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One of the most spectacular and famous bridge collapses of all was that of the the Tacoma Narrows Bridge on November 7, 1940. On that day, high, sustained winds sent the bridge into a twisting, rocking motion that led to its eventual collapse. It has been used as a classic example of the phenomenon of mechanical resonance, however, this is incorrect. Ethan Siegel has an article (behind an ad-blocker blocker) explaining how a much more intricate phenomenon known as aeroelastic flutter was responsible.
The collapse of the Tacoma Narrows Bridge on the morning of November 7, 1940, is the most iconic example of a spectacular bridge failure in modern times. As the third largest suspension bridge in the world, behind only the George Washington and Golden Gate bridges, it connected Tacoma to the entire Kitsap Peninsula in Puget Sound, and opened to the public on July 1st, 1940. Just four months later, under the right wind conditions, the bridge was driven at its resonant frequency, causing it to oscillate and twist uncontrollably. After undulating for over an hour, the middle section collapsed, and the bridge was destroyed. It was a testimony to the power of resonance, and has been used as a classic example in physics and engineering classes across the country ever since. Unfortunately, the story is a complete myth.
[...] But as the wind passed over the bridge on November 7th, a stronger, more sustained wind than it had ever experienced before, causing vortices to form as the steady wind passed over the bridge. In small doses, this wouldn't pose much of a problem, [...] Over time, they cause a aerodynamic phenomenon known as "flutter," where the extremities in the direction of the wind get an extra rocking motion to them. This causes the outer portions to move perpendicular to the wind direction, but out-of-phase from the overall up-and-down motion of the bridge. This phenomenon of flutter has been known to be disastrous for aircraft, but it was never seen in a bridge before. At least, not to this extent.
When the flutter effect began, one of the steel suspension cables supporting the bridge snapped, removing the last major obstacle to this fluttering motion. That was when the additional undulations, where the two sides of the bridge rocked back-and-forth in harmony with one another, began in earnest. With the sustained, strong winds, the continued vortices, and no ability to dissipate those forces, the bridge's rocking continued unabated, and even intensified. The last humans on the bridge, the photographers, fled the scene.
But it wasn't resonance that brought the bridge down, but rather the self-induced rocking! Without an ability to dissipate its energy, it just kept twisting back-and-forth, and as the twisting continued, it continued to take damage, just as twisting a solid object back-and-forth will weaken it, eventually leading to it breaking. It didn't take any fancy resonance to bring the bridge down, just a lack of foresight of all the effects that would be at play, cheap construction techniques, and a failure to calculate all the relevant forces.
(Score: 1) by khallow on Friday May 26 2017, @02:07PM (5 children)
In other words, resonance is a predicted variation of the response of the system to external driving by a periodic force. One doesn't actually have to drive the system at this frequency in order for the system to have this property.
(Score: 2) by AthanasiusKircher on Friday May 26 2017, @02:44PM (4 children)
Look, you clearly believe in the "broad" definition of resonance, and now you're trying to twist physics book definitions into saying what you'd like them to say rather than how many physicists actually use the term. Here's a document [aapt.org] with educational materials on the bridge collapse from the American Association of Physics Teachers. Here's what it says (p. 7):
If you'd like a slightly more technical treatment, I'd refer you to this [ohio-state.edu], written by a physics professor. I'd specifically draw your attention to the Appendices, which show the different math involved for the two cases. Or perhaps this paper [washington.edu], which was perhaps the first to strongly argue that basic physics textbooks were wrong.
In fact, that last link basically explains your issue directly (on p. 122):
As I've said repeatedly, the common use of the term "resonance" by many people accords with the way you're using the term. However, if we want to move beyond stupid debating of definitions and understand the distinction being drawn by TFA (and numerous other explanations of the bridge collapse), you simply have to accept that there is more than one definition in use -- and the "strict" definition here is trying to draw attention to a distinct difference in cause.
Come up with your own term for this distinction if you wish -- call it "externally forced resonance" or whatever if it makes you happy. The point isn't the terminology: it's that there actually IS a difference in the physical explanation compared to the "strict" definition of resonance used by many physicists.
(Score: 1) by khallow on Friday May 26 2017, @04:53PM (3 children)
No, it doesn't. I hate to have to tell a grown up professional his job, but that is wrong. First, consider what happens when one applies said periodic application of a small driving force without regard for whether it is synchronized with the resulting motion of the structure. The end result is that the motion of the structure will be synchronized with the input driving force even though no attempt was made to synchronize the two. Out of phase motion is suppressed.
The only way is to deliberately contrive the driving force so that the two are always out of phase enough to suppress the motion from this structural frequency. That didn't happen with the Tacoma bridge (and we know this due to the truism that the bridge experienced these periodic modes of movement even at low wind speed). So the synchronization requirement is a red herring.
