Model Insight

Decreasing the mass decreases the flutter speed (i.e. encourages flutter), but decreasing the moment of inertia increases flutter speed (i.e. reduces flutter). In reality, these two things are coupled when we (in this project) removed the plates. When we decreased the mass and the moment of inertia together. This makes both effects conflict and the outcome is a toss-up based on the relationship between the mass and moment of inertia for the removed plate (e.g. taking off a small diameter, heavy plate would decrease mass more, so would encourage flutter, but taking off a large diameter, lighter plate would decrease moment of inertia more, so would discourage flutter). The exact values of weight we used for the experiments were of the exact combination of mass and diameter that the moment of inertia and mass effects canceled and resulted in the same critical airspeed.

If you look at the system of ODEs, you can see what’s going on. Decreasing the mass raises the natural frequency for the plunge mode, and decreasing the moment of inertia raises the natural frequency of the pitch mode. From the ODE solution, the plunge frequency is the lower frequency eigenmode, and the pitch is the higher frequency eigenmode. This means that raising the plunge frequency (i.e. lowering the mass) brings the frequencies of the two modes closer together, and raising the pitch frequency (i.e. lowering the moment of inertia) drives the frequencies further apart. Flutter happens when the frequencies converge, so we can now see why the moment of inertia and the mass reduction have this weird effect: it’s about the distance between the eigenfrequencies.

In the real world, for designing an aircraft, things are even more complicated. Lightweighting parts of a wing affects the mass, moment of inertia, center of gravity, and (if the lightweighted component is structural) the stiffness (this means that re-arranging fuel tanks has a different effect on flutter than re-arranging wing spars). It seems that the mass distribution is more important than the mass itself. For instance, some airplanes have lead weights mounted to the ailerons on pylons so they stick out in front of the hinge line. The added mass increases the moment of inertia (and mass, of course), but also moves the center of gravity closer to the elastic axis and therefore causes a reduction in the tendency to flutter.

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