Whirl Flutter of Turboprop Aircraft Structures

By Jiří Čečrdle

Whirl Flutter of Turboprop Aircraft Structures, Second Edition explores the whirl flutter phenomenon, including theoretical, practical, analytical and experimental aspects of the matter. Sections provide a general overview regarding aeroelasticity, discussions on the physical principle and the occurrence of whirl flutter in aerospace practice, and experimental research conducted, especially from the 60s.  Other chapters delve into analytical methods such as basic and advanced linear models, non-linear and CFD based methods, certification issues including regulation requirements, a description of possible certification approaches, and several examples of aircraft certification from aerospace.

Finally, a database of relevant books, reports and papers is provided. This updated and expanded second edition covers new chapters including both analytical and experimental aspects of the subject matter.

• Provides complex information on turboprop aircraft whirl flutter phenomenon
• Presents both theoretical and practical (certification related) issues
• Includes experimental research as well as analytical models (basic and advanced) of matter
• Includes both early-performed works and recent developments
• Contains a listing of relevant books and reports

• Language: English
• Publisher: Elsevier Science
• Release date: Jan 13, 2023
• ISBN: 9780323955560

Jiří Čečrdle

Jirí Cecrdle started his professional carrier in 1995 at the Czech Aerospace Research Centre (VZLU) in Prague, Czech Republic. He has been the head of the Workgroup of Aeroelasticity there since 2004. He participated in several projects of Czech aircraft development and certification, and he also works as a Compliance Verification Engineer (CVE) and research project evaluator. His spheres of scientific interest include analytical and experimental dynamics and the aeroelasticity of aircraft structures, as well as aeroelastic optimization and model updating. His whirl flutter-related experience includes aircraft certification issues, the development of analytical tools and methods and the development of the whirl flutter aeroelastic wind tunnel demonstrator.

Book preview

9780323955560_FC

Whirl Flutter of Turboprop Aircraft Structures

Second Edition

Jiří čečrdle

Image 1

Table of Contents

Cover image

Title page

Copyright

Dedication

List of figures

About the Author

Acknowledgments

Chapter 1: Introduction to aircraft aeroelasticity and whirl flutter

Abstract

1.1: Scope of aeroelasticity

1.2: Static aeroelastic phenomena

1.3: Dynamic aeroelastic phenomena

Further reading

Chapter 2: Theoretical background of whirl flutter phenomenon

Abstract

2.1: Physical principle

2.2: Propeller whirl flutter

2.3: Tilt-rotor whirl flutter

References

Chapter 3: Whirl flutter occurrence in aerospace practice

Abstract

3.1: Introduction

3.2: Lockheed L-188C Electra II

3.3: Beechcraft 1900C

3.4: Other aircraft

References

Chapter 4: Experimental research into whirl flutter

Abstract

4.1: Introduction

4.2: Early tests (1930s)

4.3: Main developments (1960s)

4.4: Recent activities

4.5: W-WING whirl flutter demonstrator

References

Further reading

Chapter 5: Analytical methods for whirl flutter investigation

Abstract

5.1: Historical overview

5.2: Fundamental solution

5.3: Influences of major parameters

5.4: Propeller aerodynamic forces by strip theory

5.5: Lift lag effect

5.6: Blade lift curve slope and Mach number effects

5.7: Correction to number of propeller blades

5.8: Influence of wing flexibility

5.9: Influence of hinged blade flexibility

5.10: Influence of gimbaled propeller flexibility

5.11: Influence of twisted blade flexibility

5.12: Propeller aerodynamic forces by lifting surface theory

5.13: Model of coupled bending blades

5.14: Complex models for tilt-rotor applications

5.15: Rear fuselage-mounted engines

5.16: Two-bladed propellers

References

Chapter 6: Application to the aircraft certification process

Abstract

6.1: Requirements of the airworthiness regulations

6.2: Analytical approaches

References

Chapter 7: Certification examples from aerospace practice

Abstract

7.1: Single nose-mounted engine utility aircraft

7.2: Twin wing-mounted engine utility aircraft

7.3: Twin wing-mounted engine commuter aircraft with tip-tanks

References

Nomenclature

Chronological bibliography

Author Index

Subject Index

Copyright

Woodhead Publishing is an imprint of Elsevier

50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States

The Boulevard, Langford Lane, Kidlington, OX5 1GB, United Kingdom

Copyright © 2023 Elsevier Ltd. All rights reserved.

