Galloping Gertie, Engineering's Most Misunderstood Failure (vice.com)

tedlistens writes: Generations of physics teachers, textbooks, and articles have taught that the spectacular collapse of the Tacoma Narrows Bridge, 75 years ago, in November 1940, was caused by resonance. But this explanation is inaccurate, and despite the fact that the collapse is not a mystery—that the bridge, in a sense, twisted itself apart—the fallacy continues to spread. Not only that: according to a new study by Don Olson and colleagues at Texas State University and East Carolina University, parts of the famous footage that immortalized it are misleading too. According to the most complete recent research, he and his co-authors write, "the failure of the bridge was related to a wind-driven amplification of the torsional oscillation that, unlike a resonance, increases monotonically with increasing wind speed." Each time the deck of the bridge twisted now, it sought to return to its original position (inertial forces). And as it did so, twisting back with a matching speed and direction (elastic forces), the wind and the vortices caught it each time, pushing the deck just a little bit more in that direction (aerodynamic forces). With each twist and each twist back, the size of the twisting slightly increased.

Comments

Perhaps amend the definition of resonance

[John Allsup]

Intuitively, this phenomena as described has the feel of what one thinks of given the word 'resonance'. Perhaps 'pseudo-resonance' would be a good term to apply.

Re:Perhaps amend the definition of resonance

[PsychoSlashDot]

Intuitively, this phenomena as described has the feel of what one thinks of given the word 'resonance'. Perhaps 'pseudo-resonance' would be a good term to apply.

Pretty much. I'm reasonably well-read, and the summary leaves me hearing "resonance was the cause but we engineers have a bunch of other words we'd prefer to use because they're technically more accurate but for anyone not in bridge-building the distinction is meaningless."

Re:Perhaps amend the definition of resonance

[Etherwalk]

Intuitively, this phenomena as described has the feel of what one thinks of given the word 'resonance'. Perhaps 'pseudo-resonance' would be a good term to apply.

It does sound a lot like how most people would think of resonance. Although actually a bit more like a really bad relationship. Forces kept trying to make it work, but each time got a teensy bit worse and had even more baggage, until suddenly it turned into a youtube video.

Re:Perhaps amend the definition of resonance

[Matheus]

Perhaps... but the difference is as follows:

1) Resonance: This is a natural tendency of a physical object to self-increase its oscillation when caused to oscillate at the objects natural resonant frequency.

2) (What Really Happened): This would be described as a reinforced feedback loop. In this particular case the reinforcement was coming from gravity acting on the bridge in one direction while wind was acting on the bridge in the opposite direction.

The key difference here is that the amplification of oscillation leading to bridge failure was caused by **external forces not any natural resonance of the structure.

In terms of knowing why the bridge failed and how to not have a future one fail in the same manner, the difference between those two is quite important.

Re:Perhaps amend the definition of resonance

[Anonymous Coward]

TFS leaves me thinking some popular-press hack didn't understand the explanation. Pretty sure these

sought to return to its original position (inertial forces)

twisting back with a matching speed and direction (elastic forces)

Should be reversed. ie: the forces that make it return to its original position are elastic forces in the deformed bridge members, while the speed of its return are inertial forces.

The bit that makes it non-resonant is the monotonic increase with wind speed. ie, that it doesn't depend on 'just the right speed,' but that the failure would have happened faster at higher wind speed. And that the oscillation was presumably apparent even at lower wind speeds that people should have seen - probably even during construction.

Re:Perhaps amend the definition of resonance

[Darinbob]

Resonance comes when a force matches a natural frequence in an object. The bridge normally did resonate and it had a resonant frequency. It normally oscillated along its length though, rather than twisting. The higher winds when it collapsed were stronger but also very gusty. If it was just resonance then it should have resonated at its normal frequency, perhaps with greater amplitude, but still oscillating up and down along the length of the span. The twisting motion was an oscillation but not at a resonant frequency of the bridge.

It's like blowing along the width of a ribbon. Get it just right and you get a hum of a specific pitch, which can vary depending upon tension or length of the ribbon. But when it is not humming because you're blowing too hard or not aiming just right you get a flapping and fluttering instead. Which is what the movies of that bridge collapsed showed, which were unlike the earlier movies.

