1. Purdue Aeroelasticity
AAE 556 Aeroelasticity
The V-g method
Purdue Aeroelasticity

2. Airfoil dynamic motion
Purdue Aeroelasticity

3. Purdue Aeroelasticity
This is what we’ll get when we use the V-g method to calculate frequency vs. airspeed and include Theodorsen aero terms
Purdue Aeroelasticity

4. When we do the V-g method here is damping vs. airspeed
flutter
divergence
Purdue Aeroelasticity

5. Purdue Aeroelasticity
To create harmonic motion at all airspeeds we need an energy source or sink at all airspeeds except at flutter
Input energy when the aero damping takes energy out (pre-flutter)
Take away energy when the aero forces put energy in (post-flutter)
Purdue Aeroelasticity

6. 2D airfoil free vibration with everything but the kitchen sink
Purdue Aeroelasticity

7. We will get matrix equations that look like this
…but have structural damping that requires that …
Purdue Aeroelasticity

8. Purdue Aeroelasticity
The EOM’s are slightly different from those before (we also multiplied the previous equations by m)
Each term contains inertial, structural stiffness, structural damping and aero information -
Purdue Aeroelasticity

9. Purdue Aeroelasticity
Look at the “A” coefficient and identify the eigenvalue – artificial damping is added to keep the system oscillating harmonically
We change the eigenvalue from a pure frequency term to a frequency plus fake damping term. So what?
Purdue Aeroelasticity

10. The three other terms are also modified
Each term contains inertial, structural stiffness, structural damping and aero information - =
Purdue Aeroelasticity

11. To solve the problem we input k and compute the two values of W2
The value of g represents the amount of damping that would be required to keep the system oscillating harmonically. It should be negative for a stable system
Purdue Aeroelasticity

12. Now compute airspeeds using the definition of k
Remember that we always input k so the same value of k is used in both cases. One k, two airspeeds and damping values
Purdue Aeroelasticity

13. Typical V-g Flutter Stability Curve
Purdue Aeroelasticity

14. Now compute the eigenvectors
Purdue Aeroelasticity

15. Purdue Aeroelasticity
Example
Two-dimensional airfoil
mass ratio, m = 20
quasi-static flutter speed VF = 160 ft/sec
Purdue Aeroelasticity

16. Purdue Aeroelasticity
Example
Purdue Aeroelasticity

17. Purdue Aeroelasticity
The determinant
Purdue Aeroelasticity

18. Final results for this k value – two g’s and V’s
Purdue Aeroelasticity

19. Purdue Aeroelasticity
Final results
Flutter
g = 0.03
Purdue Aeroelasticity