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

[Beck_Neard]

It's different. A resonant system has a particular frequency at which it 'likes' to oscillate; this frequency will have the lowest rate of energy dissipation, and so even a small amount of energy input at this frequency will tend to get stored and amplified over time. But in this bridge (FTA):

"When the bridge bounced up and down, as it did for months and earlier in the morning of November 7th, it's thought that the vortex street was causing forced harmonic motion on the bridge. But observations and calculations made by Farquharson about the speed of the wind and the motion of the bridge before it began to twist concluded that as the bridge approached collapse, the vortices were not being shed at the bridge's resonant frequency."

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

[evilviper]

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.

I'm going to say: No

First of all... If you design a bridge that collapses, nobody is going to care when you tell them, "Yeah, but it wasn't destroyed by wind-driven amplification of the torsional oscillation! We're professionals. We had that issue covered!"

Second... The fix for both is EXACTLY the same. You need to stiffen the structure and dampen any movement.

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

[xevioso]

There's a very good reason why you would design a bridge to collapse.

Read the first one here:
http://www.s-anand.net/blog/ca...

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

[BitterOak]

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.

That's actually not true. According to the article:

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.

So, the bridge's own elastic forces worked in tandem with the externally applied forces to increase the amplitude of oscillation. The elastic forces in the bridge give the bridge a natural resonance frequency and the wind acted on the bridge with the same frequency. That's the definition of resonance. It's just like when you push someone on a swing. You apply gentle pushes with the natural frequency of the swing and the resulting amplitude can become quite large.

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

[140Mandak262Jamuna]

To me it appears even more simple. Looks like they have found the exact way in which resonance happens for this bridge structure.

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

[HornWumpus]

It was twisting in the at n=2 on the center span. Did you watch the video?

Re:Perhaps amend the definition of resonance

[endoboy]

Perhaps we should require an explanation using the "ten hundred" most common words......

Consider this an enthusiastic plug for Randall Munroe's (of XKCD fame) most recent book. "Thing Explainer-- Complicated stuff in simple words"

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

[phantomfive]

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

I'm actually fascinated to find how many people don't actually know what a resonant frequency is.

Re:Perhaps amend the definition of resonance

[Beck_Neard]

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

Link?

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

[serbanp]

Yes, you're wrong. Pushing someone on a swing *is* how resonance works; you're adding energy to the system at the right time, i.e. resonant with the natural pendulum oscillation.

The analogy doesn't work for the bridge because the wind kept a steady speed; it's as if you're continuously pushing the swing, which, obviously, does not create an oscillation.

Re:Perhaps amend the definition of resonance

[thestuckmud]

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

From the bridge's perspective, this was most certainly resonance! The air pressure field at the bridge's surface exerted force on the structure with a fundamental frequency very close to the bridge's resonant frequency.

Of course, flutter is a more complete explanation which considers the system of wind+bridge, rather than just the forces acting on the bridge. But isn't that obvious?

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

[phantomfive]

From the bridge's perspective, this was most certainly resonance! The air pressure field at the bridge's surface exerted force on the structure with a fundamental frequency very close to the bridge's resonant frequency.

No, because if the wind had blown faster, the bridge would have fallen faster. It had nothing to do with the frequency.

Re:Perhaps amend the definition of resonance

[BitterOak]

The analogy doesn't work for the bridge because the wind kept a steady speed; it's as if you're continuously pushing the swing, which, obviously, does not create an oscillation.

Even a wind at a steady speed can cause a resonance condition. Perhaps a better analogy would be drawing a bow across a violin string, or blowing across the mouthpiece of a flute. Both are examples of resonance even those the energy input contains a multitude of frequencies.

Re:Perhaps amend the definition of resonance

[wonkey_monkey]

Link?

Zelda?!

Re:Perhaps amend the definition of resonance

[gdshaw]

There's a difference:

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

By that definition you would have to say that Helmholz resonance is not a form of resonance.

As others have said, it all depends on what you define as the forcing function. The wind was applying a periodic force to the bridge due to the varying profile that it presented to the wind. It would not have been periodic in the absence of the bridge, but that's irrelevant because then there would have been no force at all (no area to act on).

Re:Perhaps amend the definition of resonance

[Roger W Moore]

Saying this wasn't resonance because the forcing function was a product of the oscillation in the first place is pedantic.

