteady Flows

683

(5)

Harmonic Balance Method

688

(11)

Conclusions

699

(5)

References for Chapter 13

701

(3)

Appendices

704

(39)

Appendix A: A Primer For Structural Response To Random Pressure Fluctuations

705

(6)

A.1 Introduction

705

(1)

A.2 Excitation-Response Relation For The Structure

705

(4)

A.3 Sharp Resonance or Low Damping Approximation

709

(1)

Nomenclature

710

(1)

References for Appendix A

710

(1)

Appendix B: Some Example Problems

711

(32)

B.1 For Chapter 2

711

(13)

B.2 For Section 3.1

724

(6)

B.3 For Section 3.3

730

(5)

B.4 For Section 3.6

735

(3)

B.5 For Section 4.1

738

(5)

Index

743

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A Modern Course In Aeroelasticity

Summary

Table of Contents

Supplemental Materials