No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher's permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions.

This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein).

Notices

Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary.

Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility.

To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein.

ISBN: 978-0-323-95555-3 (print)

ISBN: 978-0-323-95556-0 (online)

For information on all Woodhead publications visit our website at https://www.elsevier.com/books-and-journals

Unlabelled Image

Publisher: Matthew Deans

Acquisitions Editor: Chiara Giglio

Editorial Project Manager: Sara Greco

Production Project Manager: Sreejith Viswanathan

Cover Designer: Greg Harris

Typeset by STRAIVE, India

Dedication

This book is dedicated to my children, Jan and Anna.

Jiří Čečrdle

List of figures

Fig. 1.1Aeroelastic (Collar's) triangle of forces. 2

Fig. 1.2Principle of airfoil torsional divergence. 4

Fig. 1.3Principle of control surface reversion. 5

Fig. 1.4Harmonic motion of airfoil with single DOF—torsion. 7

Fig. 1.5Harmonic motion of airfoil with single DOF—bending. 7

Fig. 1.6Harmonic motion of airfoil with 2 DOFs (bending/torsion—in-phase). 8

Fig. 1.7Harmonic motion of airfoil with 2 DOFs (bending/torsion—out-of-phase—shift π/2). 8

Fig. 1.8Harmonic motion of airfoil with 2 DOFs (bending/aileron—in-phase). 9

Fig. 1.9Harmonic motion of airfoil with 2 DOFs (bending/aileron—out-of-phase—shift π/2).9

Fig. 2.1Gyroscopic system with propeller. 14

Fig. 2.2Independent mode shapes. 15

Fig. 2.3Backward and forward whirl modes. 15

Fig. 2.4Stable and unstable states of gyroscopic vibrations for backward flutter mode. 16

Fig. 2.5(A–D) Aerodynamic forces due to pitching deflection (angle Θ). 17

Fig. 2.6(A–D) Aerodynamic forces due to the yawing velocity ż (movement around vertical axis). 18

Fig. 2.7(A–D) Aerodynamic forces due to pitching angular velocity si1_e (movement around lateral axis). 19

Fig. 2.8Kinematical scheme of the gyroscopic system. 19

Fig. 2.9Influence of the propeller advance ratio (V∞/(ΩR)) on the stability of an undamped gyroscopic system. 23

Fig. 2.10Influences of structural damping and propeller—pivot point distance on whirl flutter stability. 24

Fig. 2.11Static divergence of the gyroscopic system. 25

Fig. 2.12Whirl flutter boundaries (Ω = const.). 26

Fig. 2.13Whirl flutter boundaries (KΘ = const.; KΨ = const.). 26

Fig. 2.14Whirl flutter boundaries (Jo = const.). 27

Fig. 2.15Influence of inflow angle to whirl flutter boundaries.28

Fig. 3.1Lockheed L-188 C Electra II aircraft. 32

Fig. 3.2Beechcraft 1900C aircraft.34

Fig. 4.1NACA wind tunnel model of wing and nacelle—top-view and side-view. 38

Fig. 4.2Propeller wind tunnel model. 39

Fig. 4.3Propeller simple wind tunnel model. 40

Fig. 4.4Experimental whirl flutter boundaries. 40

Fig. 4.5NASA propeller wind tunnel model. 41

Fig. 4.6Comparison of experimental aerodynamic derivatives with theory. 41

Fig. 4.7Effect of thrust to whirl flutter stability. 42

Fig. 4.8Hinged blades propeller wind tunnel model.43

Fig. 4.9Effect of blades flapping to whirl flutter stability. 43

Fig. 4.10NAL hinged blade propeller model. 44

Fig. 4.11Effect of blades flapping to whirl flutter stability. 45

Fig. 4.12Semispan wing/engine component model (NASA Langley). 46

Fig. 4.13L-188 C Electra II aeroelastic model WT measurement (NASA Langley). 47

Fig. 4.14L-188 C Electra II aeroelastic model WT measurement (NASA Langley). 48

Fig. 4.15Effect of stiffness reduction on the whirl flutter boundary for the starboard outboard engine, (KΘ/KΨ) = 1.0; g = 0.014 48

