A modern course in aeroelasticity A modern course in aeroelasticity

MECHANICS: DYNAMICAL SYSTEMS Editors: L. Meirovitch and G. /E Oravas

E. H. Dowell, Aeroelasticity of Plates and Shells. 1974. ISBN 90-286-0404-9.

D. G. B. Edelcn, Lagrangian Mechanics of Nonconservativc Non­holonomic Systems. 1977. ISBN 90-286-0077-9.

J. L. Junkins, An Introduction to Optical Estimation of Dynamical Systems. )978. ISBN 90-286-0067-1.

E. H. Dowell et al., A Modern Course in Aeroelasticity. 1978. ISBN 90-286-0057-4.

L. Meirovitch, Computational Methods in Structural Dynamics. 1980. ISBN 90-286-0580-0.

B. Skalmierski and A. Tylikowski, Stochastic Processes in Dynamics. 1982. ISBN 90-247-2686-7.

P. C. Müller and W. O. Schiehlen, Linear Vibrations. 1985. ISBN 90-247-2983-1.

Gh. Buzdugan, E. Mihäilescu and M. Rade§, Vibration Measurement. 1986. ISBN 90-247-3111-9.

G. M. L. Gladwell, Inverse Problems in Vibration. 1986. ISBN 90-247-3408-8.

G. I. Schueller and M. Shinozuka (eds.), Stochastic Methods in Structural Dynamies. 1987. ISBN 90-247-3611-0.

E. H. Dowell, H. C. Curtiss, Jr., R. H. Scanlan and F. Sisto, A Modern Course in Aeroelasticity. Second revised and enlarged edition. 1989. ISBN 0-7923-0062-9.

MECHANICS: DYNAMICAL SYSTEMS Editors: L. Meirovitch and G. /E Oravas

E. H. Dowell, Aeroelasticity of Plates and Shells. 1974. ISBN 90-286-0404-9.

D. G. B. Edelcn, Lagrangian Mechanics of Nonconservativc Non­holonomic Systems. 1977. ISBN 90-286-0077-9.

J. L. Junkins, An Introduction to Optical Estimation of Dynamical Systems. )978. ISBN 90-286-0067-1.

E. H. Dowell et al., A Modern Course in Aeroelasticity. 1978. ISBN 90-286-0057-4.

L. Meirovitch, Computational Methods in Structural Dynamics. 1980. ISBN 90-286-0580-0.

B. Skalmierski and A. Tylikowski, Stochastic Processes in Dynamics. 1982. ISBN 90-247-2686-7.

P. C. Müller and W. O. Schiehlen, Linear Vibrations. 1985. ISBN 90-247-2983-1.

Gh. Buzdugan, E. Mihäilescu and M. Rade§, Vibration Measurement. 1986. ISBN 90-247-3111-9.

G. M. L. Gladwell, Inverse Problems in Vibration. 1986. ISBN 90-247-3408-8.

G. I. Schueller and M. Shinozuka (eds.), Stochastic Methods in Structural Dynamies. 1987. ISBN 90-247-3611-0.

E. H. Dowell, H. C. Curtiss, Jr., R. H. Scanlan and F. Sisto, A Modern Course in Aeroelasticity. Second revised and enlarged edition. 1989. ISBN 0-7923-0062-9.

A modern course in aeroelasticity

Second revised and enlarged edition

Earl H. Dowell, editor, Professor of Mechanical Engineering and Materials Science Duke University, Durharn, North Carolina, U.S.A.

Howard C. Curtiss, Jr. Professor of Mechanical and Aerospace Engineering Princeton University, Princeton, New Jersey, U.S.A.

Robert H. Scanlan Professor of Civil Engineering Johns Hopkins University, Baltimore, Maryland, U.S.A.

and

Fernando Sisto Professor of Mechanical Engineering Stevens Institute of Technology, Hoboken, New Jersey, U.S.A.

Springer-Science+Business Media, B.V.

A modern course in aeroelasticity

Second revised and enlarged edition

Earl H. Dowell, editor, Professor of Mechanical Engineering and Materials Science Duke University, Durharn, North Carolina, U.S.A.

Howard C. Curtiss, Jr. Professor of Mechanical and Aerospace Engineering Princeton University, Princeton, New Jersey, U.S.A.

Robert H. Scanlan Professor of Civil Engineering Johns Hopkins University, Baltimore, Maryland, U.S.A.

and

Fernando Sisto Professor of Mechanical Engineering Stevens Institute of Technology, Hoboken, New Jersey, U.S.A.

Springer-Science+Business Media, B.V.

A Modp.rn course in aeroelasticity.

(Mecbanics, dynallical syste_ ; Includes bibliographies and indexes. 1. Aeroelasticity. 1. Dowell, E. H. H. Series.

TL574.A37M62 1989 629.132'362 88-32051 ISBN 978-0-7923-0185-1 ISBN 978-94-015-7858-5 (eBook) DOI 10.1007/978-94-015-7858-5

This is the revised and enlarged edition 01 a book published in 1978 by Sijthof! & Noordhof! International Publishers, in the series • Mechanics: Dynamical Systems' (Volume 3)

printed on acid/ree paper

All Rights Reserved © 1989 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1989 Softcover reprint ofthe hardcover 2nd edition 1989 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner

A Modp.rn course in aeroelasticity.

(Mecbanics, dynallical syste_ ; Includes bibliographies and indexes. 1. Aeroelasticity. 1. Dowell, E. H. H. Series.

