1. Aeroelasticity : Complexities and Challenges in Rotary–Wing Vehicles
C. Venkatesan
IIT Kanpur

2. AEROELASTICITY Study of fluid and structure interaction Applicable for
Civil Structures
Ships, Offshore Structures
Aero Structures
More specifically used to address issues related to flying vehicles

3. CIVIL STRUCTURES Tall chimney/Buildings Bridges Overhead cables
Flow through pipes (head exchanger)

4. AEROSPACE STRUCTURES Aircraft (Wings, control surface) Rockets
(Panels, control surface)
Helicopters
(Rotor blades, rotor/ fuselage system)
Gas Turbines (Blades)

5. BASIC INGREDIENTS A-E Static Aeroelasticity A-I Flight Mechanics
Aerodynamics
Control E A I C
A-E Static Aeroelasticity
A-I Flight Mechanics
E-I Mechanical Vibrations
/Structural Dynamics
Elasticity
Inertia
A-E-I Dynamic Aeroelasticity
A-E-I-C Aero-Servo-Elasticity

6. AEROELASTIC PROBLEMS Static aeroelasticity Dynamic aeroelasticity
Divergence
Control effectiveness / reversal
Wing deformation
Dynamic aeroelasticity
Dynamic response (Gust, landing)
Flutter

7. MATHEMATICAL FORM FORM OF BASIC EQUATION
LINEAR/ NONLINEAR/ TIME INVARIANT/ TIME VARIANT
COMPLEXITIES IN
- STRUCTURAL MODELING
- AERODYNAMIC MODELING

8. STRUCTURAL COMPLEXITY
DISTRIBUTED PARAMETER FUSELAGE (INFINITE DOF)
FE DISCRETISATION (FEW THOUSAND DOF)
MODEL TRANSFORMATION WITH TRUNCATED NUMBER OF MODES
DYNAMIC ANALYSIS IN MODAL SPACE
GEOMETRIC NONLINEARITY: LARGE DEFORMATION
MATERIAL NONLINEARITY: ELASTOMERS

9. FUSELAGE STRUCTURAL DYNAMIC MODEL
Mode 1: 3.51Hz
Mode 2: 4.15Hz
Mode 3: 5.35Hz
Mode 4: 12.05Hz
HIGH MODAL DENSITY: CLOSELY PLACED MODAL FREQUENCIES
(20 MODES WITHIN 3Hz – 30Hz)

10. AERODYNAMIC COMPLEXITY
UNSTEADY AERODYNAMICS
- SUBSONIC, TRANSONIC, SUPERSONIC
- 3-DIMENSIONAL EFFECTS
ATTACHED FLOW/ SEPARATED FLOW

11. INTRODUCTION
• Since the First Successful Flight of Truly Operational,
Mechanically Simple and Controllable Helicopter
by Sikorsky ( )
- Continued R&D Efforts to Improve Helicopter By
Incorporating New Technological Developments
As and When Matured and Available
• Composites
• Automatic Flight Control Systems
• Noise and Vibration Control
• Advances in Fundamental Understanding of
Rotor/ Fuselage Dynamics, and Aerodynamics

12. HELICOPTER: AEROELASTICIAN’S VIEW
AERODYNAMICS
- COMPLEX WAKE
- BVI
- ROTOR/FUSELAGE
DYNAMICS
- BLADE MODES
- FUSELAGE MODES
- STRUCTURAL COUPLING
- HIGH MODAL DENSITY

13. R&D EFFORTS
• INTENSELY PURSUED BY ACADEMIA AND INDUSTRY
• CONSIDERABLE PROGRESS IN THE PAST 40 YEARS
• STILL SEVERAL DISCREPANCIES EXIST BETWEEN THEORY
AND EXPERIMENT
• MODEL TESTS AND FLIGHT MEASUREMENTS PROVIDE
DATA FOR CORRELATION
• IMPROVE UNDERSTANDING OF THE PHYSICS OF THE PROBLEM
• MODIFY, DEVELOP SUITABLE MATHEMATICAL MODELS

14. HELICOPTER DYNAMICS
CLASSIFICATION OF PROBLEMS
- ISOLATED ROTOR BLADE AEROELASTICITY
(COUPLED FLAP-LAG-TORSION-AXIAL MODES)
- COUPLED ROTOR-FUSELAGE DYNAMICS

15. ROTOR BLADE MODEL
LONG-SLENDER-TWISTED BEAMS UNDERGOING
IN-PLANE BENDING (LAG), OUT-OF-PLANE BENDING (FLAP),
TORSION AND AXIAL DEFORMATIONS

16. ROTOR BLADE MODELING
FIRST MODEL 1958
(Houbolts&Brooks)
SUBSTANTIAL WORK
AFTER 1970
FINITE DEFORMATION MODEL

17. Aerodynamics in Forward Flight
Advancing Side i.e.,
Retreating side i.e.,
Advancing side : High velocity  Low angle of attack
Retreating side : Low velocity  High angle of attack
Blade stall occurs in the retreating region.