Fig. 4.16Effect of stiffness and damping reduction (KΘ—67%; g—35% of nominal) on the whirl flutter boundary for various starboard engines, (KΘ/KΨ) = 1.0 or 1.5. 49

Fig. 4.17Effect of structural damping on the whirl-flutter boundary, KΘ = 3.6e3 (in-lb/rad); (KΘ/KΨ) = 1.8. 50

Fig. 4.18Effect of starboard inner propeller overspeed on the whirl flutter boundary (others at nominal rpm). 50

Fig. 4.19Flapping blades proprotor wind tunnel model. 52

Fig. 4.20Flapping blades proprotor—results summary. 52

Fig. 4.21Flapping blades proprotor results—influence of blade flapping hinge. 53

Fig. 4.22Flapping blades proprotor results—influence of stiffness ratio. 54

Fig. 4.23Simple table-top proprotor model. 54

Fig. 4.24Proprotor model. 55

Fig. 4.25Four-blade proprotor model. 56

Fig. 4.26Three-blade proprotor model. 57

Fig. 4.27WRATS tilt-rotor aircraft component model. 57

Fig. 4.28WRATS measurement results—influence of WT medium. 58

Fig. 4.29L-610 commuter aircraft. 59

Fig. 4.30L-610 complete aeroelastic model at TsAGI T-104 wind tunnel test section. 59

Fig. 4.31L-610 aeroelastic model starboard wing/engine component. 60

Fig. 4.32L-610 aeroelastic model aileron actuation. 60

Fig. 4.33Aeroelastic model engine nonlinear attachment (1—engine mass; 2—nonlinear attachment; 3—pitch 1st attachment; 4—yaw attachment; 5—pitch 2nd and 3rd attachments; 6—hinge). 61

Fig. 4.34W-WING demonstrator nacelle design drawing (1—motor; 2—wing spar; 3—pitch attachment; 4—yaw attachment; 5—mass balancing weight). 62

Fig. 4.35W-WING demonstrator, uncoated nacelle. 62

Fig. 4.36W-WING demonstrator, uncoated nacelle integrated into the wing structure. 63

Fig. 4.37W-WING demonstrator wing and coated nacelle. 63

Fig. 4.38W-WING demonstrator wing—strain gauges in half-span section. 64

Fig. 4.39Tool for the propeller blade adjustment. 65

Fig. 4.40Engine suspension stiffness test—measurement of pitch (A) and yaw (B) stiffness. 66

Fig. 4.41Modal measurement.67

Fig. 4.42Example of motor operational margin measurement result. 68

Fig. 4.43Wind tunnel test arrangement. 69

Fig. 4.44Wind tunnel test arrangement. 69

Fig. 4.45Waterfall diagram, vibration spectra vs airflow velocity, engine front section, and pitch direction. 72

Fig. 4.46Vibration spectra growth, excitation caused by the aileron, engine front section, pitch direction, for an airflow of 20 m s− 1. 73

Fig. 4.47Vibration spectra growth, excitation caused by the aileron, engine front section, pitch direction, for an airflow of 30 m s− 1. 73

Fig. 4.48Vibration spectra growth, excitation caused by the aileron, engine front section, pitch direction, for an airflow of 35 m s− 1. 74

Fig. 4.49Vibration spectra growth, excitation caused by the aileron, engine front section, pitch direction, for an airflow of 40 m s− 1. 74

Fig. 4.50Vibration spectra growth, excitation turbulence, engine front section, pitch direction, while the flutter state is reached. 75

Fig. 4.51Vibration spectra growth, excitation turbulence, engine front section, yaw direction, while the flutter state is reached. 75

Fig. 4.52Whirl mode parameters, stable state case, (A) propeller rpm, (B) frequency, (C) damping, and (D) amplitude. 76

Fig. 4.53Whirl mode parameters, unstable case, (A) propeller rpm, (B) frequency, (C) damping, and (D) amplitude. 76

Fig. 4.54Whirl mode parameters, unstable state case—rear weight station, (A) propeller rpm, (B) frequency, (C) damping, and (D) amplitude. 77