TL574.A37M62 1989 629.132'362 88-32051 ISBN 978-0-7923-0185-1 ISBN 978-94-015-7858-5 (eBook) DOI 10.1007/978-94-015-7858-5

This is the revised and enlarged edition 01 a book published in 1978 by Sijthof! & Noordhof! International Publishers, in the series • Mechanics: Dynamical Systems' (Volume 3)

printed on acid/ree paper

All Rights Reserved © 1989 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1989 Softcover reprint ofthe hardcover 2nd edition 1989 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner

Ubrary of eoDlress Catalolilll iD hblkatioll Data

Contents

Preface xiii

Prelace to the second edition xv

Short bibliography xvii

1. Introduction . 1

2. Static aeroelastidty 3

2.1 Typical section model 01 an airfoil . 3 Typical section with control surface 8 Typical section-nonlinear effects . 12

2.2 One dimensional aeroelastic model 01 airloils 15 Beam-rod representation of large aspect ratio wing 15 Eigenvalue and eigenfunction approach 18 Galerkin's method .............. 20

2.3 Rolling 01 a straight wing. . . . . . 22 Integral equation of equilibrium 22 Derivation of equation of equilibrium 24 Calculation of C"'. . . . . . . . . 25 Sketch of function S(Yl' 1/). . . . . 25 Aerodynamic forces (including spanwise induction) 27 Aeroelastic equations of equilibrium and lumped element

solution method ..... 29 Divergence . . . . . . . . . . 31 Reversal and rolling effectiveness 31

v

Contents

Preface xiii

Prelace to the second edition xv

Short bibliography xvii

1. Introduction . 1

2. Static aeroelastidty 3

2.1 Typical section model 01 an airfoil . 3 Typical section with control surface 8 Typical section-nonlinear effects . 12

2.2 One dimensional aeroelastic model 01 airloils 15 Beam-rod representation of large aspect ratio wing 15 Eigenvalue and eigenfunction approach 18 Galerkin's method .............. 20

2.3 Rolling 01 a straight wing. . . . . . 22 Integral equation of equilibrium 22 Derivation of equation of equilibrium 24 Calculation of C"'. . . . . . . . . 25 Sketch of function S(Yl' 1/). . . . . 25 Aerodynamic forces (including spanwise induction) 27 Aeroelastic equations of equilibrium and lumped element

solution method ..... 29 Divergence . . . . . . . . . . 31 Reversal and rolling effectiveness 31

v

Contents

Integral equation eigenvalue problem and the experi-mental determination of influence functions . . 35

2.4 Two dimensional aeroelastic model o{ lifting surfaces . .. 38 Two dimensional structures-integral representation . .. 38 Two dimensional aerodynamic surfaces-integral represen-

tation .. . . . . . . . . . . . . . . 40 Solution by matrix-Iumped element approach. 40

2.5 Nonairfoil physical problems . . . . . . 42 Fluid flow through a flexible pipe . . . . 42 (Low speed) fluid flow over a flexible wall 45

2.6 Sweptwing divergence. 46

Re{erences tor Chapter 2 49

3. Dynamic aeroelasticity 51

vi

3.1 Hamilton' s principle Single particle Many particles . Continuous body Potential energy Nonpotential forces

52 52 54 54 54 57

3.2 Lagrange's equations 58 Example-typical section equations of motion 59

3.3 Dynamics ot the typical section modelot an airfoil 62 Sinusoidal motion 63 Periodic motion 65 Arbitrary motion 66 Random motion 72 Flutter-an introduction to dynamic aeroelastic insta-

bility ........ 80 Quasi-steady, aerodynamic theory ....... 83

3.4 Aerodynamic torces tor airfoils-an introduction and summary ........ . Aerodynamic theories available General approximations . . .

'Strip theory' approximation

85 89 93 93

Contents

Integral equation eigenvalue problem and the experi-mental determination of influence functions . . 35

2.4 Two dimensional aeroelastic model o{ lifting surfaces . .. 38 Two dimensional structures-integral representation . .. 38 Two dimensional aerodynamic surfaces-integral represen-

tation .. . . . . . . . . . . . . . . 40 Solution by matrix-Iumped element approach. 40

2.5 Nonairfoil physical problems . . . . . . 42 Fluid flow through a flexible pipe . . . . 42 (Low speed) fluid flow over a flexible wall 45

2.6 Sweptwing divergence. 46

Re{erences tor Chapter 2 49

3. Dynamic aeroelasticity 51

vi

3.1 Hamilton' s principle Single particle Many particles . Continuous body Potential energy Nonpotential forces

52 52 54 54 54 57

3.2 Lagrange's equations 58 Example-typical section equations of motion 59

3.3 Dynamics ot the typical section modelot an airfoil 62 Sinusoidal motion 63 Periodic motion 65 Arbitrary motion 66 Random motion 72 Flutter-an introduction to dynamic aeroelastic insta-

bility ........ 80 Quasi-steady, aerodynamic theory ....... 83

3.4 Aerodynamic torces tor airfoils-an introduction and summary ........ . Aerodynamic theories available General approximations . . .

'Strip theory' approximation

85 89 93 93

Contents

'Quasi-steady' approximation . . . . . 93 Slender body or slender (low aspect ratio) wing approximation. . . . . . . . . . . . 94

3.5 Solutions to the aeroelastic equations of motion 95 Time domain solutions .......... 96 Frequency domain solutions. . . . . . . . . 98

3.6 Representative results and computational considerations . I () I Time domain ................ 1 01 Frequency domain .............. 103 Flutter and gust response classification including para-

meter trends 105 Flutter . . . . . . . . . . . . . . . . . . . . 105 Gust response. . . . . . . . . . . . . . . . . 118

3.7 Generalized equations of motion for complex structures . 124 Lagrange's equations and modal methods 124 Kinetic energy . . . . . . . . 126 Strain (potential, elastic) energy 126 Examples .......... 129

(a) Torsional vibrations of a rod. 129 (b) Bending-torsional motion of a beam-rod 130

Natural frequencies and modes-eigenvalues and eigen-vectors ............... 13 1

Evaluation of generalized aerodynamic forces 132 Equations of motion and solution methods . 133 Integral equations of equilibrium 135 Natural frequencies and modes . . . . . . 137

Proof of orthogonality . . . . . . . . . 139 Forced motion including aerodynamic forces 140 Examples ............... 143

(a) Rigid wing undergoing translation responding to a gust . . . . . . . . . . . . . . . . . . .. 143

(b) Wing undergoing translation and spanwise bending 149 (c) Random gusts-solution in the frequency domain. 151

