Resonance vs Flutter: Explaining the Tacoma Narrows Bridge Collapse

[DaveC426913]

[Moderator's Note: This discussion was split off from another thread: https://www.physicsforums.com/threads/expunging-myths-from-the-classrooom.849853/]

The point of the article is that I and almost all other students of engineering or science were taught that the Tacoma Bridge (known as Galloping Gertie) collapse was due to resonance. However, the peer reviewed science many years ago showed that this explanation is dead wrong. Read the article yourself. It's very clear and the language is simple, even if engineering is not your field.

Well, engineering is not my field, so as a layman, I'm having trouble reading the nuanced difference between resonance and flutter. The Tacoma Narrows Bridge is definitely part of my growing up, so I'd love to post about it, but I've got nothing to report.

I grant that, to an aerodynamics expert, there's a distinction, but is there one to a layperson such as myself?

 

[Astronuc]

Well, engineering is not my field, so as a layman, I'm having trouble reading the nuanced difference between resonance and flutter.

Well, the author of the article, Alex Pasternack, cited in the initial post is apparently a writer, and not an engineer or scientist (what are his credentials? Is he a PE, or PhD in physics or structural engineering?). He does cite some articles published by engineers or physicists.

When the article refers to 'resonance', or rather the claim that it wasn't resonance, since the excitation frequency did match the fundamental frequency, then my question would be, "which fundamental frequency?". It perhaps didn't match the frequency of the fundamental mode, but that is only one frequency. There are harmonics, but then there are more complex interactions that have different modes. One of the cited papers refers to a SHM model, which would be inappropriate.

The problem of the buffeting/flutter of a bridge is highly non-linear, especially when the stiffness of the structure (stiffness) changes, and therefore the 'natural frequencies' change. Fluid-structure interaction is somewhat to extraordinarily complicated. In some cases, one sees hydraulic dampening, while in other cases, there is excitation.

For introductory courses, it's perhaps sufficient to cover basic SHM.

On the cited page of WSDOT, one finds the comment:

"Meanwhile, Professor F. B. Farquharson continued wind tunnel tests. He concluded that the "cumulative effected of undampened rhythmic forces" had produced "intense resonant oscillation." In other words, the bridge's lightness, combined with an accumulation of wind pressure on the 8-foot solid plate girder and deck, caused the bridge to fail." See - "Blind Spot"-- Design Lessons of Gertie's Failure

I'm still reading through the various cited papers, but it's not clear to me that a 'myth' is being propagated.

In any event, while schools/universities provide for one's education, they are not responsible for the competence of a person. The states reserve the right to license an individual through a licensing process. That process does include some verification of education and experience (practice under the guidance of qualified/licensed engineers) and some testing of one's proficiency.

The best part of the WSDOT page is the discussion of Torsional Flutter, which is way beyond an introductory physics/engineering level. "The primary explanation of Galloping Gertie's failure is described as "torsional flutter." It will help to break this complicated series of events into several stages."

 

[jim hardy]

I'm still reading through the various cited papers, but it's not clear to me that a 'myth' is being propagated.

thanks .

I'm simple.

A system with transfer function G
wrapped with feedback function H
has transfer function G/(1+GH)

G is complex and may have its own resonant frequency
H may have its own as well
when GH = -1 denominator is zero , so system gain may well become infinite at a new frequency, the resonant frequency of the closed loop system, different from that of either G or H ..

is that resonance?

Something changed in the bridge's torsional system transfer function . Maybe the torsional response G , maybe feedback H ; either way it found its new resonant frequency.

old jim

 

[Astronuc]

https://en.wikipedia.org/wiki/Nonlinear_resonance - "In nonlinear resonance the system behaviour – resonance frequencies and modes – depends on the amplitude of the oscillations, while for linear systems this is independent of amplitude."

The WSDOT site mentions "On the morning of November 7, 1940 shortly after 10 a.m., a critical event occurred. The cable band at mid-span on the north cable slipped. This allowed the cable to separate into two unequal segments. That contributed to the change from vertical (up-and-down) to torsional (twisting) movement of the bridge deck." - http://www.wsdot.wa.gov/TNBhistory/Machine/machine3.htm#6

and later - "It was critical that the two types of instability, vortex shedding and torsional flutter, both occurred at relatively low wind speeds. Usually, vortex shedding occurs at relatively low wind speeds, like 25 to 35 mph, and torsional flutter at high wind speeds, like 100 mph. Because of Gertie's design, and relatively weak resistance to torsional forces, from the vortex shedding instability the bridge went right into "torsional flutter." "

Of course, a bridge (truss, suspension, box, or cable-stayed), is not designed for large displacements. Draw or lift bridges can have large displacement of moving members, but not within the structural members.