Actually it is not pedantic the two types of motion are quite dissimilar: aero-elastic flutter generates an exponentially growing amplitude whereas resonance generates a large, but constant, amplitude. Aero-elastic flutter is essentially the inverse of damping whereas resonance requires an external, oscillating force which drives the system.

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.

Re:Perhaps amend the definition of resonance

[thegarbz]

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.

Couldn't it be argued that the force of the wind imparted on the bridge happened at a specific frequency since it only happened when the bridge's movement was in a certain position, and that this force is determined by the natural frequency of the bridge as the swinging was dependent on the innertial characteristics?

It still sounds like a form of resonance to me. The originating force may not be, but the effect on the system does.

Re:Perhaps amend the definition of resonance

[drinkypoo]

You do realize that resonance is a phenomenon caused by two different things vibrating at similar frequencies, right?

Is a tuning fork one thing, or two things because it has two tines? The two tines make the one fork, but without two tines a tuning fork doesn't work. Is a bridge one thing, or two things because it has two ends? The two ends of the bridge make one bridge, but the two ends of the bridge can resonate against one another. Self-resonance is a thing, and it's not just a thing in electronic circuits. The ongoing input of wind energy may have fed the reaction, but another bridge with the same wind wouldn't have broken... Obviously the difference was in the bridge.

Re:Perhaps amend the definition of resonance

[drinkypoo]

aero-elastic flutter generates an exponentially growing amplitude whereas resonance generates a large, but constant, amplitude.

The bridge disintegrated while attempting to reach a constant amplitude.

Re:Perhaps amend the definition of resonance

[pz]

When you actuate a bow across violin strings, the strings oscillate at a given frequency. When you bow faster (the wind blows harder in the case of a bridge) the amplitude gets larger. The wind speed is not the frequency of energy input.

Would you say that the violin string is not in resonance? I think more-or-less anyone would, except some particularly pedantic folk. So why would you say that the bridge was not in resonance? Unlike a violin string which is designed to sustain resonant activity, the bridge failed before its natural oscillatory amplitude was reached given the strength of the driving force.

The folks here that the bridge was not resonating because it wasn't being driven by a single frequency are missing the fact that you get perfectly good resonant activation when the driving force is broadband. The feedback howl from a PA when the microphone is pathologically positioned toward a speaker is not initially driven at one frequency, it is driven by background sounds and thermal noise. The inherent resonance in the system acts as a filter to selectively amplify only one frequency (waveform, actually, so a family of frequencies), which goes to saturation.

The exact same thing happened at Tacoma Narrows, only the bridge failed before saturation was reached. It was oscillating, and you can't get oscillations without resonant behavior.

Re:Perhaps amend the definition of resonance

[msauve]

You do realize that "resonance" doesn't mean what you think it means, right? There are lots of physics sites which disagree with you - "a resonant frequency is a natural frequency of vibration determined by the physical parameters of the vibrating object..."

Re:Perhaps amend the definition of resonance

[Sique]

But one of the most important properties of resonance (that makes it different from similar phenomena) is the fact that it happens only in a small frequency band. Resonance happens if the cause has the same frequency than the effect, and both interfere, and the interference pattern increases the amplitude.

What we had with Galloping Gertie was a positive feedback loop. It would have happened at any swing frequency.

Re:Perhaps amend the definition of resonance

[chihowa]

The analogy doesn't work for the bridge because the wind kept a steady speed; it's as if you're continuously pushing the swing, which, obviously, does not create an oscillation.

The wind kept a steady speed, but the force of the wind felt by the bridge did indeed oscillate as the bridge twisted (the surface area exposed to the wind changed with time). Just like you were standing behind the swing the entire time, but the force felt by the swing changed with time.

The moving wind was the source of the energy imparted on the oscillating bridge system, but the coupling of the wind to the bridge was not constant. Attributing this entirely to anti-dampening would imply that the force felt by the bridge was constant.

Re:Perhaps amend the definition of resonance

[AthanasiusKircher]

You do realize that "resonance" doesn't mean what you think it means, right? There are lots of physics sites which disagree with you - "a resonant frequency is a natural frequency of vibration determined by the physical parameters of the vibrating object..."

Obviously you don't realize that this quotation doesn't mean what you think it means.

"Resonance" is NOT the same as a "resonant frequency." The "resonant frequency" is the natural frequency where a system can experience resonance, but the frequency or the vibration at that frequency is NOT resonance itself.