3.8 Nonairfoil physical problems . . . . . . . . . . .. 152 Fluid flow through a flexible pipe . . . . . . . . .. 152 (High speed) fluid flow over a flexible wall-a simple

prototype for plate flutter 155

References for Chapter 3 . . . . . . . . . . . . . . . .. 160

vii

Contents

'Quasi-steady' approximation . . . . . 93 Slender body or slender (low aspect ratio) wing approximation. . . . . . . . . . . . 94

3.5 Solutions to the aeroelastic equations of motion 95 Time domain solutions .......... 96 Frequency domain solutions. . . . . . . . . 98

3.6 Representative results and computational considerations . I () I Time domain ................ 1 01 Frequency domain .............. 103 Flutter and gust response classification including para-

meter trends 105 Flutter . . . . . . . . . . . . . . . . . . . . 105 Gust response. . . . . . . . . . . . . . . . . 118

3.7 Generalized equations of motion for complex structures . 124 Lagrange's equations and modal methods 124 Kinetic energy . . . . . . . . 126 Strain (potential, elastic) energy 126 Examples .......... 129

(a) Torsional vibrations of a rod. 129 (b) Bending-torsional motion of a beam-rod 130

Natural frequencies and modes-eigenvalues and eigen-vectors ............... 13 1

Evaluation of generalized aerodynamic forces 132 Equations of motion and solution methods . 133 Integral equations of equilibrium 135 Natural frequencies and modes . . . . . . 137

Proof of orthogonality . . . . . . . . . 139 Forced motion including aerodynamic forces 140 Examples ............... 143

(a) Rigid wing undergoing translation responding to a gust . . . . . . . . . . . . . . . . . . .. 143

(b) Wing undergoing translation and spanwise bending 149 (c) Random gusts-solution in the frequency domain. 151

3.8 Nonairfoil physical problems . . . . . . . . . . .. 152 Fluid flow through a flexible pipe . . . . . . . . .. 152 (High speed) fluid flow over a flexible wall-a simple

prototype for plate flutter 155

References for Chapter 3 . . . . . . . . . . . . . . . .. 160

vii

Contents

4. Nonsteady aerodynamics 01 liftinl ud non-liftinl snrfaces . 162

4.1 Basic fluid dynamic equations 162 Conservation of mass . . . 163 Conservation of momentum 164 Irrotational ftow, Kelvin's theorem and Bernoulli's

equation ........... 165 Derivation of single equation for velo city potential 168 Small perturbation theory 170

Reduction to acousties 171 Boundary conditions. . . 172

Symmetry and anti-symmetry . 174

4.2 Supersonic flow . . . . . . . . 177 177 178 180 183 184 185 186 187 190

Two-dimensional ftow . . . . . Simple harmonie motion of the airfoil Discussion of inversion ..... . Discussion of physieal significance of results Gusts ........ . Transient motion . . . . . . Lift, due to airfoil motion Lift. due to atmospheric gusts

Three-dimensional ftow

4.3 Subsonic flow .... Derivation of the integral equation by transform methods

and solution by collocation . . . . . . . . . . . . An alternative determination of the Kernel Function using

Green's theorem ....... . Incompressible, three-dimensional ftow Compressible, three-dimensional ftow . Incompressible, two-dimensional ftow .

Simple harmonie motion of an airfoil Transient motion . . . Evaluation of integrals

4.4 Representative numerical results

4.5 Transonic flow . .

References for Chapter 4

Vlll

196

197

200 202 207 212 215 222 226

230

237

267

Contents

4. Nonsteady aerodynamics 01 liftinl ud non-liftinl snrfaces . 162

4.1 Basic fluid dynamic equations 162 Conservation of mass . . . 163 Conservation of momentum 164 Irrotational ftow, Kelvin's theorem and Bernoulli's

equation ........... 165 Derivation of single equation for velo city potential 168 Small perturbation theory 170

Reduction to acousties 171 Boundary conditions. . . 172

Symmetry and anti-symmetry . 174

4.2 Supersonic flow . . . . . . . . 177 177 178 180 183 184 185 186 187 190

Two-dimensional ftow . . . . . Simple harmonie motion of the airfoil Discussion of inversion ..... . Discussion of physieal significance of results Gusts ........ . Transient motion . . . . . . Lift, due to airfoil motion Lift. due to atmospheric gusts

Three-dimensional ftow

4.3 Subsonic flow .... Derivation of the integral equation by transform methods

and solution by collocation . . . . . . . . . . . . An alternative determination of the Kernel Function using

Green's theorem ....... . Incompressible, three-dimensional ftow Compressible, three-dimensional ftow . Incompressible, two-dimensional ftow .

Simple harmonie motion of an airfoil Transient motion . . . Evaluation of integrals

4.4 Representative numerical results

4.5 Transonic flow . .

References for Chapter 4

Vlll

196

197

200 202 207 212 215 222 226

230

237

267

s. StaU lutter

5.1 Background . .... 5.2 Analytical formulation 5.3 Stability and work flow 5.4 Bending stall fluuer . 5.5 Nonlinear mechanics description 5.6 Torsional stall fluuer . . . 5.7 General comments 5.8 Computational stalled flow

References for Chapter 5 . . .

6. Aeroelastic problems of civil eugineering strudures .

6.1 Vortex shedding .......... . Introduction . . . . . . . . . . . . Aspects of response to vortex sheddmg Empirical models of vortex-induced oscillation Commentary on vortex excitation models.

6.2 Galloping. . . . . . Across-wind galloping Wake galloping

6.3 Divergence . . . .

6.4 Flutter and buffeting Basic concepts Three-dimensional flutter and buffeting . Single-mode flutter and buffeting Indicial Function Formulations

References for Chapter 6

7. Aeroelastic problems of rotorcraft

7.1 Blade dynamies ..... . Articulated, rigid bl ade motion Elastic motion of hingeless blades .

7.2 Stall flutter . . . . . . . . 7.3 Blade motionl body coupling .

Two bladed rotors. .

References for Chapter 7 .