Fig. 4.55Whirl mode parameters, unstable state case—front weight station, (A) propeller rpm, (B) frequency, (C) damping, and (D) amplitude. 78

Fig. 4.56Effect of pitch hinge station on whirl stability (25% = rear; 46% = middle); parameters: L—light blades; H—heavy blades; LW—balance weight station (0% = front, 50% = middle, 100% = rear). 78

Fig. 4.57Effect of the mass balance weight station on whirl stability (0% = front, 50% = middle, 100% = rear); parameters: L—light blades; H—heavy blades, rear and middle pitch hinge station. 79

Fig. 4.58W-WING demonstrator FE model (structural). 80

Fig. 4.59W-WING demonstrator FE model (aerodynamic). 80

Fig. 4.60Example of W-WING analytical results—required stiffness for neutral stability (Ω = 2000 rpm, light blades), parameter: flow velocity. 81

Fig. 4.61Example of W-WING analytical results—required stiffness for neutral stability (V = 20 m s− 1, Ω = 2000 rpm), parameter: IP (light/heavy blades). 81

Fig. 4.62Example of W-WING analytical results—required stiffness for neutral stability (V = 20 m s− 1, heavy blades), parameter: propeller revolutions.82

Fig. 5.1Effective quasisteady angles. 88

Fig. 5.2Whirl flutter critical dimensionless frequency and damping (G = (γΨ/γΘ) = 1.0 and γ² = (KΨ/KΘ) = 1.4) according to Ref. [5]. 90

Fig. 5.3Influence of the propeller hub distance on the backward whirl mode critical damping (G = (γΨ/γΘ) = 1.0 and γ² = (KΨ/KΘ) = 1.0) according to Ref. [5].92

Fig. 5.4Stability boundaries—assessment of the stiffness asymmetry via KRMS (γΨ = γΘ = 0.03; Ω = 1020 rpm) according to Ref. [5]. 93

Fig. 5.5Stability boundaries—assessment of the damping asymmetry (γAVG = 0.03; KRMS = 12.3e + 6 (in-lb/rad)) according to Ref. [5]. 94

Fig. 5.6Arbitrary position of propeller disc. 94

Fig. 5.7Blade section (angles and velocities). 95

Fig. 5.8Blade section lift force components. 98

Fig. 5.9Blade integrals (fundamental formulation of Ref. [4]). 100

Fig. 5.10Lift curve slope distribution of AV-844 and AV-725 propellers. 107

Fig. 5.11(A and B) Aerodynamic derivative of the AV-844 and AV-725 propellers. 107

Fig. 5.12(A and B) Anorerodynamic derivative of the AV-844 and AV-725 propellers. 108

Fig. 5.13(A and B) Aerodynamic derivative of the AV-844 and AV-725 propellers108

Fig. 5.14(A and B) Aerodynamic derivative of the AV-844 and AV-725 propellers108

Fig. 5.15(A and B) Aerodynamic derivative of the AV-844 and AV-725 propellers. 109

Fig. 5.16(A and B) Aerodynamic derivative of the AV-844 and AV-725 propellers. 109

Fig. 5.17(A and B) Example of the influence of the blade lift curve slope distribution to the whirl flutter speed. 110

Fig. 5.18Example of the influence of the blade lift curve slope distributions on the whirl flutter stability margins. 111

Fig. 5.19Consideration of the wing flexibility (A) rigid wing, (B) wing bending flexibility, and (C) wing bending and torsional flexibility. 113

Fig. 5.20Influence of the wing flexibility on the whirl flutter: (A) rigid wing, (B) wing bending flexibility, and (C) wing bending and torsional flexibility. 114

Fig. 5.21Analytical model with four DOFs including wing bending and torsional flexibility. 115

Fig. 5.22Aerodynamic forces and moments. 121

Fig. 5.23Flapping blade whirl modes ((re/R) = 0.13). 128

Fig. 5.24Scheme of the flapping blade dynamic system. 129

Fig. 5.25Forces on blade section. 136

Fig. 5.26Scheme of the gimbaled propeller dynamic system. 148

Fig. 5.27Twisted blade mode and deformation components. 156

Fig. 5.28Mechanical instability of the system with flexible twisted blades. 157

Fig. 5.29Stability boundaries for a system with twisted blades—forward whirl. 158

