Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: Tacoma Narrows resonator followup



At 09:33 12/8/00 -0800, Leigh wrote:
>>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 read my H&R, my prime
source, this is resonance. Why is it not?

/snip/

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.

/snip/

Leigh

I expect it will be helpful to sketch the competing theories
in silhouette:
1] Turbulent pulses at about 0.2 Hz excite a torsional mode
of the roadway of the center span - which resonates destructively.

/problem: the moderate turbulence in the 42 mph airflow was
aperiodic/

2] Karmann vortex streets excite a torsional mode of the roadway
of the center span - which resonates destructively.

/problem: the vortex shedding frequency of that structure at that
windspeed was 1 Hz, not the observed 0.2Hz/

3] Aeroelastic lifting was not computed for this Depression Era
design so the light girder roadbed galloped in moderate winds during
the 2 year construction period.
On the fateful day, a few months after completion with periodic
lifting shedding vortices at <1 Hz, a center span cable clamp shifted
reducing further the torsional stiffness and providing a non linear
oscillator shedding vortices at 0.2 Hz.

/problem: this view is shared in broad detail by structural and civil
engineers but is unfamiliar to many physics teachers and text book
writers./