Re:Perhaps amend the definition of resonance

[Schmorgluck]

Yup, and this is what happened to the Angers Bridge back in 1850 too, or at least something similar. And yet for more than a century French physics teachers used it as a spectacular illustration of resonance, even though it's not that simple.

Re:Perhaps amend the definition of resonance

[phantomfive]

There's a difference:

Resonance: a force at a particular frequency that causes increased motion.
This: a powerful force caused increased motion.

In this case it was just a powerful wind. The frequency didn't matter. If the wind had been faster, the bridge would have fallen sooner, whereas if it were resonance, a higher frequency would have reduced the chances of breakage.

Re:Perhaps amend the definition of resonance

[Beck_Neard]

Nope, this isn't resonance, it's aeroelastic flutter: https://en.wikipedia.org/wiki/...

The important distinction is that resonance requires some oscillating energy input whereas flutter doesn't. Resonance doesn't directly depend on wind speed whereas flutter does.

To be fair, the article does a surprisingly bad job of explaining it, hence the confusion.

Re:Perhaps amend the definition of resonance

[HornWumpus]

Aeroelastic flutter is only a problem when it happens at the resonant frequency of the underlying physical object.

Like when the forces are a consequence of the original motion.

The bridge was torquing at it's center span's natural frequency x 2 (IIRC).

Saying this wasn't resonance because the forcing function was a product of the oscillation in the first place is pedantic. Yes it was flutter, but destructive flutter is a resonant phenomenon.

Re:Perhaps amend the definition of resonance

[HornWumpus]

It wasn't resonant with the wind. It was resonant with the aero forces generated by the twisting bridge.

It all depends on what you define as the 'forcing function'.

None of this is news. Nobody ever said the wind was gusting at the same frequency as the bridge. It's always been understood what happened.

I put this whole thing down to reddit morons splitting hairs.

Complete aside. The state employee that was supposed to buy insurance on the bridge pocketed the premium, until it started to really gallop. If it had stayed up another day, he would have gotten away with it.

Re:Perhaps amend the definition of resonance

[msauve]

Resonance of the bridge, not the wind.

The authors seem the type who try to get out of a speeding fine by arguing the difference between speed and instantaneous velocity. GLWT. For the general public, "resonance" is a perfectly reasonable explanation.

Re:Perhaps amend the definition of resonance

[AthanasiusKircher]

Resonance of the bridge, not the wind.

You do realize that resonance is a phenomenon caused by two different things vibrating at similar frequencies, right? If you pluck a guitar string (introduce energy) and the string produces a standing wave at a certain frequency, it string is NOT participating in resonance, as is defined in physics. It's just vibrating at a natural frequency. Similarly, if the wind adds a bunch of energy to the bridge in a non-periodic fashion, and the bridge oscillates in a standing wave (natural frequency of vibration, like the guitar string's "pitch"), it isn't "resonance."

Re:Perhaps amend the definition of resonance

[AthanasiusKircher]

It wasn't resonant with the wind. It was resonant with the aero forces generated by the twisting bridge.

What the hell are you talking about? Where are "aero forces" coming from except from the, well, AIR -- I.e., the wind??

It all depends on what you define as the 'forcing function'.

I can't seem to figure out what you're talking about except maybe that the bridge reinforced its own standing wave vibrations at its natural frequency. But that isn't resonance, and that's not a "forcing function." That's just an object vibrating at its natural mode of vibration when energy is introduced into the system. If you randomly strum a guitar string in a non-periodic fashion, it will create a standing wave pattern and vibrate at a certain frequency due to its natural modes of vibration. But that isn't resonance, and there's no "forcing function" setting up or reinforcing the standing waves.

None of this is news. Nobody ever said the wind was gusting at the same frequency as the bridge. It's always been understood what happened.

You're right that none of this is news, but there were alternative explanations in the past. You're right that no one said the wind was gusting in an oscillation frequency of some sort with the bridge. What some people did theorize, though, is that the wind was causing eddies to shed off the bridge in such a way that created periodic reinforcement of the bridge's motion, I.e., resonance. In the case, the speed of the wind (constant speed not oscillating) would determine the frequency of eddy shedding, which would therefore cause resonance only at certain wind speeds.