Fig. 5.30Stability boundaries for a system with twisted blades—backward whirl. 159

Fig. 5.31Velocities at the propeller. 160

Fig. 5.32Helical coordinate system at the propeller. 161

Fig. 5.33Doublet-Lattice method. 170

Fig. 5.34Four-blade large-area propeller (C-130E). 171

Fig. 5.35Multiblade swept-tip propeller (A-400M).171

Fig. 5.36Twin counter-rotating propeller (An-22). 171

Fig. 5.37Typical Campbell diagram of the natural frequencies of bending of a rotating propeller. 173

Fig. 5.38Typical blade 1st bending mode shape. 173

Fig. 5.39Typical blade 2nd bending mode shape. 174

Fig. 5.40Harmonic dynamic response patterns of a rotating four-blade propeller (flapping mode). 174

Fig. 5.41Harmonic dynamic response patterns of a rotating four-blade propeller (in-plane mode). 175

Fig. 5.42Tilt-rotor aircraft dynamic system outline. 178

Fig. 5.43Tilt-rotor gimbal geometry. 179

Fig. 5.44Tilt-rotor blade hinge geometry. 180

Fig. 5.45Tilt-rotor control system geometry. 180

Fig. 5.46Tilt-rotor blade cross-section. 185

Fig. 5.47CAMRAD II model of tilt-rotor aircraft rotor. 186

Fig. 5.48Examples of XV-15 rotor blade planforms—(A) baseline; (B) tip segment airfoil shifted; (C) tip segment airfoil sweep; elastic axis (EA) unchanged; (D) tip segment airfoil sweep + EA sweep. 186

Fig. 5.49Symmetric whirl mode V-g diagram—comparison of thick wing and thin wing with baseline and modified rotor blades (15% CG offset at tip blade segment). 187

Fig. 5.50Assessed V-22 rotor blade planforms. 188

Fig. 5.51Effects of sweep and mass offset on stability of symmetric bending mode at V = 300 kts; δ3 = − 30 degrees—legend in accordance with Fig. 5.50. 188

Fig. 5.52Definition of blade sweep, aerodynamic sweep, panel sweep angle, and sweep offset. 189

Fig. 5.53Blade sweep, aerodynamic sweep, panel sweep angle, and sweep offset on stability of symmetric bending mode at V = 300 kts; δ3 = − 30 degrees—legend in accordance with Fig. 5.52. 190

Fig. 5.54Prop-rotor multibody model. 191

Fig. 5.55Engine suspension characteristics. 193

Fig. 5.56Generalized forces and reference frames. 194

Fig. 5.57In-plane velocity perturbations. 195

Fig. 5.58Out-of-plane velocity perturbations. 196

Fig. 5.59Blade-fixed reference frames. 197

Fig. 5.60Blade section velocities, (A) clockwise, (B) counterclockwise rotation. 198

Fig. 5.61Whirl flutter stability margin, dependence of flutter advance ratio with dimensionless engine pitch frequency. 202

Fig. 5.62Whirl flutter stability boundaries for a two-bladed propeller.209

Fig. 6.1V-H envelope for aeroelastic certification according to CS/FAR 23 regulations. 215

Fig. 6.2Basic and extended V-H envelope for aeroelastic certification according to CS/FAR 25 regulations. 217

Fig. 6.3Propeller coordination system used for NASTRAN analysis. 221

Fig. 6.4Structural FE model of wing/engine component. 226

Fig. 6.5Aerodynamic FE model of wing and engine component. 227

Fig. 6.6Flutter speed dependence on pitch and yaw frequencies.228

Fig. 6.7Construction of stability margin. 229

Fig. 6.8Whirl flutter stability margin. 229

Fig. 6.9Rate of reserve with respect to whirl flutter stability margin. 230

Fig. 6.10Graphical interpretation of sensitivity coefficient. 232

Fig. 6.11Whirl flutter stability margins. 237

Fig. 6.12V-g-f diagram—optimized structure. 238

Fig. 6.13Rate of reserve with respect to whirl flutter stability margins. 239

Fig. 6.14Comparison of stability margins given by standard and optimization approaches. 240

