From: dino@euclid.colorado.edu (dino)
Newsgroups: alt.folklore.urban
Subject: The Tacoma Narrows
Date: 28 Mar 1995 01:34:40 GMT
Organization: University of Colorado, Boulder
Lines: 200
Message-ID: <3l7p3g$nf3@lace.Colorado.EDU>
References: <D6032C.p7@murdoch.acc.Virginia.EDU> <95084.163652JSM158@psuvm.psu.edu> <3l7bt6$fri@mozo.cc.purdue.edu>
NNTP-Posting-Host: euclid.colorado.edu

Collapsing bridges seem popular on AFU these days. We have...

branden@hillres22.cc.purdue.edu (Crash) writes:
>Queenie (JSM158@psuvm.psu.edu) wrote:

<snip!>

>: everything has a characteristic frequency at which it vibrates. When
>: sound waves at that frequency are directed at the object, the waves
>: merge with the vibrations of the object, intensifying them until the
>: object is ripped apart - the principle used by singers to shatter

<snip!>

>Yep, that's the 1940 Tacoma Narrows Bridge collapse in Washington state.
>Standard fare for freshman-year mechanics courses at reputable science and
>engineering-oriented colleges and universities.  And your description is
>pretty acuurate regarding the phenomena involved.

---

No it isn't. But I had wanted to knock this one off for a long time, and
you gave me the opportunity, so don't feel like I am flaming you.

The following is abstracted from an article in _The American Journal of
Physics_, 59 (2), February 1991, pp 118 -- 124; the title of the article is:

  Resonance, Tacoma Narrows bridge failure, and undergraduate physics
  textbooks

From the article's abstract (*'s frame things in italics, all pytos mine):

  The Tacoma Narrows bridge disaster of 1940 is still very much in the public
  eye today. Notably, in many undergraduate physics texts the disaster is
  presented as an example of *forced resonance* of a mechanical oscillator,
  with the wind providing an external periodic frequency that matched the 
  natural structural frequency. This oversimplified explanation has existed
  in numerous texts for a long time and continues this day, with even more
  detailed presentations in some new and updated texts. Engineers on the other
  hand, have studied the phenomenon over the past half-century, and their
  current understanding differs fundamentally from the viewpoint expressed
  in most physics texts.  In the present article the engineers viewpoint is
  expressed to the physics community ... substantial disagreement exists.
  ... one misleading identification of forced resonance arises from the
  notion that the periodic natural vortex shedding of wind over the structure
  was the source of the damaging external excitation. It is then demostrated
  that the ultimate failure of the bridge was in fact related to an
  aerodynamically induced condition of *self excitation* or "negative damping"
  in a torsional degree of freedom. The aeroelastic phenomenon involved was
  an *interactive* one in which developed wind forces were strongly linked
  to structural motion. This paper emphasizes ... physically as well as
  mathematically, *forced resonance* and *self-excitation* [my note: no
  masturbation follow-ups, please] are fundamentally different phenomena.
  The article closes with a quantitative assesment of the Tacoma Narrows
  phenomenon that is in full agreement with the documented action of the
  bridge itself in its final moments and a full, dynamically scaled model
  of it studied in the 1950s.
 
(end of abstract)

Some comments from the article: 

  ... Its failure  on November 7, 1940 attracted wide attention at the time
  and has elicited recurring references ever since, notably in undergraduate
  physics textbooks. ... The main issues in this instance are: What was the
  exact nature of the wind-driven occurrences at Tacoma Narrows, and can they
  be considered correctly to be cases of resonance? 

<comments on physics texts deleted>

  These invoke inferences about the Tacoma Narrows episode that differ
  from present engineering understanding of the failure. However, we also
  point out below, areas of at least partial agreement. Our aim is to set the
  record a bit straighter than it now appears to be -- at least as popularly
  understood.

<more comments on physics texts deleted>

  II. TEXTBOOK ACCOUNT

  Typically, *resonance* is first presented qualitatively along these lines:
   
   In general, whenever a system capable of oscillation is acted upon by 
   a periodic series of impulses have frequency equal to one of the natural
   requencies of the system, the system is set into oscillations of 
   relatively large magnitude.

The article further comments on why the TN bridge episode was described as
resonance, commenting on popular accounts in physics textbooks, in which
the central span of the bridge resonated (now assumed) until said resonance
became so great that it collapsed, and how the wind blowing over the surface 
and support cables of the TN bridge generated very large wave disturbances
that destroyed the unfortunate bridge.