That was the old resonance explanation. That explanation is wrong, because it was the strength of the wind, not its tuned specific speed, which caused the motion. The more energy, the stronger the vibrations -- kind of like strumming the guitar string harder. But without a periodicity, you're not driving the oscillations by lining up with them... and thus it's NOT resonance as classically understood in physics.

Re:Perhaps amend the definition of resonance

[amalcolm]

As electronic engineers we talk about resonant circuits. They have a natural frequency, and when excited correctly, they resonate. So yes, I guess, strictly, you're right, but evferyday usage trumps here, I think.

Re:Perhaps amend the definition of resonance

[drinkypoo]

The resonance of the bridge wasn't involved at all. For resonance, the wind would have to match the resonant frequency of the bridge.

No, the argument is that the bridge was self-resonant . Self-resonance isn't just for electronics; when you strike a bell or tuning fork and it resonates at a specific frequency, you're experiencing self-resonance.

Aeroelastic flutter

[sjbe]

Hey Texas dumb-shits, "wind-driven amplification of the torsional oscillation..." Sure as hell sounds like resonance to me. Unless they have some other definition.

The proper term for it is aeroelastic flutter. It's a well understood phenomena most famous in jet airplanes but it occurs other places too including apparently this bridge.

Re:Aeroelastic flutter

[Anonymous Coward]

Check your own wikipedia references.

Aeroelastic flutter is a type of "Simple harmonic motion".
"Simple harmonic motion" is a type of "resonance"

Simple harmonic motion
"...The motion is sinusoidal in time and demonstrates a single resonant frequency."

Resonance is :
  "a phenomenon that occurs when a vibrating system or external force drives another system to oscillate with greater amplitude at a specific preferential frequency."

This is like saying "A mallard isn't a bird, it is a duck."

Re:Aeroelastic flutter

[lgw]

Not all oscillation is resonance. This was a positive feedback loop that would have happened regardless of the bridge's resonant frequency. Resonance is the result of the incoming energy having a frequency similar to the natural vibration frequency of the object. This would have happened at high constant windspeed, or as it did from non-periodic (but frequent) gusts.

Re:Aeroelastic flutter

[AthanasiusKircher]

Wow. The fact that this AC has been modded up to "+5 Insightful" makes me truly worry about the "nerd" factor at Slashdot these days. Not only do mods believe an AC spouting nonsense, but they aren't even capable of checking that nonsense or knowing enough basic physics to contradict it.

Let's clear this up. It's really quite simple.

Check your own wikipedia references.

Aeroelastic flutter is a type of "Simple harmonic motion"
. "Simple harmonic motion" is a type of "resonance"

You're skipping over a few steps here. Simple harmonic motion is NOT a "type of resonance." Let's explore further. As you say:

Simple harmonic motion

"...The motion is sinusoidal in time and demonstrates a single resonant frequency."

There's a difference between a "resonant frequency" and "resonance." SHM occurs at a specific frequency which is a natural mode of vibration of the system. That specific frequency could be USED to create resonance, but SHM isn't resonance itself.

Resonance is :
"a phenomenon that occurs when a vibrating system or external force drives another system to oscillate with greater amplitude at a specific preferential frequency."

Exactly. Notice the external force part. The external force needs to DRIVE the motion at a specific frequency. THAT is resonance.

Or, let me try to put it in even simpler terms an AC might be able to understand:

Resonance: A system has a natural vibrational frequency of X. An external force also has a periodicity of X. Even a small external force with the same periodicity could drive the system to vibrate significantly. Example: place a tuning fork with pitch "middle C" on a piano string tuned to "middle C." The vibrations of one can drive the other to vibrate, because they both tend to vibrate at THE SAME frequency (both internal frequency and frequency of driving force).

