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Purdue Aeroelasticity
AAE 556 Aeroelasticity The V-g method Purdue Aeroelasticity
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Airfoil dynamic motion
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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
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When we do the V-g method here is damping vs. airspeed
flutter divergence Purdue Aeroelasticity
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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
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2D airfoil free vibration with everything but the kitchen sink
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We will still get matrix equations that look like this
…but have structural damping that requires that … Purdue Aeroelasticity
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Here is how the equations are slightly different
Each term contains inertial, structural stiffness, structural damping and aero information - = Purdue Aeroelasticity
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Purdue Aeroelasticity
One approximation and one definition allows us to construct an eigenvalue problem We change the eigenvalue from a pure frequency term to a frequency plus fake damping term. So what? Purdue Aeroelasticity
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The three other terms can also be modified
Each term contains inertial, structural stiffness, structural damping and aero information - = Purdue Aeroelasticity
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Purdue Aeroelasticity
We input k and compute W 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
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Now compute airspeed 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
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Typical V-g Flutter Stability Curve
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Now compute the eigenvectors
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Purdue Aeroelasticity
Example Two-dimensional airfoil mass ratio, m = 20 quasi-static flutter speed VF = 160 ft/sec Purdue Aeroelasticity
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Purdue Aeroelasticity
Example Purdue Aeroelasticity
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Purdue Aeroelasticity
The determinant Purdue Aeroelasticity
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Final results for this k value – two g’s and V’s
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Purdue Aeroelasticity
Final results Flutter g = 0.03 Purdue Aeroelasticity
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