Re: Tacoma Narrows resonator followup

[Leigh Palmer <palmer@SFU.CA>]

>  >>4. What mechanism started and supported  the oscillations of that bridge?
> > The bridge deck, initially more or less having the wind velocity
> > in-plane, got a little bit out of plane and the wind reinforced
> > this distortion. A vortex was shed, allowing the distortion to
> > relax and, it turns out, overshoot its equilibrium position, at
> > which time the opposite polarity distortion is driven to
> > increase by the wind until another vortex is shed, the deck
> > relaxes past equilibrium, usw. When the wind was gentler, this
> > oscillation did not grow in amplitude to bridge failure, which
> > gave the bridge its nickname of "Galloping Gertie".
>
> This also makes great sense to me that the entire bridge deck is acting as
> an aeolian harp. These vortex pushes strike me as giving pulses that match
> the natural frequency of the bridge deck. As I rad my H&R, my prime
> source, this is resonance. Why is it not?

First, let me say that it is nice to have a dialog with another
teacher, especially Ken Fox. Teaching is a frustrating business,
especially for those of us who feel at the end of the semester,
while marking exams, that we have somehow failed. I gave my last
exam (possibly the last of my career) yesterday.

The vortex shedding is not driving the motion. The frequency of
vortex shedding is determined by the frequency of the torsional
oscillation of the bridge; it is not inherent in the wind. If
bridge were not oscillating the frequency would be different.
This is not the phenomenon usually referred to as (von Karmann)
vortex shedding. That phenomenon refers to the vortices downwind
of a static object, stereotypically an infinite cylinder
oriented transversely to the wind direction. In my picture of
this phenomenon the vortices themselves are not exerting a
driving force. They are the turbulent response to the sudden
release of stagnation pressure at the edge of the deck near the
point of maximum amplitude of torsion. It is the stopping of the
moving air mass, stagnation, that is doing the work necessary to
twist the bridge deck. In the von Karmann case the oscillation
frequency is entirely due to the parameters of the fluid flow
and the cross-sectional geometry of the obstruction. In the
bridge case the frequency of vortex shedding is exactly the same
as the frequency of oscillation of the bridge, and that
frequency is dependent upon amplitude in this nonlinear case.
The oscillating bridge is driving the vortex shedding.

Leigh