Re: Tacoma Narrows Bridge Resonance?

[Ron Ebert <ebert@CITRUS.UCR.EDU>]

At 11:42 AM 7/7/99 -0500, Paul O. Johnson wrote:
> Leigh Palmer wrote:
>
> > It always bothers me when the Tacoma Narrows Bridge collapse is cited as an
> > example of resonance. It's not. The wind was steady, more or less, and
there
> > was no significant component at the bridge's resonant frequency. It is a
case
> > of nearly pure DC excitation.
> >
> > It's a great film, but it's an example of aeolian excitation, like
blowing on
> > a taut piece of grass between your thumbs. I have many good
demonstrations of
> > resonance. Using the Tacoma Narrows Bridge as an "example" can only obscure
> > the concept in the mind of a student.
>
> 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?

There is an article in the June 2, 1990 issue of Science News (page 334)
disputing the simple resonance explanation. Simple resonance can be
described by linear differential equations, but this is not applicable to
structures like the Tacoma Narrows bridge. They have to be described by
more complicated non-linear differential equations. Factors that make
bridges prone to large scale oscillations have to be isolated. Bridges can
respond to a whole range of forcing frequencies. The roadbed, the stays
that connect the main cables, the main cables themselves and the towers can
all respond to forces acting on them in complex ways.


Ron Ebert
UCR Physics Department
ron.ebert@ucr.edu
http://phyld.ucr.edu