Fig. 6.15Full-span structural model of L 410NG commuter aircraft. 243

Fig. 6.16Engine vibration modes: (A) symmetric pitch, (B) antisymmetric pitch, (C) symmetric yaw, and (D) antisymmetric yaw. 244

Fig. 6.17Whirl flutter stability margins—symmetrical revolutions, identical directions of revolution (CW-CW), legend: prim = primary flutter (SΘ/AΨ), sec = secondary flutter (AΘ/SΨ), (1.xx) = VFR, HFR. 245

Fig. 6.18Whirl flutter stability margins—symmetrical revolutions, inverse directions of revolution (CW-CCW), legend: (1.xx) = VFR, HFR. 246

Fig. 6.19Whirl flutter stability margins—a single rotor omission, legend: ΩL/ΩR, (1.xx) = VFR, HFR. 247

Fig. 6.20Whirl flutter stability margins—unsymmetrical revolutions, identical directions of revolution (CW-CW), primary flutter only, legend: ΩL/ΩR, (1.xx) = VFR, HFR248

Fig. 6.21Whirl flutter stability margins—unsymmetrical revolutions, inverse directions of revolution (CW-CCW), legend: ΩL/ΩR, (1.xx) = VFR, HFR.249

Fig. 7.1Aero Ae 270 Ibis aircraft. 252

Fig. 7.2Computational model of Ae 270 Ibis aircraft (engine and engine bed component). 252

Fig. 7.3V-H envelope according to CS/FAR 23 regulations—Ae 270 Ibis aircraft. 253

Fig. 7.4Whirl flutter stability margin—Ae 270 Ibis aircraft. 254

Fig. 7.5Evektor EV-55M Outback aircraft. 255

Fig. 7.6Structural half-span model of EV-55M Outback aircraft. 256

Fig. 7.7Aerodynamic half-span model of EV-55M Outback aircraft. 257

Fig. 7.8Geometry and velocities around the propeller [5]. 257

Fig. 7.9Geometry considered for correction for the propeller slipstream. 258

Fig. 7.10V-H envelope according to CS/FAR 23 regulations—EV-55M Outback aircraft. 260

Fig. 7.11EV-55M Outback aircraft—whirl flutter stability margins, no downwash considered, parameter: fuel loading. 261

Fig. 7.12EV-55M Outback aircraft—1st wing symmetric bending frequency dependence on fuel loading. 262

Fig. 7.13EV-55M Outback aircraft—whirl flutter stability margins, fuel loading 100%, parameter: downwash effect included/excluded. 263

Fig. 7.14EV-55M Outback aircraft—whirl flutter stability margins, fuel loading 50%, parameter: downwash effect included/excluded.263

Fig. 7.15EV-55M Outback aircraft—whirl flutter stability margins, no downwash considered, parameter: fuel loading, comparison with nominal frequencies. 264

Fig. 7.16EV-55M Outback aircraft—whirl flutter stability margin, fuel loading 0%, comparison with nominal frequencies and ± 30% stiffness variance margin. 265

Fig. 7.17Structural full-span model of EV-55M Outback aircraft. 266

Fig. 7.18Aerodynamic full-span model of EV-55M Outback aircraft. 266

Fig. 7.19Let L-410 UVP-E20 Turbolet aircraft. 267

Fig. 7.20Structural half-span model of the L-410 UVP-E Turbolet aircraft. 268

Fig. 7.21Aerodynamic half-span model of the L-410 UVP-E Turbolet aircraft. 270

Fig. 7.22Fuel distribution of the L-410 UVP-E Turbolet aircraft. 271

Fig. 7.23The V-H envelope according to the CS/FAR 23 regulations—L-410 UVP-E Turbolet aircraft. 272

Fig. 7.24L-410 UVP-E20 aircraft—whirl flutter stability margins, no downwash considered, parameter: wing mass configuration (numbered according to Fig. 7.22). 272

Fig. 7.25L-410 UVP-E20 aircraft—whirl flutter stability margins—comparison with nominal frequencies, parameter: wing mass configuration (numbered according to Fig. 7.22). 273

Fig. 7.26L-410 UVP-E20 H-80 aircraft—whirl flutter stability margins, no downwash considered, parameter: wing mass configuration (numbered according to Fig. 7.22). 273