Contents

270

270 271 273 274 275 277 280 283

288

290

292 292 295 298 308

314 314 320 323

327 327 335 343 345 348

355

356 358 368 380 385 407

408

ix

s. StaU lutter

5.1 Background . .... 5.2 Analytical formulation 5.3 Stability and work flow 5.4 Bending stall fluuer . 5.5 Nonlinear mechanics description 5.6 Torsional stall fluuer . . . 5.7 General comments 5.8 Computational stalled flow

References for Chapter 5 . . .

6. Aeroelastic problems of civil eugineering strudures .

6.1 Vortex shedding .......... . Introduction . . . . . . . . . . . . Aspects of response to vortex sheddmg Empirical models of vortex-induced oscillation Commentary on vortex excitation models.

6.2 Galloping. . . . . . Across-wind galloping Wake galloping

6.3 Divergence . . . .

6.4 Flutter and buffeting Basic concepts Three-dimensional flutter and buffeting . Single-mode flutter and buffeting Indicial Function Formulations

References for Chapter 6

7. Aeroelastic problems of rotorcraft

7.1 Blade dynamies ..... . Articulated, rigid bl ade motion Elastic motion of hingeless blades .

7.2 Stall flutter . . . . . . . . 7.3 Blade motionl body coupling .

Two bladed rotors. .

References for Chapter 7 .

Contents

270

270 271 273 274 275 277 280 283

288

290

292 292 295 298 308

314 314 320 323

327 327 335 343 345 348

355

356 358 368 380 385 407

408

ix

Contents

8. Aeroelasticity in turbomachines

8.1 Aeroelastic environment in turbomachines 8.2 The compressor performance map . . . 8.3 Blade mode shapes and materials 01 construction 8.4 Nonsteady potential flow in cascades. . 8.5 Compressible flow . . . . . . . . 8.6 Periodically stalled flow in turbomachines 8.7 Stall flutter in turbomachines 8.8 Choking flutter . . . 8.9 Aeroelastic eigenvalues

8.10 Recent trends

References for Chapter 8 . .

9. Unsteady transonie aerodynamies and aeroelasticity

Summary

Nomenclature

9.1 lntroduction

9.2 Linear/ nonlinear behavior in unsteady transonic aerody­namies . . . . . . . . . . Motivation and general background NACA 64A006 airfoil Mach number trends Conclusions

9.3 Viable alternative solution procedures to finite difference

411

412 414 417 419 425 428 432 434 435

438

441

443

443

444

445

446 446 448 453 457

methods 459

x

Hounjet .... 459 Cockey .... 460 A possible synthesis 461

9.4 Nonuniqueness Early work Recent work . Studies of Williams and Salas Aileron buzz . . . . . .

9.5 Effective, efficient computational approaches for determining aeroelastic response . . . .

Various ~pproaches and their merits

462 462 462 469 470

471 471

Contents

8. Aeroelasticity in turbomachines

8.1 Aeroelastic environment in turbomachines 8.2 The compressor performance map . . . 8.3 Blade mode shapes and materials 01 construction 8.4 Nonsteady potential flow in cascades. . 8.5 Compressible flow . . . . . . . . 8.6 Periodically stalled flow in turbomachines 8.7 Stall flutter in turbomachines 8.8 Choking flutter . . . 8.9 Aeroelastic eigenvalues

8.10 Recent trends

References for Chapter 8 . .

9. Unsteady transonie aerodynamies and aeroelasticity

Summary

Nomenclature

9.1 lntroduction

9.2 Linear/ nonlinear behavior in unsteady transonic aerody­namies . . . . . . . . . . Motivation and general background NACA 64A006 airfoil Mach number trends Conclusions

9.3 Viable alternative solution procedures to finite difference

411

412 414 417 419 425 428 432 434 435

438

441

443

443

444

445

446 446 448 453 457

methods 459

x

Hounjet .... 459 Cockey .... 460 A possible synthesis 461

9.4 Nonuniqueness Early work Recent work . Studies of Williams and Salas Aileron buzz . . . . . .

9.5 Effective, efficient computational approaches for determining aeroelastic response . . . .

Various ~pproaches and their merits

462 462 462 469 470

471 471

Coments

Time domain 472 Frequency domain . 473 Summary comparison 474 Nonlinear flutter analysis 474

9.6 Nonlinear /lutter analysis in the frequency domain 475 Motivation and background 475 Typical airfoil section 477 Aerodynamic describing function 47X Aeroelastic system equations 4X 1 Extension of the describing function 4X4 Results and discussion 4X4 Conc1usions 494

9.7 Concluding remarks 495 Some present answers 495 Future work 496

References tor Chapter 9 49X

Appendix I A primer for structural response to random pressure f1uctuations . . . 503

References tor Appendix I 509

Appendix 11 Some example problems 511

Subjed index 55 1

Author index 555

xi

Coments

Time domain 472 Frequency domain . 473 Summary comparison 474 Nonlinear flutter analysis 474

9.6 Nonlinear /lutter analysis in the frequency domain 475 Motivation and background 475 Typical airfoil section 477 Aerodynamic describing function 47X Aeroelastic system equations 4X 1 Extension of the describing function 4X4 Results and discussion 4X4 Conc1usions 494

9.7 Concluding remarks 495 Some present answers 495 Future work 496

References tor Chapter 9 49X

Appendix I A primer for structural response to random pressure f1uctuations . . . 503

References tor Appendix I 509

Appendix 11 Some example problems 511

Subjed index 55 1

Author index 555

xi

Preface

Areader who achieves a substantial command of the material con­tained in this book should be able to read with understanding most of the literature in the field. Possible exceptions may be certain special aspects of the subject such as the aeroelasticity of plates and sheIls or the use of electronic feedback control to modify aeroelastic behavior. The first author has considered the former topic in aseparate volume. The latter topic is also deserving of aseparate volume.

In the first portion of the book the basic physical phenomena of divergence, control surface eflectiveness, flutter and gust response of aeronautical vehicles are treated. As an indication of the expanding scope of the field, representative examples are also drawn from the non­aeronautical literature. To aid the student who is encountering these phenomena for the first time, each is introduced in the context of a simple physical model and then reconsidered systematicaIly in more compli­cated models using more sophisticated mathematics.

