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

Airfoil dynamic motion Purdue Aeroelasticity

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

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

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

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

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

Here is how the equations are slightly different Each term contains inertial, structural stiffness, structural damping and aero information - = Purdue Aeroelasticity

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

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

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

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

Typical V-g Flutter Stability Curve Purdue Aeroelasticity

Now compute the eigenvectors Purdue Aeroelasticity

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

Purdue Aeroelasticity Example Purdue Aeroelasticity

Purdue Aeroelasticity The determinant Purdue Aeroelasticity

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

Purdue Aeroelasticity Final results Flutter g = 0.03 Purdue Aeroelasticity