18. Unsteady Motion of Airfoil
Sources of unsteadiness in Helicopter rotor blade A) B) C)

19. Velocity Components
Velocity distribution and effective angle of attack :
Unsteady motion + High angle of attack  DYNAMIC STALL

20. COUPLED ROTOR-FUSELAGE DYNAMICS
• VEHICLE DYNAMICS (FLYING AND HANDLING QUALITIES)
- FUSELAGE RIGID BODY
- BLADE FLAP DYNAMICS (DOMINANT)
- FREQUENCY RANGE 0.3Hz – 1.5Hz
• AEROMECHANICAL INSTABILITIES (GROUND/ AIR RESONANCE)
- BLADE LAG DYNAMICS (DOMINANT)
- FREQUENCY RANGE 2Hz – 5Hz
• HELICOPTER VIBRATION
- FLEXIBLE FUSELAGE
- FLAP-LAG-TORSION MODES
- FREQUENCY RANGE (ABOVE 10Hz)

21. GROUND RESONANCE

22. ROTOR MODES vs BLADE MOTION
(a) Collective (b) Cosine cyclic (c) Sine cyclic (d) Alternating
SHIFT OF ROTOR SYSTEM C.G FROM CENTRE IN CYCLIC MODES
AS THE BLADES ROTATE, MOVEMENT OF ROTOR C.G CAUSES
CHURNING MOTION TO HELICOPTER

23. GROUND RESONANCE  
• BLADES: FLAP, LAG
• FUSELAGE: PITCH, ROLL
• BLADE MOTION IN
ROTATING FRAME
• FUSELAGE MOTION IN
NON-ROTATING FRAME

24. GROUND RESONANCE STABILITY ANALYSIS  
• LINEARISED STABILITY EQUATIONS
INERTIA, STRUCTURAL, AERODYNAMIC
EFFECTS INCLUDED IN MASS, DAMPING
AND STIFFNESS MATRICES
{q} – ROTOR/FUSELAGE/ INFLOW DOF
EIGENVALUES S=i
- MODAL DAMPING (NEGATIVE STABLE; POSITIVE UNSTABLE)
 - MODAL FREQUENCY

25. GROUND RESONANCE STABILITY: EXPERIMENT
{BOUSMAN, US ARMY RES. & TECH. LAB (1981)}
TEST SETUP
BLADE ATTACHMENT
SEVERAL BLADE CONFIGURATIONS TESTED
CONF-1: NON-ROTATING NATURAL FREQ: F0=3.13Hz L0=6.70Hz
CONF-4: NON-ROTATING NATURAL FREQ: F0=6.63Hz L0=6.73Hz

26. MODAL FREQUENCY CORRELATION (CONF.-1) {UNIFORM INFLOW MODEL}
_____ Uniform Inflow
Δ o Experiment
, Hz
, RPM
ROLL
PITCH

27. MODAL FREQUENCY CORRELATION (CONF.-4) {UNIFORM INFLOW MODEL}
, RPM
, Hz
______ Uniform Inflow
Δ o  Experiment
ROLL
PITCH-FLAP

28. MODAL FREQUENCY CORRELATION (CONF.-4) {TIME VARYING INFLOW MODEL}
______ Perturbation Inflow Dynamic Inflow
Δ o  Experiment
, RPM
, Hz

29. WHAT IS GOOD FOR THE GOOSE, IS NOT GOOD FOR THE GANDER
REMARKS
CORRELATION STUDY TAUGHT THE LESSON:
• A GOOD (OR ADEQUATE) ANALYTICAL MODEL FOR ONE ROTOR CONFIGURATION MAY NOT BE ADEQUATE
FOR OTHER ROTOR CONFIGURATIONS
REMINDS THE PROVERB
WHAT IS GOOD FOR THE GOOSE,
IS NOT GOOD FOR THE GANDER

30. FLIGHT DATA Freq. contents Time signal moment PWR SPECTRUM Ch A 1
5.250Hz
.736E+3 NM 2
4.450
.573E+3 3
5.100
.547E+3 4
4.650
.506E+3 5
4.100
.320E+3 6
4.950
.278E+3 7
0.200
.276E+3 8
4.850
.270E+3 9
3.950
.210E+3 10
4.250
.164E+3
moment
Time signal

31. DYNAMIC STALL Lift coefficient Moment coefficient Drag coefficient
Courtesy: Principles of Helicopter Aerodynamics G.J.Leishmann

32. Unsteady Aerodynamic Coefficients
Reduced freq.
k= k= k=0.1

33. RESPONSE STUDY
2-D Airfoil response simulating cross-section of a rotor blade
Response of 2-D airfoil undergoing pitching and heaving in a pulsating flow is analysed
The pitching motion and oncoming flow velocity are taken as

34. HEAVE RESPONSE 0% 3% 5% C.G location Response Frequency content
Phase plane plots
Effect of initial condition
Liaponov Exponent
0% % %

35. TORSIONAL RESPONSE 0% 3% 5% Frequency content Phase plane plots
0% % 5%
C.G. Location
Response
Frequency content
Phase plane plots
Effect of initial condition
Liaponov Exponent

36. CONCLUDING REMARKS
• SEVERAL ISSUES STILL NOT UNDERSTOOD FULLY
• CONTINUED RESEARCH TO IMPROVE HELICOPTER
PERFORMANCE
• VERY FERTILE FIELD FOR CHALLENGING RESEARCH
THANK YOU