From the same site you linked, have a look at this graphic, which basically says:

"Resonance involves the existence of natural frequencies which are easy to excite and which a vibrating system picks out from a complex excitation."

Resonance is NOT simply vibrations occurring at a resonant frequency within a system. That's just basic oscillation or vibration or standing waves or whatever. It's not resonance. Resonance is the excitation/driving of vibrations at that frequency by an external force. If the external force isn't selectively driving the oscillation at the resonant frequency in some way, it's not resonance.

If I pluck a guitar string and it sounds at its particular natural frequency ("resonant frequency"), colloquially some people say the string is "resonating." But from a physics standpoint, that's not technically correct -- the string just has standing waves oscillating at a natural mode of vibration. But if I touch a vibrating tuning fork at the same pitch to the guitar string, causing the string to vibrate at the same frequency, THEN I have resonance.

Re:Perhaps amend the definition of resonance

[msauve]

"which a vibrating system picks out from a complex excitation"

Like a wind musical instrument or an organ pipe. Or like a wind which blows across a bridge.

Re:Perhaps amend the definition of resonance

[Impy the Impiuos Imp]

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."

It sounds like what I understood it to be all along, like pushing someone on a swing, a little bit higher each time. I just assumed that was what they meant by resonance. Hell, even the wavike instability between two surfaces rubbing against each otber is a subset of this.

Re:Perhaps amend the definition of resonance

[jimbob6]

When you blow into a flute. The harder you blow the louder it gets. Yes that's resonance. It's just the resonance of the bridge. When you tap on a crystal. The harder you tap the larger the electric wave out at the resonance frequency of the crystal. That's how resonators work unstructured energy IN causes a structured response dependent on the resonant property's of the object being acted on. constructive interference is accepted while destructive is rejected. This article is just semantics.

Re:Perhaps amend the definition of resonance

[phantomfive]

It was oscillating, and you can't get oscillations without resonant behavior.

No, that's not true at all lolol. Objects have natural resonance. You can often see this in a bathroom stall, singing notes up the scale, and one note will be amplified much more than the others. You can often hear it playing an organ, as you play notes down the scale, different items in the room will shake loudly in resonance.

In the case of the bridge, it would be each "gust" of wind hit at just the moment when the bridge was ready to swing in the direction of the bridge (except when I say "gust," I mean vortex shedding, which you can also see when you drop a piece of paper and it falls back and forth. Each time the vortex was ready to push the bridge in a different direction, gravity was ready to push it in that same direction. That would be what is meant by resonance).

In this case, that wasn't the problem: the problem was just a very powerful wind. It had nothing to do with frequency. Seriously, there are an astounding number of people here who don't understand the topic (you included).

As for your example of the violin string, that's an interesting question, I don't know the answer, I'll have to look into that.

Re:Perhaps amend the definition of resonance

[phantomfive]

The frequency of the bridge is the period from one sway to the next. If it were resonance, then the wind would be gusting at the same period as the sways in the bridge. That is not what happened, which is why it wasn't resonance.

Re:Perhaps amend the definition of resonance

[Impy the Impiuos Imp]

This isn't true. When the wind blows fast enough, it will overcome the springback and the bridge will just hang sideways like a windsock.

Re:Perhaps amend the definition of resonance

[phantomfive]

Couldn't it be argued that the force of the wind imparted on the bridge happened at a specific frequency since it only happened when the bridge's movement was in a certain position, and that this force is determined by the natural frequency of the bridge as the swinging was dependent on the innertial characteristics?

If that happened, it would have been resonance (so good job, you're the first person who's replied to me who actually seems to understand resonance). But it had nothing to do with frequency of the force, and was instead just a really strong wind.

Re:Perhaps amend the definition of resonance

[phantomfive]

That would have been really cool to see, but I think the bridge would have collapsed at that point.

Re:Perhaps amend the definition of resonance

[phantomfive]

I don't know who is making that argument, but it had nothing to do with this bridge.

Re:Perhaps amend the definition of resonance

[phantomfive]

The wind was applying a periodic force to the bridge due to the varying profile that it presented to the wind

The periodic force of the wind was not relevant to the reason the bridge fell (although there was a periodic effect that came from vortex shedding, it didn't cause the bridge to fall).

Re:Perhaps amend the definition of resonance

[phantomfive]

The original theory of what happened was that it fell because it was resonant with the vortex shedding of the bridge. The type of resonance you describe (where the wind resistance changes periodically) wasn't what caused the bridge to collapse.

