# I Is aeroelastic flutter a type of resonance?

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1. Jul 9, 2016

### Tangent100

Sorry if this aint undergrad its hard to tell what is and what isnt.

I wanted to know if these two things linked or are they completely different? Im looking at the causes of the narrows bridge collapse... it would seem that the flutter has to do with vibrations but not exactly with resonance for me.

2. Jul 9, 2016

### Staff: Mentor

Maybe if you describe what "resonance" means to you and then describe how exactly aeroelastic flutter does or doesn't apply, we can go from there.

3. Jul 9, 2016

### FactChecker

They are not the same. Resonance refers to one thing vibrating at a frequency that causes something else to vibrate at a higher amplitude at some related frequency. The bridge collapse is more accurately described as an unstable mode of the entire bridge system that was excited by a constant (not vibrating) energy input from the wind.

"a result of aeroelastic flutter caused by a 42 mph (68 km/h) wind. The bridge collapse had lasting effects on science and engineering. In many undergraduate physics texts the event is presented as an example of elementary forced resonance with the wind providing an external periodic frequency that matched the natural structural frequency, even though the real cause of the bridge's failure was aeroelastic flutter."

4. Jul 9, 2016

### Staff: Mentor

The energy (force) input of the wind is not constant in aeroelastic flutter. As the name "flutter" implies, the forcing function is periodic, which is why the oscillation happens. A constant energy (force) input can only cause a constant/static deformation.

5. Jul 9, 2016

### FactChecker

You can start with a perfectly smooth, constant, free stream of air, put a flag in it and the flag will flutter.
The free stream wind is constant, not fluttering. It is the interaction of the bridge dynamics and aerodynamics with the wind that causes the flutter. It is a mode of the entire system that was unstable.

Last edited: Jul 9, 2016
6. Jul 10, 2016

According to the classical definition of resonance, flutter is not an example, as has already been discussed by @FactChecker. However, as air flows are rarely (i.e. never) completely steady, it wouldn't be unusual (or at the very least it certainly not impossible) for the instability typically known as flutter to occur concurrently with resonant forcing. Flutter itself, though, is not classically the result or resonance.

7. Jul 10, 2016

### Staff: Mentor

Ok....so, the wind is constant/steady -- but it applies a periodic force to the bridge, doesn't it? How does that not fit the definition of resonance?
Could you post this definition so I can see why it excludes flutter? Can you tell me exactly what part of the definition flutter violates?

I see people saying what flutter is and saying it doesn't fit the definition of resonance without actually making a connection between the two. Here's the wiki definition:
The wind provides a "vibrating" external force to the bridge (or flag), doesn't it? So how does that not fit the definition?

Last edited: Jul 10, 2016
8. Jul 10, 2016

### FactChecker

I agree.
I guess because the wind force oscillation is as much a result of the bridge dynamics as it is a cause of it. The whole thing is a circular feedback dynamic system and must be analyzed as such. The way they define "resonance" sounds more like a simple cause-effect definition -- the input is oscillating and it drives something else at a related frequency. It seems like resonance is just the forward half of the flutter feedback problem.

9. Jul 10, 2016

### Staff: Mentor

I'm not sure there are many systems where there would be no interaction/feedback between the driver and the system. Another commonly cited example is when people march in step on a bridge and match its frequency. The marching is already periodic, sure, but the oscillation of the bridge causes the force the marchers apply to increase and even causes them to change their marching cadence (frequency of the applied force). So it doesn't seem reasonable to me to exclude cases where the driving force arises from an interaction.

Perhaps more to the point; science is supposed to be quantitative and definitions should arise from the math. So does this quibble over the definition have any relevance to the math of resonance? Can we not use a similar equation of forced oscillation to describe these scenarios?

Last edited: Jul 10, 2016
10. Jul 10, 2016

### FactChecker

They are not so much excluded as the problem and method of analysis have a different name.

The mathematics of a dynamic closed loop system is often much different and more complicated than the mathematics of the open loop response to a given input frequency of a part of the system.

I like your example of people walking at a certain pace on the bridge. If the marching pace is determined by a fixed thing, like marching music, then I think that is a good example of resonance. On the other hand, suppose there was no marching music and you tried to include a model how the motion of the bridge influenced the pace of a group walking. That would be a closed loop dynamic system. You can imagine how different that might be.

Last edited: Jul 10, 2016
11. Jul 10, 2016

### Staff: Mentor

The math describing what creates the functions of any oscillating system depends on the particular structure and dynamics. Some are more complicated than others. But all have the same basic parts: a periodic forcing function, an periodic natural vibration and perhaps damping.
Or you might not try to model how the motion of the bridge changed the marching frequency and just focus on modeling what happens when they match.

My main concern here is that limiting the definition in this way implies that you can't use many of the same mathematical tools on the problems. Things get even harrier when you have a system where the oscillation isn't even due to elasticity or isn't even physical, such as oscillation internally or externally with a control system.

Backing-up a bit:
One of the arguments about the Tacoma Narrows bridge was in finding the cause of the forcing function: there were two candidates, one being vortex shedding and the other aeroelastic flutter, which is a lift and drag effect. For some reason people (such as whomever wrote the wiki) call vortex shedding induced oscillation a "resonance" and aeroelastic flutter not a resonance, even though both are due to fluid dynamics forces and both arise from the steady wind you say is an important distinction.