Beyond the introductory portion of the book, there are several special features of the text. One is the treatment of unsteady aerodynamics. This crucial part of aeroelasticity is usually the most difficult for the experienced practitioner as weIl as the student. The discussion is developed from the basic fluid mechanics and includes a comprehensive review of the fundamental theory underlying numerical lifting surface analysis. Not only the weIl known results for subsonic and supersonic flow are covered; but also some of the recent developments for transonic flow, which hold promise of bringing eflective solution techniques to this important regime.

Professor Sisto's chapter on Stall Flutter is an authoritative account of this important topic. A difficult and still incompletely understood phenomenon, stall flutter is discussed in terms of its fundamental aspects as weIl as its significance in applications. The reader will find this chapter particularly helpful as an introduction to this complex subject.

XIII

Preface

Areader who achieves a substantial command of the material con­tained in this book should be able to read with understanding most of the literature in the field. Possible exceptions may be certain special aspects of the subject such as the aeroelasticity of plates and sheIls or the use of electronic feedback control to modify aeroelastic behavior. The first author has considered the former topic in aseparate volume. The latter topic is also deserving of aseparate volume.

In the first portion of the book the basic physical phenomena of divergence, control surface eflectiveness, flutter and gust response of aeronautical vehicles are treated. As an indication of the expanding scope of the field, representative examples are also drawn from the non­aeronautical literature. To aid the student who is encountering these phenomena for the first time, each is introduced in the context of a simple physical model and then reconsidered systematicaIly in more compli­cated models using more sophisticated mathematics.

Beyond the introductory portion of the book, there are several special features of the text. One is the treatment of unsteady aerodynamics. This crucial part of aeroelasticity is usually the most difficult for the experienced practitioner as weIl as the student. The discussion is developed from the basic fluid mechanics and includes a comprehensive review of the fundamental theory underlying numerical lifting surface analysis. Not only the weIl known results for subsonic and supersonic flow are covered; but also some of the recent developments for transonic flow, which hold promise of bringing eflective solution techniques to this important regime.

Professor Sisto's chapter on Stall Flutter is an authoritative account of this important topic. A difficult and still incompletely understood phenomenon, stall flutter is discussed in terms of its fundamental aspects as weIl as its significance in applications. The reader will find this chapter particularly helpful as an introduction to this complex subject.

XIII

Preface

Another special feature is aseries of chapters on three areas of .advanced application of the fundamentals of aeroelasticity. The first of these is a discussion of Aeroelastic Problems of Civil Engineering Struc­tures by Professor Scanlan. The next is a discussion of Aeroelasticity of Helicopters and V /STOL aircraft by Professor Curtiss. The final chapter in this series treats Aeroelasticity in Turbomachines and is by Professor Sisto. This series of chapters is unique in the aeroelasticity literature and the first author fe eis particularly fortunate to have the contributions of these eminent experts.

The emphasis in this book is on fundamentals because no single volume can hope to be comprehensive in terms of applications. However, the above three chapters should give the reader an appreciation for the relationship between theory and practice. One of the continual fascina­tions of aeroelasticity is this elose interplay between fundamentals and applications. If one is to deal successfully with applications, asolid grounding in the fundamentals is essential.

For the beginning student, a first course in aeroelasticity could cover Chapters 1-3 and selected portions of 4. For a second course and the advanced student or research worker, the remaining Chapters would be appropriate. In the latter portions of the book, more comprehensive literature citations are given to permit ready access to the current literature.

The reader familiar with the standard texts by Scanlan and Rosen­baum, Fung, Bisplinghofl, Ashley and Halfman and Bisplinghofl and Ashley will appreciate readily the debt the authors owe to them. Recent books by Petre* and Forschingt should also be mentioned though these are less accessible to an english speaking audience. It is hoped the reader will find this volume a worthy successor.

*Petre, A., Theory 0/ Aeroelasticity. Vol. I Staties, Vol. 11 Dynamies. In Romanian. Publishing House of the Academy of the Socialist Republic of Romania, Bucharest, 1966. t Forsching, H. W., Fundamentals 0/ Aeroelastieity. In German. Springer-Verlag, Berlin, 1974.

XIV

Preface

Another special feature is aseries of chapters on three areas of .advanced application of the fundamentals of aeroelasticity. The first of these is a discussion of Aeroelastic Problems of Civil Engineering Struc­tures by Professor Scanlan. The next is a discussion of Aeroelasticity of Helicopters and V /STOL aircraft by Professor Curtiss. The final chapter in this series treats Aeroelasticity in Turbomachines and is by Professor Sisto. This series of chapters is unique in the aeroelasticity literature and the first author fe eis particularly fortunate to have the contributions of these eminent experts.

The emphasis in this book is on fundamentals because no single volume can hope to be comprehensive in terms of applications. However, the above three chapters should give the reader an appreciation for the relationship between theory and practice. One of the continual fascina­tions of aeroelasticity is this elose interplay between fundamentals and applications. If one is to deal successfully with applications, asolid grounding in the fundamentals is essential.

For the beginning student, a first course in aeroelasticity could cover Chapters 1-3 and selected portions of 4. For a second course and the advanced student or research worker, the remaining Chapters would be appropriate. In the latter portions of the book, more comprehensive literature citations are given to permit ready access to the current literature.

The reader familiar with the standard texts by Scanlan and Rosen­baum, Fung, Bisplinghofl, Ashley and Halfman and Bisplinghofl and Ashley will appreciate readily the debt the authors owe to them. Recent books by Petre* and Forschingt should also be mentioned though these are less accessible to an english speaking audience. It is hoped the reader will find this volume a worthy successor.

*Petre, A., Theory 0/ Aeroelasticity. Vol. I Staties, Vol. 11 Dynamies. In Romanian. Publishing House of the Academy of the Socialist Republic of Romania, Bucharest, 1966. t Forsching, H. W., Fundamentals 0/ Aeroelastieity. In German. Springer-Verlag, Berlin, 1974.