Re:Perhaps amend the definition of resonance

[msauve]

He's too busy laughing out loud, out loud. Perhaps he considers that resonance.

Re:Perhaps amend the definition of resonance

[thegarbz]

But even in the presence of wind didn't the bridge twist at its fundamental frequency? Kind of like a pendulum, or think an upside down flexible pole being swung by a wind, that always happens at a natural frequency determined by the design of the pole regardless of wind speed.

The initial cause may have just been strong wind, but doesn't resonance come into play after that initial cause?

Re:Perhaps amend the definition of resonance

[phantomfive]

I don't think so, it was just fluttering around, and that's what destroyed it.

(Although beforehand, when it was just swaying, it was probably at its natural frequency).

Re:I live near it.

[Etherwalk]

I live near the bridge, and have driven across it a few times.

It is now a large artificial reef in the water. Which it fell into in 1940.

https://en.wikipedia.org/wiki/...

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.

Re:Aeroelastic flutter

[lindseyp]

Here's an older paper:

http://www.ketchum.org/billah/...

The distinction is drawn at the end of part III. Seems to me to be pure semantics. If the bridge were driven to flutter at a self-resonant frequency then yes, it was a resonant phenomenon. Does causing a wine glass to emit a tone by running your finger around the rim constitute a resonant phenomenon? The variation of the driving force being at the resonant frequency is caused by the wine glass vibrating at that frequency already, as was the variation on the torsional forces on the bridge being caused by the bridge already vibrating.

Re:Aeroelastic flutter

[AthanasiusKircher]

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.

The sentence comes from the Wikipedia article on resonance. Read it in context. It's clear that it's referencing an oscillating driving force. The force's period doesn't have to line up exactly, but the closer it is, the more resonance. That's the point of what a "resonant frequency" is -- it's the frequency you can drive a system with an external oscillating force to produce maximum amplitude response.

This is really fundamental to the definition of resonance. If the driving force has a period very different from the natural vibrational mode of the system!, we say there is "less resonance." If the driving force isn't periodic at all, it isn't periodically reinforcing the motion and is thus not "resonating" with the system at all. It's just providing energy to the system, which will tend to adopt certain modes of natural vibration... but in that case the system isn't really "resonating" with anything else.

To put it another way, if you want to calk flutter "resonance," you could just as well call strumming a guitar string in a haphazard way "resonance." Except that's not resonance -- it's just the string vibrating at a natural frequency when energy is introduced.

Re:Aeroelastic flutter

[thegarbz]

Can a bridge vibrate unstably at any frequency other than its resonance frequency?

There's no doubt here there was positive feedback, but I would argue the incoming energy did have a similar frequency to the natural frequency on the object as the force on the bridge depended on the current position of the bridge. I.e. just because the wind was constant doesn't mean the force on the bridge was.

Re:Aeroelastic flutter

[Hognoxious]

The external force needs to DRIVE the motion at a specific frequency.

I never realised I needed to blow on and off 256 times a second to get a middle C. Maybe that's why I can't play the flute.

Re:Aeroelastic flutter

[LeadSongDog]

Resonance requires a driving force with the same frequency as the system that's vibrating

Close. If some part of the driving force is at that same frequency, you still get resonance. Feed enough noise into a hi-Q bandpass filter and you get resonant tone at the centre frequency. Apply positive feedback and the tone gets louder. With loop gain greater than unity it grows until limited either by the available power (saturation and clipping) or by physical damage that changes the system (either shifting its centre frequency, e.g. due to a broken window in the room changing its echo delay, or else reducing the loop gain, e.g. due to a torn speaker cone). This is true whether the system loop is speaker/airpressure/mike/amplifier/repeat or attack angle/normal airpressure/lift/torque/repeat.

Most Misunderstood Failure?

[sunderland56]

I dunno, I bet there are a LOT more people that didn't understand all of the failings of Windows Vista.

Re:Most Misunderstood Failure?

[WillAffleckUW]

You mean Windows 8. They all drove across the I-90 floating bridge that sunk, when it was pressure washed by people who didn't understand that it's the displacement that makes floating bridges float, not the weight of the bridge.

Same lack of foresight. Many of those people are working on Bertha, the Tunnel of Doom, in Seattle.

Re:Most Misunderstood Failure?

