1. Purdue Aeroelasticity
AAE Aeroelasticity
Flutter-Lecture 20
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
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3. Flutter and frequency merging
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4. Purdue Aeroelasticity
What we are looking for
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5. Free vibration with the air on looking for clumps of parameters
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6. Purdue Aeroelasticity
The prize
Remember what the bars mean.
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7. Calculate the determinant what do you hope to discover?2b
c.g.
shear center
aero center
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8. Quadratic equation for frequency squared
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9. The A, B terms are airspeed dependent
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10. Divergence is a special case
set
then
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11. Purdue Aeroelasticity
Divergence
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12. 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.
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13. Purdue Aeroelasticity
The transition point between stability and instability for this idealization is frequency merging
Two solutions with the same frequencies
instability
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14. Frequency depends on airspeed
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15. Transition to instability
?????
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16. Purdue Aeroelasticity
Two roots
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17. Purdue Aeroelasticity
Frequency merging
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18. Solution for frequency
When the airspeed is zero then these eigenvalues are real and distinct - they also depend on airspeed ...
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19. Purdue Aeroelasticity
When the frequencies are real and distinct then no energy is input or extracted over one cycle
Mode shapes are important
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