XIV

Preface to the second edition The authors would like to thank all those readers who have written with comments and errata for the First Edition. Many of these have been incorporated into the Second Edition. They would like to thank especially Professor Holt Ashley of Stanford University who has been most helpful in identifying and correcting various errata.

Also the opportunity has been taken in the Second Edition to bring up-to-date several of the chapters as weil as add a chapter on unsteady transonic aerodynamics and aeroelasticity. Chapters 2, 5, 6, and 8 have been substantially revised. These cover the topics of Static Aeroelasticity, Stall Flutter, Aeroelastic Problems of Civil Engineering Structures and Aeroelasticity in Turbomachines, respectively. Chapter 9, Unsteady Tran­sonic Aerodynamics and Aeroelasticity, is new and covers this rapidly developing subject in more breadth and depth than the First Edition. Again the emphasis is on fundamental concepts rather than, for example, com­puter code development per se. Unfortunately due to the press of other commitments. it has not been possible to revise Chapter 7, Aeroelastic Problems of Rotorcraft. However, the Short Bibliography has been expan­ded for this subject as weil as for others. It is hoped that the readers of the First Edition and also new readers will find the Second Edition worthy of their study.

xv

Preface to the second edition The authors would like to thank all those readers who have written with comments and errata for the First Edition. Many of these have been incorporated into the Second Edition. They would like to thank especially Professor Holt Ashley of Stanford University who has been most helpful in identifying and correcting various errata.

Also the opportunity has been taken in the Second Edition to bring up-to-date several of the chapters as weil as add a chapter on unsteady transonic aerodynamics and aeroelasticity. Chapters 2, 5, 6, and 8 have been substantially revised. These cover the topics of Static Aeroelasticity, Stall Flutter, Aeroelastic Problems of Civil Engineering Structures and Aeroelasticity in Turbomachines, respectively. Chapter 9, Unsteady Tran­sonic Aerodynamics and Aeroelasticity, is new and covers this rapidly developing subject in more breadth and depth than the First Edition. Again the emphasis is on fundamental concepts rather than, for example, com­puter code development per se. Unfortunately due to the press of other commitments. it has not been possible to revise Chapter 7, Aeroelastic Problems of Rotorcraft. However, the Short Bibliography has been expan­ded for this subject as weil as for others. It is hoped that the readers of the First Edition and also new readers will find the Second Edition worthy of their study.

xv

Short bibliography

Books

Bolotin, V. V., Nonconservative Problems of tlle Elastic Theory of Stability, Pergamon Press, 1963.

(BAH) Bisplinghofl, R. L., Ashley, H. and Halfman, R. L., Aeroelasticity, Addison­Wesley Publishing Company, Cambridge, Mass., 1955.

(BA) Bisplinghofl, R. L. and Ashley, H., Principles of Aeroelasticity, John Wiley and Sons, Inc., New York, N.Y., 1962. Also available in Dover Edition.

Fung, Y. C., An Introduction to the Theory of Aeroelasticity, John Wiley and Sons, Inc., New York, N.Y., 1955. Also available in Dover Edition.

Scanlan, R. H. and Rosenbaum, R., Introduction to the Study of Aircraft Vibration and Fluner, The MacmiIIan Company, New York, N.Y., 1951. Also available in Dover Edition.

(AGARD) AGARD Manual on Aeroelasticity, Vois. I-VII, Beginning 1959 with con­tinual updating.

Ashley, H., Dugundji, J. and Rainey, A. G., Notebook for Aeroelasticity, AIAA Professional Seminar Series, 1969.

Dowell, E. H., Aeroelasticity of Plates and Shells, Noordhofl International Publishing, Leyden, 1975.

Simiu, E. and Scanlan, R. H., Wind Effects on Structures-An Introduction to Wind Engineering, John Wiley and Sons, 1978.

Johnson, W., Helicopter Theory. Princeton University Press, 1980. Dowell, E. H. and Ilgamov, M .• Studies in Nonlinear Aeroelasticity, Springer­

Verlag. 1988.

In parentheses, abbreviations tor the above books are indicated which are used in the text.

Survey artic/es

Garrick, I. E., 'Aeroelasticity-Frontiers and Beyond', 13th Von Karman Lecture, J. of Aircraft, Vol. 13, No. 9, 1976, pp. 641-657.

Several Auiliors, 'Unsteady Aerodynamics. Contribution of the Structures and Materials Panel to the Fluid Dynamics Panel Round Table Discussion on Unsteady Aerodynamics', Goettingen, May 1975, AGARD Report R-645, March 1976.

Rodden, W. P., A Comparison of MetIIods Used in Interfering Lifting Surface Theory, AGARD Report R-643, March 1976.

XVII

Short bibliography

Books

Bolotin, V. V., Nonconservative Problems of tlle Elastic Theory of Stability, Pergamon Press, 1963.

(BAH) Bisplinghofl, R. L., Ashley, H. and Halfman, R. L., Aeroelasticity, Addison­Wesley Publishing Company, Cambridge, Mass., 1955.

(BA) Bisplinghofl, R. L. and Ashley, H., Principles of Aeroelasticity, John Wiley and Sons, Inc., New York, N.Y., 1962. Also available in Dover Edition.

Fung, Y. C., An Introduction to the Theory of Aeroelasticity, John Wiley and Sons, Inc., New York, N.Y., 1955. Also available in Dover Edition.

Scanlan, R. H. and Rosenbaum, R., Introduction to the Study of Aircraft Vibration and Fluner, The MacmiIIan Company, New York, N.Y., 1951. Also available in Dover Edition.

(AGARD) AGARD Manual on Aeroelasticity, Vois. I-VII, Beginning 1959 with con­tinual updating.

Ashley, H., Dugundji, J. and Rainey, A. G., Notebook for Aeroelasticity, AIAA Professional Seminar Series, 1969.

Dowell, E. H., Aeroelasticity of Plates and Shells, Noordhofl International Publishing, Leyden, 1975.

Simiu, E. and Scanlan, R. H., Wind Effects on Structures-An Introduction to Wind Engineering, John Wiley and Sons, 1978.

