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

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

[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: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.

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: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.