[bruce_the_loon]

The Lacey V. Murrow sinking wasn't because of pressure washing without understanding displacement, they knew exactly how much they could flood the pontoons with contaminated water from hydraulic demolition of the bridge sidewalks during an expansion project. They failed to plan for a storm that dumped rain and lake water into the pontoons because they didn't close the watertight doors between demolition shifts.

It was an engineering failure, but not due to lack of understanding about displacement, just an assumption they'd be the only source of water in the pontoons.

Not the most misunderstood

[Jack Griffin]

If by "most misunderstood" we mean misunderstood by the most people, then that title would have to belong to the collapse of the twin towers.
So many people still can't understand how a building could fall straight down, instead of sideways like in the cartoons. Forget resonance or oscillation, how about getting gravity into the public conscious. I guess it is just a theory after all...

Re:Not the most misunderstood

[h33t l4x0r]

Before going there you should ask yourself: Do I really want to go there?

Resonance vs flutter

[JoeyRox]

https://www.quora.com/Whats-th...

refutes "woodpecker" slander, though

[dltaylor]

I suspect we've all heard/read the slander "If houses were built the way software is written, the first woodpecker that come along would destroy civilization.". This example, and the Tay bridge disaster, are demonstrations of how we learned (usually) NOT to build bridges. Software is often as new to this field as those bridges were to Civil Engineering, so there are lessons to be learned.

The real distinction is that most software projects don't take a decade and cost billions (California's government examples, notwithstanding), so the managers of the projects have no incentive to allow us to use proven best practices; instead, they allow "fad of the week" development practices and push for instant results, regardless of the impending maintenance and security disaster they're requesting.

Re: refutes "woodpecker" slander, though

[iamacat]

Software fails catastrophically because one light bulb burning out causes the whole house to disintegrate. Production clusters with redundant servers, network switches and power supplies are a better equivalent of a house built to codes. I hope self driving car control systems follow the later model.

Not a fallacy

[techno-vampire]

In logic, a fallacy is a form of faulty reasoning. This is not a fallacy, it's a mistaken explanation of the causes of the collapse. Not the same thing at all.

WHo did it?

[AndyKron]

So.... Who shot John F. Kennedy?

Re:WHo did it?

[bobbied]

So.... Who shot John F. Kennedy?

Why, John W. Booth did, in the library, with the wrench....

Re:WHo did it?

[Bentbob]

It was J.R., in his sleep, with the musket that was seen earlier in Act 1 hanging up on a wall.

Re:WHo did it?

[dcw3]

It was the butterfly flapping it's wings.

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.

Re:Not resonance, anti-damping

[Anonymous Coward]

I never thought I'd see a resonance cascade, let alone create one...

Re:Not resonance, anti-damping

[Anonymous Coward]

" Resonance is when a periodic force is applied to the system"
Ever see a violin bow or EBow? Ever wonder how they resonate the strings without having to match the resonant frequency? like wind on the bridge..

Re:Not resonance, anti-damping

[Impy the Impiuos Imp]

Lal!

Finally

[Shompol]

After 20 years since studying the subject someone explained it to me. It is a kind of resonance since the wind force was applied in phase, but no one ever bothered with the details.

Re:I live near it.

[bobbied]

I live near the bridge, and have driven across it a few times.

RIIIIGHT...

Let me guess, you want to sell me a bridge too...

Basically

[50000BTU_barbecue]

If I may extrapolate what I know about open-reel tape decks, this sounds like flutter. But in the other axis.

Re:That is a resonance

[Darinbob]

Which is why there you so seldomly run across Professor Anonymous Coward in any physics department.

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.

Re:Rediscovered?

[Harlequin80]

+1 this. When I did my engineering degree in the 90s this was the reason that was put forward for the collapse. Best part about my physics lecturer is he started by saying that this bridge is used by most of the different schools to argue different reasons. If you do aerospace it will be the wind, if you do civils it will be resonance etc etc. The bridge is used as a cool subject for assignments, the teacher chooses what they want the assignment to be about.

Re:I live near it.

[HornWumpus]

Just the salvage rights.

Re:Not resonance?

[HornWumpus]

It is.

But the forcing function was a product of the motion and didn't have it's own freqency. Which makes it flutter.

Now...wait for it...flutter is an example of resonance.

Galloping Gertie was an inside job

[Cito]

Everyone knows Nikola Tesla's Oscillator can't resonate steel beams.