12. Jul 10, 2016

### FactChecker

An unstable system does not need a periodic forcing function to start a divergent oscillation. In that case it just seems strange to use the term "resonance". You might be right that this is just quibbling over terminology. Still, I interpret "resonance" differently.

But then you don't know what frequency(s) you should worry about. It is the combined response of the components to the full range of frequencies that determines the stability and modes of the system.

That is a good point. The same mathematics often applies. But adding feedback will be more complicated.

13. Jul 10, 2016

But in doing that you are ignoring a central feature of the system in his example.

The problem is that vortex shedding, while arising from a steady breeze, still has a characteristic frequency that is often determined by the Strouhal number. For example, a cylinder almost always exhibits a Strouhal number of about 0.2, which means there is a very definite vortex shedding frequency that arises for a given free-stream velocity and cylinder size. This is not the case with flutter, where you can start the unstable oscillations without any sort of characteristic flow frequency such as from vortex shedding.

However, as I alluded to before, these two types of oscillations don't necessarily occur separately, even though they certainly can. It is certainly possible to have a situation where an object exhibits flutter completely on its own, and then the vortex shedding frequency also happens to be very similar to the unstable flutter frequency, in which case you could legitimately have a resonantly-reinforced flutter. In other words, fluttering objects can experience resonance as well, but resonance is not required for flutter.

14. Jul 10, 2016

### Staff: Mentor

Can you give an example -- are you saying aeroelastic flutter is one? I thought we were agreed that the air provided a periodic force to the wing/bridge?
Isn't the worrisome frequency always the natural frequency of the object?

15. Jul 10, 2016

### Staff: Mentor

Yes, for example a flag, which basically has no structure, will flutter. My understanding is that the structure of a wing will impact the flutter frequency: it will tend to make the flutter match the natural frequency (which is why it would be called "aeroelastic").

16. Jul 10, 2016

There can be many different unstable modes for a given object, and those modes can change as the object deforms or sustains damage. It is even possible for two unstable modes within the same structure to excite one another, particularly if their associated frequencies drift close to one another or if their amplitudes become large enough that they can interact nonlinearly.

Think about something simple like a mass attached to a spring. Then place that system in a steady, uniform air flow such that it is blowing in a direction that compresses the spring. Ignore gravity. Since this is a dynamic situation, start that mass out with the spring uncompressed. The air pushes that and compresses the spring. However, since the mass has some inertia, it will tend to overshoot the equilibrium point a little bit, and start moving against the force in the opposite direction, where it will tend to overshoot a bit again, and so on. That is an oscillation that was started by a completely steady airflow. The air flow will certainly be affected by this oscillation in the vicinity of the mass-spring system, but any unsteady flow in that region is a direct result of the oscillating mass, not the cause, as is the case in resonance.

Clearly this system has damping (in the form of drag) and it will eventually settle to its equilibrium point. However, for more complex structures, this isn't necessarily the case. As a structure (such as a wing) deflects, the vibrational modes to which it is unstable will change slightly as a result of the new shape and the new tensions and compressions throughout the different parts of the structure. Sometimes these issues will cause the structure to overshoot the equilibrium point by a larger amount than their initial deflection, which can continue until catastrophic failure occurs. This is essentially what is typically called flutter, and it doesn't require any oscillations in the air flow to drive the instability.

Now, the above situation may occur in the same flow system as vortex shedding, or by its deflection, cause vortex shedding to occur transiently, and these two effects can resonate with each other (or conversely, one can effectively add damping to the other), but each can certainly occur without the other also being present.

17. Jul 10, 2016

### FactChecker

I would say that the air as disturbed by the bridge aerodynamics and motion provides a periodic force. But without the bridge, the air flow would be steady.
Not necessarily. The air density and speed changes things. Does a flag even have a natural frequency?

Last edited: Jul 10, 2016
18. Jul 10, 2016

### Staff: Mentor

Good grief, we had long threads on this topic a while back,

A flag is a bad example because it is unstable in the extended position pointing downwind. Even a constant force can drive unstable oscillations. The flag's weight wants to collapse it vertically by gravity, but the part of the flag attached to the pole is fixed. That causes diagonal creases and the creases have extra wind resistance.

So flags are unlike other resonances and unlike other fluttering things. They make a bad example of either.

19. Jul 10, 2016

### FactChecker

Flags are at one extreme end of a continuum with minimal-structure flags at one end and rigid, 0 flex structures at the other. There is a lot of work going on with very high aspect wings that have much less rigidity than traditional wings. They are somewhere in that continuum. We shouldn't imply that only flags can have a constant free-stream air flow driving unstable oscillations. That is wrong.

Last edited: Jul 10, 2016
20. Jul 11, 2016

### Andy Resnick

There was indeed a discussion earlier, it's a subtle topic so the continuing confusion is not surprising. Resonant vibration and induced flutter are not the same. Resonance occurs when a structure is excited at a single frequency, but distributed systems (distributed in mass and stiffness) do not have a single resonant frequency; when oscillatory motion is excited in such a continuous system, it's due to an instability in the fluid-structure interaction.

http://www.engr.mun.ca/~hinch/FSI/NOTES/SHAKES.pdf