1. Purdue Aeroelasticity
AAE Aeroelasticity
Flutter-Lecture 20
Reading:
; ;
Purdue Aeroelasticity

2. Quasi-steady flutter with a typical section vibration idealization
Flutter is a self-excited, dynamic, oscillatory instability requiring the of motion and interaction between two different modes an external energy supply
Quasi-steady aerodynamic loads capture some dynamic effects of the lift force, but ignore lags between motion and developing forces and moments
Assumed harmonic motion
Purdue Aeroelasticity

3. Purdue Aeroelasticity
The prize
Remember what the bars mean.
Purdue Aeroelasticity

4. Calculate the determinant what do you hope to discover?2b
c.g.
shear center
aero center
Purdue Aeroelasticity

5. Quadratic equation for frequency squared
Purdue Aeroelasticity

6. The A, B terms are airspeed dependent
Purdue Aeroelasticity

7. Divergence is a special case
set
then
Purdue Aeroelasticity

8. Purdue Aeroelasticity
Divergence
Purdue Aeroelasticity

9. Solution for natural frequencies
When the airspeed is zero then these eigenvalues are real and distinct. They stay that way as airspeed increases. That means our original assumption of harmonic (sinusoidal) motion is correct.
Purdue Aeroelasticity

10. Purdue Aeroelasticity
The transition point between stability and instability for this idealization is frequency merging
Two solutions with the same frequencies
instability
Purdue Aeroelasticity

11. Frequency depends on airspeed
Purdue Aeroelasticity

12. Transition to instability
?????
Purdue Aeroelasticity

13. Purdue Aeroelasticity
Two roots
Purdue Aeroelasticity

14. Purdue Aeroelasticity
Frequency merging
Purdue Aeroelasticity

15. Solution for frequency
When the airspeed is zero then these eigenvalues are real and distinct - they also depend on airspeed ...
Purdue Aeroelasticity

16. Purdue Aeroelasticity
When the frequencies are real and distinct then no energy is input or extracted over one cycle
Mode shapes are important
Purdue Aeroelasticity

17. Purdue Aeroelasticity
Free vibration is usually either “in-phase” or “180 degrees out of phase”
negative
work
positive work
In phase motion
Sinusoidal motion assumption does not permit anything else
Out of phase motion
positive
work
negative work
Purdue Aeroelasticity

18. Flutter has 90o out of phase motion phase motion
negative
positive
Complex eigenvalue results are an example of math trying to talk to us
Purdue Aeroelasticity