Re:That is a resonance

[thechemic]

Agreed: clearly this is resonance. The bridge was observed oscillating at several different frequencies since it construction. However, it was only when the wind speed reached 42 miles an hour did the bridge oscillate at 1 cycle per 5 seconds. This particular frequency caused the bridge oscillation to gain energy, and the bridge tore itself apart.

"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.

There couldn't be a more perfect example of resonance.

I recall

[kilodelta]

The old Jamestown Bridge in Rhode Island. That thing was a terror to drive over. It was all steel grate. Guess they figured you wouldn't get resonance or stresses from that. But driving over it wasn't fun.

Now it's a big concrete structure. Nothing is moving that.

Re:Not resonance?

[lgw]

What I learned, back in the day, was that resonance was a coupling between the period of the input energy and the natural period of the system. If the input energy is steady or aperiodic, oscillation in the system doesn't automatically make it resonance. Is this not the way most engineers use the term?

Terrible summary

[ishmaelflood]

Seems to be a heap of stuff in the summary that isn't in the article "Each time the deck of the bridge twisted now, it sought to return to its original position (inertial forces)" etc- all of which defies physics on Planet Earth.

As others have pointed out, "Tacoma Narrows wasn't a resonance" has been a bit of a mantra for 20 years or more, obviously things take a while to get to Texas.

Re:Terrible summary

[gweihir]

Well, actually it was resonance, just one fed by wind, not by traffic. My guess is this confusion is because structural engineers think "traffic" when hearing "resonance" and "bridge"? Other disciplines do not have that limitation.

Of course it was a resonance.

[mbone]

Of course it was a resonance - the excitation of a normal mode of a physical structure. That the excitation was due to complicated non-linear aerodynamics doesn't change the obvious fact that a normal mode was being excited.

Re:Of course it was a resonance.

[gweihir]

Rather obvious. Whether it is a bridge or a tuning-fork is pretty immaterial, it is a filter.

As to you climate-change denier morons: The only good thing about you people is that future generations will remember you by your extreme stupidity.

Re:Of course it was a resonance.

[mbone]

Neat fact: the non-linear aerodynamics will always tend to excite a structural mode around its natural frequency.

The fact that it's technically not steady state behavior and thus isn't rightly referred to in the language of linear steady-state analysis ("resonance") just goes to show you how it's the transient phenomena that real engineering is about. Any idiot can come to any comforting conclusion about steady state and average trends, but if you don't rigorously account for the nonlinearities and the transients, you don't have shit. I'm looking at you climate "scientists".

All physical systems (e.g., mechanical structures) are in fact non-linear. The simple fact is, though, that it is useful to analyze the response of a wide variety of systems to outside forcing in terms of the excitation of normal modes, either as an entirely linear system, or one with weak non-linearities (say, a limited amount of mode-mode cross-talk). If modes are excited, it is still appropriate to use the mathematics of resonant excitation, regardless of whether it is steady-state or not. This can be and is done for messy systems like oceans, planets, stars and even galaxies, as well as the more typically linear systems of mechanical and civil engineering.

The mathematical advantage here is that "all linear systems are basically alike, while each non-linear system is non-linear in its own fashion."

Re:Of course it was a resonance.

[mbone]

As to you climate-change denier morons: The only good thing about you people is that future generations will remember you by your extreme stupidity.

I didn't catch that before. Of course, the modeling of climate science is actually mathematically very advanced; the system is never in steady state and even resonant type behavior like the El Nino-Southern Oscillation is not very linear. What the "deniers" don't seem to get is that the science was actually settled almost 30 years ago. The rest of the world has moved on, but we are saddled with a stupidity resonance being excited by a constant stream of money from petroleum interests.

Re:Not resonance?

[jbengt]

What I learned, back in the day, was that resonance was a coupling between the period of the input energy and the natural period of the system.

So, hearing a musical note when you pluck a guitar string doesnt involve resonance, because a single pluck doesn't match any natural period of the string?

Re:Not resonance?

[lgw]

Indeed, but the sound you hear from the other strings, the reason your fingering on the other strings matters, that's resonance, as is the natural amplification of lower notes from the sound box in an acoustic guitar. The string itself: that's simple harmonic oscillation.

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.

News to me

[gweihir]

I learned about this bridge 20 years ago, and it was taught as "oscillations induced by wind". Of course, these need to be at or close to a resonance point, or they just get dampened out.

Seems to be a non-story.