Aeroelastic flutter: A system still has a natural vibrational frequency of X. But the external force is simply LARGE and roughly CONSTANT. The external force does NOT necessarily have a periodicity, and if it does, it isn't equal to X. So why does the "flutter" occur? Basically, there's too much energy flowing into the system and it can't dissipate it naturally. Random perturbations get it moving. Due to the natural characteristics of the system, it will tend to preferentially vibrate at one of its natural frequencies. Think of a flag fluttering in the wind -- you can see certain wavelike patterns happening even if the wind is relatively constant. The bridge is a little more complicated: it's more like a flag that's tethered on both sides. Again, in a strong wind you might see flutter "waves" happening -- that's not due to the periodicity of the wind, but to the natural reinforcement of standing waves in the flag itself when there's too much energy being pushed into it that it can't dissipate.

TL;DR -- Resonance requires a driving force with the same frequency as the system that's vibrating. Even a tiny external force could be potentially catastrophic if it reinforces the natural frequency of the system. Flutter just requires a large external force pushing energy into the system. The remedy in the case of the bridge is completely different -- for resonance, you'd have to worry about a particular windspeed for a particular length of bridge or something like that. Even a gentle wind might be able to set off nasty vibrations when resonance (matching frequencies) occurs. For flutter, you just need more damping material in general.

Re:Aeroelastic flutter

[lindseyp]

Resonance is :
"a phenomenon that occurs when a vibrating system or external force drives another system to oscillate with greater amplitude at a specific preferential frequency."

Exactly. Notice the external force part. The external force needs to DRIVE the motion at a specific frequency. THAT is resonance.

The original sentence might be slightly ambiguous but it doesn't explicitly state that the external force needs to drive the motion at the specific frequency. It just says there needs to be an external force, and that it drives another system to oscillate at a specific frequency. I don't know where the sentence came from but I'm curious as to whether flutter is a resonant phenomenon or not.

Not resonance, anti-damping

[Roger W Moore]

Actually it really is not like resonance but more like and anti-damping force. Resonance is when a periodic force is applied to the system and, when the frequency of that force matches the natural vibration frequency of the system, the steady-state response gives a large amplitude response. The key difference is that with resonance the system is in a steady state with a constant amplitude. With "anti-damping" (called aero-elastic flutter in this case) the amplitude of the system increases with each oscillation since you effectively have a negative damping ratio.

Hence there is a clear difference in the motion between resonance and anti-damping which you can determine by studying the motion which the paper seems to have done. It is NOT just a fancy name for a resonance effect: the behaviour is transitory and not steady-state. However this has been known for over a decade now and I'd be surprised if it were still being taught as resonance in introductory physics courses. Certainly for the one I teach I describe it in terms of damping and point out the fallacy of the resonance explanation.

Rediscovered?

[JazzHarper]

Isn't this conclusion pretty much identical to the findings sixty years ago? It's no surprise that the explanation was oversimplified to "resonance" by the popular press, but to claim that this is an entirely new result misrepresents what engineers learned from the failure.

Has no one heard of Fourier transforms?

[MouseTheLuckyDog]

When it comes down to it, the basic argument is that the phenomena is aeroelastic flutter not resonance, because the driving force is nearly constant.

However, I suspect if you work it all out the change in amplitude of the rotation is proportional to the Fourier transform of the driving force at the natural frequency of the bridge.

Why is that? The nearly constant driving force is not nearly constant.
It is a composition of oscillating forces spanning a range of frequencies. Of all those forces, only the force oscillating at the natural frequency contributes--hence it is proportional to the Fourier transform.

Definitions wrong

[Roger W Moore]

I don't know where you got those definitions from but they are wrong. Aeroelastic flutter is essentially a form of anti-damping force applied to a simple harmonic oscillator and is neither a type of resonance nor the motion itself: you still need an oscillator to experience the anti-damping.

Simple harmonic motion is just the sinusoidal motion in time. To exhibit resonance you actually need a DAMPED harmonic oscillator (otherwise you have infinite amplitude at resonance) and not all damped harmonic oscillators exhibit resonance: only ones where the damping ratio is less than 1/sqrt(2) will show resonance.

Resonance is when an external force drives a damped, harmonic oscillator at a frequency which generates a maximum amplitude response in the steady state. This last part is very important and is why aero-elastic flutter is not resonance. In resonance the amplitude is large but constant, with aeroelastic flutter it grows exponentially and is part of the transient solution of the damped harmonic oscillator. You can also have aeroelastic flutter in a damped system which cannot show resonance.