Fig. 7.27L-410 UVP-E20 H-80 aircraft—whirl flutter stability margins—comparison with nominal frequencies, parameter: wing mass configuration (numbered according to Fig. 7.22). 274

Fig. 7.28L-410 UVP-E20PT aircraft—whirl flutter stability margins, no downwash considered, parameter: wing mass configuration (numbered according to Fig. 7.22). 274

Fig. 7.29L-410 UVP-E20PT aircraft—whirl flutter stability margins—comparison with nominal frequencies, parameter: wing mass configuration (numbered according to Fig. 7.22). 275

Fig. 7.30L-410 aircraft whirl flutter stability margins comparison—mass configuration 01. 276

Fig. 7.31L-410 aircraft whirl flutter stability margins comparison—mass configuration 04. 276

Fig. 7.32L-410 aircraft whirl flutter stability margins comparison—mass configuration 06. 277

Fig. 7.33L-410 aircraft whirl flutter stability margins comparison—mass configuration 11. 277

About the Author

Jiří Čečrdle was born in 1969 in Prague, Czech Republic. He graduated from the Faculty of Mechanical Engineering, Czech Technical University, Prague. He completed his MSc in Aircraft Design in 1993 and PhD in Mechanics of Stiff and Deformable Bodies in 2003. He started his professional career as a research assistant in the Strength of Structures Division, Czech Aerospace Research Centre (VZLU), Prague, Czech Republic, in 1995. Later, he was promoted to the position of researcher in 1996, scientist in 2003, and finally senior scientist in 2004. Since then, he has also been the head of the Workgroup of Aeroelasticity at the Strength of Structures Division. In the meantime, he also completed four mid-term work stays at the German Aerospace Center (DLR), Institute of Aeroelasticity, Göttingen, Germany, between 2002 and 2005.

His spheres of scientific interest include the analytical and experimental dynamics and aeroelasticity of aircraft structures as well as aeroelastic optimization and model updating. He participated in several Czech aircraft development and certification projects (e.g., L-610G—twin-engine turboprop commuter for 40 passengers; L-159—jet light attack aircraft; Ae 270—single-engine turboprop utility aircraft for 8 passengers; Raven 257—twin piston engine utility aircraft for 9 passengers; EV-55/EV-55M—twin-engine turboprop utility aircraft for 9–13 passengers). Recently, he has participated in the development of the new generation (NG) of the L-410 twin-engine turboprop commuter aircraft for 19 passengers and the L-39 advanced jet trainer aircraft. He also works as a compliance verification engineer (CVE).

He was involved in several Czech and European research projects dealing with the topics of aeroelastic flutter, aeroelastic response analysis, development of nonlinear aeroelastic wind tunnel demonstrator, aeroelastic experiments of the active aeroelastic demonstrators, analytical methods for general aviation aircraft certification, aeroelastic sensitivity analysis, and dynamic model updating and optimization methods. He also works as a research project evaluator.

He has been interested in the topic of whirl flutter since 1999. His experience includes aircraft certification issues and the development of analytical tools and methods and the whirl flutter aeroelastic wind tunnel demonstrator.

He is the author or coauthor of approximately 100 conference papers, articles in technical and scientific journals, and chapters in technical books. He is also a member of the Expert Commission for Engineering and Technology of the Research, Development and Innovation Council, an advisory body to the Government of the Czech Republic, and a member of the review board for PhD examinations at the Czech Technical University, Prague. His biographical profile has been included in valuable databases such as Marquis Who's Who. He is an Associate Fellow of the American Institute of Aeronautics and Astronautics (AIAA).

The author may be contacted via e-mail: [e-mail].

Acknowledgments

First, I acknowledge the Czech Aerospace Research Centre (VZLU), Prague, Czech Republic, for granting permission to use the results of whirl flutter-related tasks performed at VZLU (within the framework of Czech and European research projects and the aircraft certification projects during the period 1999–2013, which are mentioned in this book) as well as Josef Jironč (Head of Department, Strength of Structures), Radek Doubrava (Head of Group, Structure Analyses), and Zuzana Šranková (Secretary, Structure Analyses) for providing additional support.