So more like the reed of a saxophone

[Zenin]

So more like the reed of a saxophone, a powerful and steady blow across it will cause it to resonate...sorry, cause it to flutter at its natural frequency.

Compared with a tuning fork. If you have a C tuning fork and hold it near a piano when you play any C, the fork will noticeably vibrate from the tiny force of audio vibrations reaching it. It resonates with the weak, but in tune, audio force.

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.

Can have flutter when system cannot resonate

[Roger W Moore]

The distinction is drawn at the end of part III. Seems to me to be pure semantics. If the bridge were driven to flutter at a self-resonant frequency then yes, it was a resonant phenomenon.

Resonance is a steady state phenomenon so if the amplitude is exponentially growing this is evidence of anti-damping (which is what aero-elastic flutter is) and not resonance. Both mathematically and observably the two phenomenon are different. Furthermore you can have aero-elastic flutter in a system which has enough damping that it cannot resonate (which is the case when the damping ratio is >1/sqrt(2) ).

Wikipedia not right

[Roger W Moore]

Resonance occurs when the external driving forces drives the system such that it produces a maximum amplitude response in the steady state (last part is important). If you are not driving it at this precise frequency (which is actually slightly less than the natural, undamped oscillation frequency due to damping) then you are not at resonance. In physics you do not use terms such as more or less resonance: it's like being pregnant either there is a resonance or there is not and for systems where the damping ratio is >1/sqrt(2) there is no resonance.

You can talk about the width of the resonance and generally the less damping there is the narrower the resonant peak is and the larger the resonant amplitude. If you are off-resonance you would say that you get a lower amplitude response. Aeroelastic flutter is a transitory response which gives an exponentially growing amplitude. Furthermore it can occur in systems which cannot exhibit resonance because of too much damping.

Waste of debate over the term "resonant"

[Anonymous Coward]

The historical footage clearly shows the bridge collapsed because of a torsional vibration in it's center span.
It's a resonant phenomenon, like a multitude of other physical physical phenomenon involving a natural vibrating mode and a driving force.
In this case the driving force was aerodynamic in nature and included strong positive feedback once the torsional vibrations started the day the bridge collapsed.

The only group that might have 'got it wrong' are any physics teachers or others that have been narrowly defining "resonance" only as the behavior of a simple harmonic oscillator passively responding to a sinusoidal forcing function. Such a system can be modelled with fairly simple differential equations that can be handled in a general physics class. It is better termed "passive resonance". When the concept is taught in physics it is helpful to contrast it with microphone feedback or wing flutter, each of which are far more complex and involve active, positive feedback. Once that point is made clear, then the concept of resonance can continue to be used to describe natural vibration modes that can be pushed to the point of destruction in certain situations.

We really don't need to redefine the catastrophic failure of the Tacoma Narrows Bridge as something other than 'resonant'.

Re:Waste of debate over the term "resonant"

[mbone]

Mod this parent up. A nice summary.

Re:I live near it.

[AntronArgaiv]

I live near the bridge, and have driven across it a few times.

RIIIIGHT...

Let me guess, you want to sell me a bridge too...

I walked across the new one at Thanksgiving. My son lives less than a mile from it (there are now two). They rebuilt Gertie, using the original foundations, and there's an air vent down the middle. The new bridge is much wider and has a sidewalk/bike path.

learned this on history channel

[Osgeld]

15 fucking years ago, how much did this twin university "study" cost the taxpayers?

Re:Not resonance?

[PPH]

a single pluck doesn't match any natural period of the string?

What is the Fourier Transform of a step function?

Common engineering knowledge

[bkr1_2k]

I thought this was common knowledge amongst engineers. Hell, I'm an electrical that only took one mechanical class and I heard this in college. My wife (she's a structural engineer) and I even recently had a conversation about it with some other friends.\

More importantly, to a layperson, it's the same thing. Technically not correct to call it "resonance" but they don't care about the differences. Most engineers don't even care.

In my antedeluvian physics courses ...

[BenBoy]

... they'd have called it forced, (under)damped harmonic motion, no? Given that this is slashdot, it may well be called that in the article I couldn't be troubled to read ;-)

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I hate the purveying of pure bullcrap

[sgt_doom]

As a lifelong activist and truth-seeker, I despise the constant purveying of bullshit! The original engineer who designed a decent enough bridge was ordered to submit lower standard building materials by management in order to save money --- he refused and was fired, the next substandard and dishonest engineer complied the rest is history --- END OF STORY, douchetards!