Good explanation of aeroelastic flutter

[dEdt]

After looking into the Tacoma Narrows Bridge collapse, I tried to find out what this thing called aeorelastic flutter is and what causes it. Unfortunately, I didn't get a very good answer for either question, especially the latter one, and was hoping someone could help me out.

 

[Bobbywhy]

There is a fairly clear description of “aeorelastic flutter” on Wikipedia:
“Flutter is a self-feeding and potentially destructive vibration where aerodynamic forces on an object couple with a structure's natural mode of vibration to produce rapid periodic motion.”
It continues with more detailed descriptions of how it works.
http://en.wikipedia.org/wiki/Aeroelasticity

Here are two videos, both by NASA. The introduction gives an excellent explanation of the phenomenon. The first is of an aircraft’s horizontal tail section undergoing aeorelastic flutter. The second video is of the famous bridge you have already mentioned.

 

[Danger]

If memory serves, it was one of the major hurdles on the way to supersonic flight.

 

[AlephZero]

One way to understand the basic idea is to think about paddling a canoe. Suppose you keep the paddle in the water all the time, but you "feather" the blade on the return strokes to propel the canoe in one direction.

You can think of the motion of the paddle as two oscillations (one forwards and backwards, and the other rotating it to feather the blade) which are at the same frequency but 90 degrees out of phase with each other.

Now think about an aircraft wing that has two vibration modes, flapping up and down and twisting. If the vibration freqencies of the two modes are almost the same, it is possible for the air flowing over the wing to behave like the canoe paddle but "in reverse", with the driving force coming from the air and making the wing vibrate.

Of course in real life you try to design aircraft wings, turbine blades, etc, so they don't have vibration modes with similar frequences, and this can't happen!

If you look at videos of the Tacoma bridge, you can see the motion is a combination of vertical oscillation and twisting, though it's not so easy to separate out the two components as in the examples I gave.

 

[dEdt]

Thanks for the answers guys! Two more questions though about the Tacoma Narrows bridge:

1) Why/how does the air add more energy each cycle? I imagine that the wind adds energy by pushing it (sort of like it's explained here: ), but wouldn't this also remove energy when the bridge rotates in the opposite direction of the force?

2) Is there a simple reason why that particular torsional mode was excited, rather than the simpler one where the bridge as a whole twists in phase?

 

[AlephZero]

The ley thing is the coupling effect between two different modes of vibration. Think about the plane wing again. If the wing twists a bit for some reason, the angle of attack changes. That changes the lift force on the wing, which makes it start to flap up or down. But the up and down motion also changes the airflow over the wing, which can create a force causing it to twist.

To get flutter, the vibration frequencies of the two modes have to be similar, and the transfer of energy between the modes has to be such that it makes the amplitude of the motion increase rather than decrease. This is similar to pushing a child's swing. It's no use pushing at the wrong frequency (you need to push once per cycle, otherwise sone pushes will add energy to the swing and some will remove it) and you have to push at the right point in each cycle, otherwise you will tend to stop the swing rather than make it swing higher.

Every vibration mode of the bridge will be excited by random fluctuations in the wind to some degree, but unless there is a feedback mechanism, those random motions won't increase in amplitude. Probably the "simpler" torsional mode would have a different vibration frequency, and there were no other vibration modes at that frequency for it to interact with.

Predicting theoretically whether flutter will occur is difficult. It is possible to get a fairly reliable estimate of which pair(s) of vibration modes are the most likely to flutter, but getting an absolute "yes or no" answer to whether they WILL flutter is a much harder question to answer. Usually, you use theoretical predictions as a measure of the amount of "safety margin" and compare a new design with similar structures that have already been built, or with models tested in wind tunnels.