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posted by Fnord666 on Thursday May 25 2017, @09:34PM   Printer-friendly
from the tacoma-bridge-is-falling-down,-falling-down dept.

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.


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  • (Score: 2) by TGV on Friday May 26 2017, @06:12AM (13 children)

    by TGV (2838) on Friday May 26 2017, @06:12AM (#515856)

    I don't know if the definition requires a driving force with the same frequency. In physics of sound, one speaks of resonance of strings and hollow bodies, where the driver is a sharp impulse or a steady stream of noise.

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  • (Score: 2) by AthanasiusKircher on Friday May 26 2017, @06:19AM (12 children)

    by AthanasiusKircher (5291) on Friday May 26 2017, @06:19AM (#515859) Journal

    Read the Wikipedia article linked in the summary. As I said, people use different definitions in different contexts, which is what this entire discussion is being caused by. The people who are saying "this isn't resonance" are using the definition I tried to explain in my post. The Wikipedia article on the Tacoma bridge collapse also contains a detailed discussion of resonance vs. non-resonance explanations that use this definition. I do not dispute that others sometimes use the word to mean something else.

    • (Score: 2) by TGV on Friday May 26 2017, @07:13AM (10 children)

      by TGV (2838) on Friday May 26 2017, @07:13AM (#515872)

      I don't think the article says that. And Wikipedia is not an authoritative source for physics definitions: it's meant to make the topic understandable for laymen. You may be right that there are multiple definitions circulating.

      • (Score: 2) by AthanasiusKircher on Friday May 26 2017, @12:57PM (9 children)

        by AthanasiusKircher (5291) on Friday May 26 2017, @12:57PM (#515938) Journal

        Yes, obviously Wikipedia isn't an "authoritative source for physics definitions." I merely referenced it because it was already in the summary. But that doesn't mean it's wrong either -- it depends on the sources actually used by Wikipedia articles. I would have hoped that you'd just take a moment and look at those, rather than dismissing it.

        Okay, so let's go for "authoritative sources": I just pulled a couple college physics textbooks off my bookshelf. Paul Tipler in Physics for Scientists and Engineers says: "If the driving frequency is approximately equal to the natural frequency of the system, the system will oscillate with a very large amplitude. ... This phenomenon is called resonance." Young and Freedman in University Physics say "The fact that there is an amplitude peak at driving frequencies close to the natural frequency of the system is called resonance." (Note that I taught intro physics in the past, which is why I have multiple physics textbooks on my bookshelf.)

        I could go on, though even Merriam-Webster is clear about the definition [merriam-webster.com]: 1.b(1): "a vibration of large amplitude in a mechanical or electrical system caused by a relatively small periodic stimulus of the same or nearly the same period as the natural vibration period of the system."

        Anyhow, you don't have to accept this as the ONLY valid definition. My personal experience is that in many fields people apply the word "resonance" much more loosely. I think it comes from a sort of slippage where natural frequencies ARE still "resonant frequencies," even if they aren't driven by resonance in a particular instance. So people start applying the word to any vibration at those "resonant frequencies." That's my guess about the current broader usage, though I don't know that for certain.

        But my point is that this "myth debunking" regarding the Tacoma bridge occurs periodically (no pun intended) mainly because misunderstandings about the strict vs. loose usage of the term resonance. The reason I think physicists in particular are sensitive about this issue is because the Tacoma bridge was cited frequently in a number of intro physics textbooks years ago as an example of the STRICT resonance definition (based on the theory of wind speed producing vortices that matched the natural frequency of the bridge), and thus some people who were taught that in a physics class (generally along with the specific math describing such forced vibrations at a natural frequency grossly increasing amplitude) react strongly when they find out it was a "myth."

        • (Score: 1) by khallow on Friday May 26 2017, @02:07PM (5 children)

          by khallow (3766) Subscriber Badge on Friday May 26 2017, @02:07PM (#515961) Journal

          "If the driving frequency is approximately equal to the natural frequency of the system, the system will oscillate with a very large amplitude. ... This phenomenon is called resonance."

          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)

            by AthanasiusKircher (5291) on Friday May 26 2017, @02:44PM (#515973) Journal

            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):

            As described in the 1991 paper by Billah and Scanlan, the motion of the bridge was an example of “an aerodynamically induced condition of self-excitation or negative damping in a torsional degree of freedom.” It was not a case of resonance.... True, there are some features similar to resonance: a large periodic motion at one of the natural frequencies of oscillation of the structure, maintained by a relatively small continuously applied source of energy. But true resonance requires the periodic application of a small driving force in synchronism with a natural frequency of the structure. The wind had no such frequency....

            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):

            Could this be a resonant phenomenon? It would appear not to contradict the qualitative definition of resonance quoted earlier [from some physics textbooks], if we now identify the source of the periodic impulses as self-induced, the wind supplying the power, and the motion supplying the power-tapping mechanism. If one wishes to argue, however, that it was a case of externally forced linear resonance [as many physics textbooks had done, and the only form of "resonance" actually discussed in most physics textbooks], the mathematical distinction... is quite clear, self-excited systems differing strongly enough from ordinary linear resonant ones.

