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

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

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

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

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

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

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