Re: Midterm Question - Sort of

[Leigh Palmer <palmer@SFU.CA>]

> Now just a doggone minute, Leigh. I've been quite happy with my understanding
> of this bridge collapse, viz, a resonance condition caused by the frequency of
> vortex flipping. From Goodstein's explanation in Mechanical Universe, the
> vortices of the wind around the cables flips forth and back at a rate which is
> proportional to the DC wind speed. As that rate grows nearer to the bridge's
> natural frequency, the vibration amplitude increases until ... kaboom.
>
> Is this hogwash? Is not aeolian excitation caused by this very effect?
>
> poj
> Collin County College

Well, that's a bit like saying that the steady bowing of a violin
string is an example of resonance. There are certainly *normal modes
of oscillation* for the bridge (and the violin string), and these
modes can be excited by an external source of energy in a nonresonant
interaction. Resonance I take to refer to the excitation of a normal
mode by an *applied* periodic forcing function, clearly not the case
encountered here. The applied forcing function is, more or less, DC.

If resonance is not taken to mean what I say above then the word
becomes less meaningful; it applies to almost any periodic phenomenon.
See, for eaxmple, French, "Vibrations and Waves", Chapter 4. He has a
nice example of resonance from the Talmud, by the way:

  "In the case of a cock putting its head into an empty utensil
   of glass where it crowed so that the utensil thereby broke,
   the whole cost shall be payable."

I'm surprised that in this group there is not another ex radio ham.
Resonance is what one tunes an antenna system for when driving it
from a transmitter.

It was not the cables of the bridge that shed vortices at the bridge
normal mode oscillation frequency, but rather the bridge deck itself.
That is, indeed, the mechanism responsible for aeolian oscillation.
I believe the bridge actually flexed in more than one of its normal
modes. I won't check that just now, but maybe someone else can help
me. I seem to have no allies in this discussion. Have I slaughtered
a sacred cow?

Leigh

(An aside: My father is a civil engineer. He and Mervin Schuhart
designed the first four-level highway interchange in the world, "The
Stack", in LA. I too worked for the California Division of Highways
as an Engineering Aid summers while I was an undergraduate. I got
the second highest mark on the Junior Civil Engineer examination in
my last year there, beaten only by one fellow who received extra
points because he was a veteran. I'm not naive; I am thin-skinned.)