The article continues:

  The final, catastrophic event at  Tacoma Narrows did, in fact, fit part of
  the above qualitative defintition of resonance -- as we shall discuss --
  *if* the more penetrating question of where the "periodic series of
  impulses" came from is temporarily set aside, for it was indeed a single
  torsional mode of the bridge that wa driven to destructive amplitude by the
  wind, as will be discussed at a later point.

<comments on physics books and simple differential equations of oscillators
 deleted>

The article further comments that after this is told to physics students,
an explanation follows, to effect, 

    "The wind produced a fluctuating resultant froce in resonance with a
    natural frequency of the structure. This caused a steady increase in
    amplitude until the bridge was destroyed."

The article basically says that this is BS and too simple minded, that
physics texts are vague about "just what the exciting force was" and this
resulted in the necessary periodicity. Texts will say it was due to "gale
winds," or "gusts of wind," et cetera. However, such do not have well-defined
periodicity. Further:
  
  Seeking such periodicity must lead to closer investigation of the
  aerodynamics of bluff bodies ... The so-called *periodic vortex shedding"
  effect is a first, very tempting, candidate to which to attribute the 
  necessary periodicity.

  Bluff bodies (such as bridge decks) in fluid streams do in fact shed
  periodic vortex wakes, tripped off by body shape and viscosity, ...
  which oscillate in consequence. ... Unfortunately, this explanation is
  incorrect. We now know that this is *not* what occurred at Tacoma Narrows.

The article follows with a section on "Vortex-Induced Vibration," which
deals with bluff (non-streamlined) bodies with flow over them and how said
flow doesn't follow the contours of the body, breaking away at some points.
In short, the article discards this as a cause of the TN's collapse, saying:

  It has been now long since demonstarted that from the standpoint of
  phenomenology, even such vortex-induced oscillations do not constitute a
  case of simple resonance. ... Vortex-induced vibration is clearly not a
  linear resonance even if the structure itself has linear properties, since
  the exciting force amplitude *F* is a nonlinear function of the system
  response.

  IV. THE DESTRUCTIVE MECHANISM AT THE TACOMA NARROWS

  ... took place under a wholly different -- and catastrophic -- set of
  circumstances. The wind speed at the time... was 42 mph, and the frequency
  he observed for the final destructive oscillation was 12c/m or 0.2 Hz. At
  42 mph, the natural frequency of vortex shedding ... be close to 1 Hz,
  wholly *out of sync* with the actual... It can be concluded that natural
  vortex shedding was *not* the cause of the collapse. This rules out one type
  of periodic exciting force implied by a few of our references.

(comments on how engineers want to design bridges that won't collapse in the
 wind deleted)

The article further comments on how the destruction was duplicated in a scale
model bridge built by one Scruton. The physics starts to get involved, and
they conclude that the collapse was due to "single-degree-of-freedom torsional
flutter" due to "complex, separated flow." In short, the article does conclude:

  ... 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*, the mathematical distinction between
  Eqs. (1) and (3) is quite clear, self-exciting [my note: again, no follow-ups
  about masturbation] systems differing strongly from ordinary linear
  resonant ones. The texts that we have consulted have not gone this far in
  explanation.

It also comments:

  We note that numerous instructional texts in mathematics [68-76] allude
  to the Tacoma Narrows incident, and most of these, too, could be made
  more precise and insightful in the light of the current analysis of the
  problem.

They even have some borderline UL-related comments in Closing Remarks:

  The Tacoma Narrows incident will remain a celebrated example because of
  its spectacular nature and the freak recording of this disaster by
  witnessing photographers. The sensational photographs have made it into
  an irresistable pedagogical example -- and indeed, much is to be learned
  from it. Because it lodges itself so in the memory, it is doubly important
  for educators to draw correct lessons from this classic and sensational
  event. While it is understandable how so many textbooks have, over the
  years, oversimplified the physics involved, it is probably time -- given
  the advanced state of the knowledge -- to offer the next generation
  of subtler, more complex, and *correct* explanations.

<rest deleted>

OK, I am a math geek, not a physics geek, and glossed over most of the
physics myself. However... we may conclude (and a search of the FAQ and
cathouse revealed nothing):

F. The Tacoma Narrows bridge collapsed due to simple resonance.

T. It wasn't so simple.

dino "will destroy bridges for food" m.