Second, notice the terming of the flutter-based forcing on the Tacoma bridge as "relatively small continuously applied source of energy". The wind was continuous, but its effect on the bridge most certainly was not. As a result, that same label applies just as snugly to "periodic application of a small driving force in synchronism with a natural frequency of the structure". There is no consideration of the frequency spread of the input driving force from wind flutter and other effects.
Consider the situation where you have a driving force which consists of many different frequencies, including said small periodic driving force of the natural frequency of the structure. Does the small driving force component not exist because of the other components of the driving force? Of course not. You can still get resonant motion even in the presence of other external driving input.
So our wind input via flutter provides the necessary periodic driving force, in addition to other components that are irrelevant to the definition of resonance, and the dynamics of the system insure that the resulting motion mode of the bridge would be synchronized with the input driving force because out of phase motion would be suppressed. Thus, we have resonance even by the definition of a professional who claims otherwise.
And further, it is an ontological contradiction to introduce external matters into an internal definition. Resonance is an internal property. Introducing the requirement of a particularly rigid form of external forcing (one that is often difficult to come by in the real world as in the Tacoma bridge example!) breaks the definition.
Notice here how the whole argument above about whether the bridge broke up due to resonance has devolved into a mostly irrelevant argument about the characterizing of the forcing from the wind as it was applied to the bridge and a mistaken allegation about the lack of synchronization of the wind input with the motions from the bridge's natural frequencies (if the bridge is moving, it's been synchronized for some period of time prior). That's what happens when you define things incorrectly. Extraneous considerations that are irrelevant to the problem need to be inserted. And when you fail to get these extraneous considerations to work out, due to happenstance or error on your part, then you have an almost defined situation which as we see in this discussion can waste a lot of time.
This is not an isolated situation, but unfortunately a common occurrence in many professions. For example, we see a similar situation with the International Astronomers Union definitions [wikipedia.org] of "planet" and "dwarf planet" (which you have taken the other side [soylentnews.org] on). It works ok for the Solar System, but the Solar System is not the universe. And once you attempt to extend the definition to other star systems, the criteria of "clearing a neighborhood" is ridiculously hard to confirm. There are currently observed objects (from light occultation observations of really distant star systems) that IMHO probably will remain suspected planets longer than Neptune has been a planet (171 years).
Another example is microaggressions [wikipedia.org]. From Wikipedia (highlighting a definition):
Here, the extraneous matter of the first definition are "marginalized group". If I'm casually degrading anyone because of what group I perceive them as belonging to, then by definition I am marginalizing that group (degrading speech being a common marginalizing activity after all). At that point, you're just speaking of routine casual bigotry with actual group identity being quite irrelevant to the definition.
But insertion of that term is convenient for people who want to microaggress. Just define the group you're microaggressing against as a non-marginalized group and presto, approved bigotry. Here, the problem is not that we're going to spend fruitless hours arguing over whether something is a microaggression, but rather the definition is used for selective bigotry against marginalized groups which can be conveniently redefined as non-marginalized groups.
So going back to the original discussion of resonance. No, I will not accept a definition of internal behavior of a system that devolves into pedantic and irrelevant argument about the characteristics of the external inputs. The definition as presented is broken for engineering purposes.
(Score: 1) by khallow on Friday May 26 2017, @05:02PM
(Score: 2) by AthanasiusKircher on Friday May 26 2017, @05:37PM (1 child)
Whatever, man. You can continue to get all hot and bothered because some people (apparently a lot of people who consider themselves professional physicists) use a different definition of resonance than you. Or you can just adopt the laissez-faire attitude I've been trying to espouse: different people use this term differently. I'm more interested in the physical phenomenon than restricting terms to only one's preferred definition.
What's real is the fact that actual structural engineers need to model these two phenomena differently. The mathematical models necessary to deal with them are different. Yes, both depend on natural frequencies of the systems in question, but otherwise they have significant differences in behavior and occur under different conditions. I really don't care what we call them.
And by the way, regarding Pluto, I still don't care what people call it. If that's a "side," I guess I'm on it. You seem to be the one getting really annoyed because some people aren't using terms the way you'd like them to.
(Score: 1) by khallow on Friday May 26 2017, @06:07PM
Let's recall what the title of this thread is. As you claimed earlier on, the whole "IT WASN'T REALLY RESONANCE, YOU KNOW!!" thing is based on differing definitions (and I already made my stand on what I think "THE" [soylentnews.org] definition should be). At that point, there's zero science content. We just have different labels for the same thing, though I can't help but notice who has to keep making pedantic distinctions about what "isn't" resonance (not my problem apparently). Then when such advocates actively ignore (twice - Ethan Siegel's article and the link I commented on earlier) how the Tacoma bridge event matches even their definition as I noted earlier (both small periodic forcing and synchronization were present counter to claim), the whole thing slides into farce and negative science content. We're dumber for having these arguments when proponents, arguing on the basis of definition, can't be bothered to determine beforehand whether the situation even violates their definition.