Further acknowledgments are due to the outstanding achievers in the field of whirl flutter, who performed the research work referred to in this book, namely Wilmer H. Reed III and Raymond G. Kvaternik (formerly NASA Langley Research Center, VA, United States), C.E. Hammond and H.L. Runyan (NASA Langley Research Center, VA, United States), William P. Rodden (formerly MSC Software, CA, United States), Wayne Johnson (formerly NASA Ames Research Center, CA, United States), Cecil W. Acree (NASA Ames Research Center, CA, United States), Omri Rand (Technion—Institute of Technology, Israel), Alireza Rezaeian and Wolf Krueger (DLR, Germany), Fritz Kiessling (formerly DLR, Germany), Alain Dugeai (ONERA, France), Fred Nitzsche (formerly Embraer, S.A., Brazil), Robert E. Donham (formerly Lockheed Aeronautical Systems, CA, United States), and K.V. Krishna Rao (formerly NAL, India), and many others.

Acknowledgments are also due to the following aerospace research organizations and aerospace technical societies: National Aeronautical Laboratory (NAL), Bangalore, India (specifically J.S. Mathur, Chief Scientist); German Aerospace Research Center (DLR), Germany (specifically Lorenz Tichy, Director, Institute of Aeroelasticity); French Aerospace Research Center (ONERA), France; NASA Ames Research Center, CA, United States (specifically Robert M. Padilla, Patent Counsel); Embraer, S.A., Sao Jose dos Campos, Brazil (specifically Luciano Afonso da Silva, Pedro Higino Cabral, and Renato Otto Dinitz); American Institute of Aeronautics and Astronautics (AIAA), Reston, VA, United States (specifically Heather A. Brennan, Director, Publications, and Katrina Buckley, Managing Editor, Books); Elsevier Science, Ltd.; and American Helicopter Society (AHS), Alexandria, VA, United States (specifically Mike Hirschberg, Executive Director).

Special acknowledgments go to the NASA Langley Research Center, VA, United States (one of the leading aerospace research organizations in the field of whirl flutter) not only for granting permission to use their research (specifically Robin W. Edwards, Patent Counsel) but also for the efforts to search the archives for the originals of aged photos (specifically Mary E. Garner).

My thanks go to aircraft spotters Bill Hough, Orlando Suarez, Petr Kadlec, and Petr Štěrba for granting permission to use their photographs; to Svatomír Slavík (Czech Technical University, Czech Republic) and Jan Vimmr (University of West Bohemia, Czech Republic), Czech aircraft manufacturers Aero Vodochody Aerospace, a.s. (specifically Pavel Kučera, Head, Design Analysis), Evektor, spol. s.r.o., Kunovice (specifically Petr Štěrba, Deputy Director), and Aircraft Industries, a.s., Kunovice (specifically Ilona Plšková, General Director), Czech aircraft maintenance company Aeroservis, spol. s.r.o., Brno (specifically Jan Václavík, CEO) for granting permission to use the data from aircraft certification-related projects; and last, but not least, to Evžen Šlechta for creating graphical representations of the handmade sketches.

Chapter 1: Introduction to aircraft aeroelasticity and whirl flutter

Abstract

This chapter provides brief information regarding aeroelasticity. The chapter defines the scope of aeroelasticity and provides an overview of aerospace engineering, describing aeroelastic primary problems and achievements in the context of aviation history. Next, the physical principles of the most important static and dynamic aeroelastic phenomena, such as divergence, control surface reversion, flutter, and buffeting, are outlined.

Keywords

Aeroelasticity; Aeroelastic phenomena; Divergence; Control reversion; Flutter; Buffeting

1.1: Scope of aeroelasticity

Aeroelasticity is a notably new branch of applied mechanics that studies the interaction between fluid matters and flexible solid bodies. The typical application of aeroelasticity is in the branch of aircraft engineering. However, aeroelastic issues are applicable also for civil engineering (e.g., slender buildings, towers, smokestacks, suspension bridges, electric lines, and pipelines) or transportation engineering (cars, ships, submarines). Also important are its applications in machine engineering (compressors, turbines).

In the following text, we will focus on aerospace aeroelasticity. Aeroelasticity in regard to aircraft structures is defined as the branch that investigates the phenomena that emerge due to the interaction of aerodynamic (in particular unsteady), inertial, and elastic forces emerging during the relative movement of a fluid (air) and a flexible body