            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)

              by khallow (3766) Subscriber Badge on Friday May 26 2017, @04:53PM (#516024) Journal

              True, there are some features similar to resonance: a large periodic motion at one of the natural frequencies of oscillation of the structure, maintained by a relatively small continuously applied source of energy. But true resonance requires the periodic application of a small driving force in synchronism with a natural frequency of the structure.

              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):

              A microaggression is the casual degradation of any marginalized group. The term was coined by psychiatrist and Harvard University professor Chester M. Pierce in 1970 to describe insults and dismissals he regularly witnessed non-black Americans inflict on African Americans. Eventually, the term came to encompass the casual degradation of any socially marginalized group, such as the poor or the disabled. Psychologist Derald Wing Sue defines microaggressions as "brief, everyday exchanges that send denigrating messages to certain individuals because of their group membership".

              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

                by khallow (3766) Subscriber Badge on Friday May 26 2017, @05:02PM (#516029) Journal
                If you have substantial oscillation at a structure's natural frequency (which is the internal characteristic/behavior I refer to in my parent post), something of the appropriate frequency is driving it. That is the only observation you need to make to confirm resonance though the driver of the resonance can be poorly understood (as aerodynamic flutter was at the time), or noisy and poorly synchronized.
              • (Score: 2) by AthanasiusKircher on Friday May 26 2017, @05:37PM (1 child)

                by AthanasiusKircher (5291) on Friday May 26 2017, @05:37PM (#516042) Journal

                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

                  by khallow (3766) Subscriber Badge on Friday May 26 2017, @06:07PM (#516055) Journal

                  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.

                  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.

        • (Score: 2) by TGV on Friday May 26 2017, @02:36PM (2 children)

          by TGV (2838) on Friday May 26 2017, @02:36PM (#515969)

          > If the driving frequency is approximately equal to the natural frequency of the system, the system will oscillate with a very large amplitude

          But that doesn't imply that the frequencies have to be the same. A square wave would contain many more frequencies and still provoke the same phenomenon. A noise source too.

          I think resonance is something that's hard to define in language. You can constrain it, but natural language isn't precise enough, and everyone builds their own concept of it, probably leading to the confusion. I would personally go with "where response peaks".

          • (Score: 2) by AthanasiusKircher on Friday May 26 2017, @02:52PM (1 child)

            by AthanasiusKircher (5291) on Friday May 26 2017, @02:52PM (#515975) Journal

            But that doesn't imply that the frequencies have to be the same. A square wave would contain many more frequencies and still provoke the same phenomenon. A noise source too.

            Actually, no they wouldn't, if you're applying the definitions here strictly. The point of "strict" resonance (according to the definitions I quoted) is the disproportionate affect on amplitude with even a small driving force, which is a direct result of the specific frequency matching (or at least relatively close frequency matching). If you instead drive the system with noise, the system may still oscillate at its natural frequency, but the amplitude magnification effect seen at resonance will not occur. Instead, you'll have a lot of "wasted" energy. Kind of like if you pushed someone on a swing sort of randomly rather than in sync with the natural period of the swing: yes, the swing might still get "going" somewhat, but it won't have the additive resonant effect.

            Again, use a different term if you want. Add qualifiers to the word "resonance" if it makes you happy. What I'm trying to explain is why this story keeps coming up (people talking past each other with different definitions), as well as the fact that there IS an actual quantitative difference to the phenomenon of flutter (see my other recent post for links).

            • (Score: 1) by khallow on Friday May 26 2017, @05:11PM

              by khallow (3766) Subscriber Badge on Friday May 26 2017, @05:11PM (#516034) Journal

              If you instead drive the system with noise, the system may still oscillate at its natural frequency, but the amplitude magnification effect seen at resonance will not occur.

              Actually, it will for short periods of time. That can be enough for a system that is really sensitive to its natural frequency to cause problems. And most noise is not white noise so it is possible for strong resonance to appear in a noisy system - the noise more or less cancels out while a hidden "periodic application of a small driving force in synchronism with a natural frequency of the structure" dominates the resulting behavior of the system.

    • (Score: 0) by Anonymous Coward on Friday May 26 2017, @12:16PM

      by Anonymous Coward on Friday May 26 2017, @12:16PM (#515927)

      Read Von Karman's report if you really want the background (link earlier in this thread). This wasn't the first suspension bridge that galloped.

      Aeroelasticity was just beginning to be understood in aircraft structures at that time, it was too "advanced" for mere civil engineers designing bridges to have studied in school. Even today, it is multi-disciplinary, so may not be taught well in university where the different disciplines often are kept separate?

      https://en.wikipedia.org/wiki/Aeroelasticity [wikipedia.org]

      Aeroelasticity is the branch of physics and engineering that studies the interactions between the inertial, elastic, and aerodynamic forces that occur when an elastic body is exposed to a fluid flow. Although historical studies have been focused on aeronautical applications, recent research has found applications in fields such as energy harvesting [1] and understanding snoring.[2] The study of aeroelasticity may be broadly classified into two fields: static aeroelasticity, which deals with the static or steady response of an elastic body to a fluid flow; and dynamic aeroelasticity, which deals with the body’s dynamic (typically vibrational) response. Aeroelasticity draws on the study of fluid mechanics, solid mechanics, structural dynamics and dynamical systems.