Johnson, W., Helicopter Theory. Princeton University Press, 1980. Dowell, E. H. and Ilgamov, M .• Studies in Nonlinear Aeroelasticity, Springer­

Verlag. 1988.

In parentheses, abbreviations tor the above books are indicated which are used in the text.

Survey artic/es

Garrick, I. E., 'Aeroelasticity-Frontiers and Beyond', 13th Von Karman Lecture, J. of Aircraft, Vol. 13, No. 9, 1976, pp. 641-657.

Several Auiliors, 'Unsteady Aerodynamics. Contribution of the Structures and Materials Panel to the Fluid Dynamics Panel Round Table Discussion on Unsteady Aerodynamics', Goettingen, May 1975, AGARD Report R-645, March 1976.

Rodden, W. P., A Comparison of MetIIods Used in Interfering Lifting Surface Theory, AGARD Report R-643, March 1976.

XVII

Short bibliography

Ashley, H., 'Aeroelasticity', Applied Mechanics Reviews, February 1970. Abramson, H. N., 'Hydroelasticity: A Review of Hydrofoil Flutter', Applied Mechanics

Reviews, February 1969. Many Authors, 'Aeroelastic Effects From a Flight Mechanics Standpoint', AGARD, Con­

ference Proceedings No. 46, 1969. Landahl, M. T. and Stark, V. J. E., 'Numerical Lifting Surface Theory-Problems and

Progress', AIAA Journal, No. 6, No. 11, November 1968, pp. 2049-2060. Many Authors, 'Symposium on Fluid-Solid Interaction', ASME Annual Winter Meeting,

November 1967. Kaza, K. R. V., 'Development of Aeroelastic Analysis Methods for Turborotors and

Propfans-Inc1uding Mistuning', in Lewis Structures Technology, Vol. I, Proceedings, NASA Lewis Research Center, 1988.

Ericsson, L. E. and Reding, J. P., 'Fluid Mechanics of Dynamic Stall, Part I, Unsteady F10w Concepts, and Part 11, Prediction of Full Scale Characteristics', J. Fluids and Structures, Vol. 2, No. 1 and 2, 1988, pp. 1-33 and 113-143, respectively.

Mabey, D. G., 'Some Aspects of Aircraft Dynamic Loads Due to Flow Separation', AGARD-R-750, February, 1988.

Yates, E. c., Jr. and Whitlow, W., Jr., 'Development of Computational Methods for Unsteady Aerodynamics at the NASA Langley Research Center', in AGARD-R-749, Future Research on Transonic Unsteady Aerodynamics and its Aeroelastic Applications, August 1987.

Gad-el-Hak, M., 'Unsteady Separation on Lifting Surfaces', Applied Mechanics Reviews, Vol. 40, No. 4, 1987, pp. 441-453.

Hajela, P. (Ed.), 'Recent Trends in Aeroelasticity, Structures and Structural Dynamics', University of Florida Press, Gainesville, 1987.

Jameson, A., 'The Evolution of Computational Methods in Aerodynamics', J. Applied Mechanics, Vol. 50, No. 4, 1983, pp. 1052-\070.

See bass, R., 'Advances in the Understanding and Computation of Unsteady Transonic F1ows', in Recent Advances in Aerodynamics, edited by A. Krothapalli and C. Smith, Springer­Verlag, 1984.

McCroskey, W. J., 'Unsteady Airfoils', in Annual Review 01 Fluid Mechanics, 1982, Vol. 14, pp. 285-311.

Tijdeman, H. and Seebass, R., 'Transonic Flow Past Oscillating Airfoils', in Annual Review 01 Fluid Mechanics, 1980, Vol. 12, pp. 181-222.

Ormiston, R.,Warmbrodt, W., Hodges, D. and Peters, D., 'Survey of Army/NASA Rotocraft Aeroelastic Stability Research', NASA TM 101026 and USAASCOM TR 88-A-00S, 1988.

Journals

AHS Journal AIAA Journal ASCE Transactions, Engineering Mechanics Division ASME Transactions, Journal of Applied Mechanics International Journal of Solids and Structures Journal of Aircraft Journal of Fluids and Structures Journal of Sound and Vibration

Other journals will have aeroelasticity articles, of course, but these are among those with the most consistent coverage.

The impact of aeroelasticity on design is not discussed in any detail in this book. For

xviii

Short bibliography

Ashley, H., 'Aeroelasticity', Applied Mechanics Reviews, February 1970. Abramson, H. N., 'Hydroelasticity: A Review of Hydrofoil Flutter', Applied Mechanics

Reviews, February 1969. Many Authors, 'Aeroelastic Effects From a Flight Mechanics Standpoint', AGARD, Con­

ference Proceedings No. 46, 1969. Landahl, M. T. and Stark, V. J. E., 'Numerical Lifting Surface Theory-Problems and

Progress', AIAA Journal, No. 6, No. 11, November 1968, pp. 2049-2060. Many Authors, 'Symposium on Fluid-Solid Interaction', ASME Annual Winter Meeting,

November 1967. Kaza, K. R. V., 'Development of Aeroelastic Analysis Methods for Turborotors and

Propfans-Inc1uding Mistuning', in Lewis Structures Technology, Vol. I, Proceedings, NASA Lewis Research Center, 1988.

Ericsson, L. E. and Reding, J. P., 'Fluid Mechanics of Dynamic Stall, Part I, Unsteady F10w Concepts, and Part 11, Prediction of Full Scale Characteristics', J. Fluids and Structures, Vol. 2, No. 1 and 2, 1988, pp. 1-33 and 113-143, respectively.

Mabey, D. G., 'Some Aspects of Aircraft Dynamic Loads Due to Flow Separation', AGARD-R-750, February, 1988.

Yates, E. c., Jr. and Whitlow, W., Jr., 'Development of Computational Methods for Unsteady Aerodynamics at the NASA Langley Research Center', in AGARD-R-749, Future Research on Transonic Unsteady Aerodynamics and its Aeroelastic Applications, August 1987.