 

[anorlunda]

is that resonance?

Yes it is Jim, but talking about "forced excitation resonance failures" is a more narrow context.

If you strike a bell it will ring at its resonant frequency, as long as the linear and/or nonlinear effects of the strike supply nonzero energy at that frequency.

But suppose that the external forcing function has lots of energy at the resonant peak. The simplest vivid example is when a champagne glass shatters when a singer hits just the right note, but broad spectrum loud noise will not shatter the glass. Both the bell and the glass follow the same resonance math. The failure comes when we have the coincidence of an object with a resonance peak frequency and external stimulus with significant energy at or near that same frequency. (e.g. the glass' resonant frequency and the singer hitting almost exactly that frequency)

That is why this footbridge in London oscillated with pedestrian footstep excitation, but not when pushed by other signals like wind. It was very interesting because the bridge swings induced the pedestrians to modify their pace to be in-step with the swings. Both the bridge and the pedestrians hit resonance peaks.


Remember the Mythbusters episode "Breakstep Bridge?" They attempted to demonstrate exactly what we are talking about. They failed to break the bridge because they couldn't match the resonance peak frequency close enough. If they had modified the bridge design to have a strong resonance peak around 1 Hz, they may have done better..



Explaining the Tacoma Narrows Bridge failure as due to resonance, is to liken the failure to shattering of the champagne glass. In contrast, the fluttering of a flag in the wind is a different phenomena and it is not associated by a resonance peak in the flag's fabric. Watch closely and you should see that flag flutter frequency does not seem to be closely correlated with flag size or shape.

 

[DaveC426913]

Explaining the Tacoma Narrows Bridge failure as due to resonance, is to liken the failure to shattering of the champagne glass. In contrast, the fluttering of a flag in the wind is a different phenomena and it is not associated by a resonance peak in the flag's fabric. Watch closely and you should see that flag flutter frequency does not seem to be closely correlated with flag size or shape.

Yes. This is exactly what I was getting at. Flutter is comparable to a flag in the wind. But surely the energy comes from the wind itself. The flag is merely passive.

In the case of TNB, that's suggesting (to me) that the wind must have been hurricane force to literally push the bridge around - which is of course not the case. Surely the fact that the bridge itself started flopping - to an extent not proportional to wind speed - is an indication of resonance.

Point of order: technically this is off-topic, since the OP is about educational inertia. I could start a new thread if participants prefer. Or this could be split off, starting with my first post above.

 

[anorlunda]

I could start a new thread if participants prefer.

That might be better. Education aside, the engineering problems explaining TNB are difficult and interesting.

I started a thread in 2013 about fluttering. From that, I learned some interesting physics.
https://www.physicsforums.com/threads/tatterproof-flag-design-needed.686921/

 

[Drakkith]

Point of order: technically this is off-topic, since the OP is about educational inertia. I could start a new thread if participants prefer. Or this could be split off, starting with my first post above.

I've split several posts off from the main thread into this one.

 

[anorlunda]

Thanks for splitting this thread.

As I look at the TNB oscillations below, then I look at flutters propagating in a flag, I can't help but to imagine similarities. (How's that for a non-scientific statement )

[EDIT: The TNB picture below is sped up. Not real time. The actual oscillations had periods of 12-19 seconds.]



Both the flag and the bridge have nonlinear constraints that greatly complicate comparisons. The corners of the flag closest to the flagpole are not free to move much. The flag is in the vertical plane,so that gravity tends to make it collapse diagonally. The bridge deck seems to be anchored to the vertical piers, note that very little of the bride oscillation is transmitted past the piers. Also the tortional oscillations interact with the suspension cables.

If we are looking for clarity and a simple explanation, I think we will fail. What resonances exist? What originates the oscillations? What pumps energy into the oscillations as they propagate? I suspect mixed nonlinear answers to all those questions.

If the main question is resonance versus flutter, then:

In fact, resonance is a similar phenomenon to flutter, to the extent that it involves the "reinforcement" of existing oscillations and can lead to a dramatic and possibly destructive amplification of energy.

I just reread the section of The Strangest, Most Spectacular Bridge Collapse (And How We Got It Wrong) entitled, When resonance attacks (and doesn't). Pasternak does a pretty good job of discussing exactly the question of resonance versus flutter. I think that the strongest evidence against the resonance cause is that none of the resonance peaks of the structure lie close to the observed oscillations in the frequency domain.

 

[OCR]

Pasternak does a pretty good job of discussing exactly the question of resonance versus flutter.

Great link!...

Other sources seem to agree... the cause was aeroelastic fluttering...