Gad-el-Hak, M., 'Unsteady Separation on Lifting Surfaces', Applied Mechanics Reviews, Vol. 40, No. 4, 1987, pp. 441-453.

Hajela, P. (Ed.), 'Recent Trends in Aeroelasticity, Structures and Structural Dynamics', University of Florida Press, Gainesville, 1987.

Jameson, A., 'The Evolution of Computational Methods in Aerodynamics', J. Applied Mechanics, Vol. 50, No. 4, 1983, pp. 1052-\070.

See bass, R., 'Advances in the Understanding and Computation of Unsteady Transonic F1ows', in Recent Advances in Aerodynamics, edited by A. Krothapalli and C. Smith, Springer­Verlag, 1984.

McCroskey, W. J., 'Unsteady Airfoils', in Annual Review 01 Fluid Mechanics, 1982, Vol. 14, pp. 285-311.

Tijdeman, H. and Seebass, R., 'Transonic Flow Past Oscillating Airfoils', in Annual Review 01 Fluid Mechanics, 1980, Vol. 12, pp. 181-222.

Ormiston, R.,Warmbrodt, W., Hodges, D. and Peters, D., 'Survey of Army/NASA Rotocraft Aeroelastic Stability Research', NASA TM 101026 and USAASCOM TR 88-A-00S, 1988.

Journals

AHS Journal AIAA Journal ASCE Transactions, Engineering Mechanics Division ASME Transactions, Journal of Applied Mechanics International Journal of Solids and Structures Journal of Aircraft Journal of Fluids and Structures Journal of Sound and Vibration

Other journals will have aeroelasticity articles, of course, but these are among those with the most consistent coverage.

The impact of aeroelasticity on design is not discussed in any detail in this book. For

xviii

Short bibliography

insight into this important area the reader may consult the following volumes prepared by the National Aeronautics and Space Administration in its series on SPACE VEHICLE DESIGN CRITERIA. A1though these documents focus on space vehicle applications, much of the material is relevant to aircraft as weil. The depth and breadth of coverage varies considerably from one volume to the next, but each contains at least abrief State-of-the-Art review of its topic as weil as a discussion of Recommended Design Practices. Further some important topics are included which have not been treated at all in the present book. These include, as already mentioned in the Preface,

Aeroelasticity of plates and shells (panel tlutter) (NASA SP-8004) Aeroelastic eflects on control system dynamics (NASA SP-8016, NASA SP-8036 NASA SP-8079)

as weil as

Structural response to time-dependent separated tluid tlows (bufleting) (NASA SP-8001) fluid motions inside elastic containers (fuel sloshing) (NASA SP-8009, NASA SP-8031) Coupled structural-propulsion instability (POGO) (NASA SP-8055)

It is intended to revise these volumes periodically to keep them up-to-date.

NASA SP-8001 1970 Bufleting During Atmospheric Ascent

NASA SP-8002 1964 F1ight Loads Measurements During Launch and Exit

NASA SP-8003 1964 F1utter, Buzz, and Divergence

NASA SP-8004 1972 Panel F1utter

NASA SP-8006 1965 Local Steady Aerodynamic Loads During Launch and Exit

NASA SP-8008 1965 Prelaunch Ground Wind Loads

NASA SP-8012 1968 Natural Vibration Modal Analysis

NASA SP-8016 1969 Eflects of Structural F1exibility on Spacecraft Control Systems

NASA SP-8009 1968 Propellant Slosh Loads

NASA SP-8031 1969 Slosh Suppression

NASA SP-8035 1970 Wind L\>ads During Ascent

NASA SP.-8036 1970 Eflects/of Structural F1exibility on Launch Vehicle Control Systems

NASA SP-8050 1970 Structural Vibration Prediction

NASA SP-8055 1970 Prevention of Coupled Structure-Propulsion Instability (POGO)

NASA SP-8079 1971 Structural Interaction with Control Systems.

XIX

Short bibliography

insight into this important area the reader may consult the following volumes prepared by the National Aeronautics and Space Administration in its series on SPACE VEHICLE DESIGN CRITERIA. A1though these documents focus on space vehicle applications, much of the material is relevant to aircraft as weil. The depth and breadth of coverage varies considerably from one volume to the next, but each contains at least abrief State-of-the-Art review of its topic as weil as a discussion of Recommended Design Practices. Further some important topics are included which have not been treated at all in the present book. These include, as already mentioned in the Preface,

Aeroelasticity of plates and shells (panel tlutter) (NASA SP-8004) Aeroelastic eflects on control system dynamics (NASA SP-8016, NASA SP-8036 NASA SP-8079)

as weil as

Structural response to time-dependent separated tluid tlows (bufleting) (NASA SP-8001) fluid motions inside elastic containers (fuel sloshing) (NASA SP-8009, NASA SP-8031) Coupled structural-propulsion instability (POGO) (NASA SP-8055)

It is intended to revise these volumes periodically to keep them up-to-date.

NASA SP-8001 1970 Bufleting During Atmospheric Ascent

NASA SP-8002 1964 F1ight Loads Measurements During Launch and Exit

NASA SP-8003 1964 F1utter, Buzz, and Divergence

NASA SP-8004 1972 Panel F1utter

NASA SP-8006 1965 Local Steady Aerodynamic Loads During Launch and Exit

NASA SP-8008 1965 Prelaunch Ground Wind Loads

NASA SP-8012 1968 Natural Vibration Modal Analysis

NASA SP-8016 1969 Eflects of Structural F1exibility on Spacecraft Control Systems

NASA SP-8009 1968 Propellant Slosh Loads

NASA SP-8031 1969 Slosh Suppression

NASA SP-8035 1970 Wind L\>ads During Ascent

NASA SP.-8036 1970 Eflects/of Structural F1exibility on Launch Vehicle Control Systems

NASA SP-8050 1970 Structural Vibration Prediction

NASA SP-8055 1970 Prevention of Coupled Structure-Propulsion Instability (POGO)

NASA SP-8079 1971 Structural Interaction with Control Systems.

XIX