Tacoma Narrows Bridge Collapse
Date: Winter 2011-2012
Did aeroelastic flutter or natural resonance destroy the Tacoma Narrows Bridge in Washington State?
The wind coming around the cables broke off creating eddies. When
they hit a harmonic, it sings like an aeolian harp. This set up a
resonance in the bridge.
---Nathan A. Unterman
I think the two are usually mixed together.
The aerodynamics provides positive feedback,
a displacement-encouraging component of force, a "pumping force".
Mechanical elasticity is usually what turns the motion around
and makes it go back and forth through zero displacement, the "restoring force".
It is conceivable to have pure aerodynamic flutter,
for aerodynamics to provide most of the restoring force,
namely alternating vortices determined purely by time and air-flow conditions.
But there is often some mechanical participation causing reversals,
such as twisting of a wing-like shape with it's own torsional elasticity and inertia,
or the vertical velocity of a wire influencing the reversal of the vortex shedding.
Simple natural resonance is very dominant in a big strong thing like that bridge.
I think the restoring force was almost all mechanical elasticity,
and the pumping force was from aerodynamic lift changes
resulting from that twisting you've seen in the motion picture.
Are you aware of the two phases of sine-wave oscillating situations?
Sine and cosine of time.
"Inertia" and "elasticity" provide forces proportional to the sine of time.
They make stable coasting oscillations that go on forever, neither growing bigger nor smaller.
"Loss" and "pumping" provide forces 90 degrees out of phase, proportional to the cosine of time.
These forces are usually smaller than the inertia and elasticity,
but they incrementally change the amount of energy in the oscillation,
make the oscillation gradually grow bigger of smaller.
Loss is the elastic losses and squeakiness in the metal bridge, and other similar drags and frictions,
which is why the bridge usually settles down after it's bumped, instead of jiggling endlessly.
Pumping was the aerodynamic push, which happened to get stronger than the loss,
and made the oscillation grow instead of shrink until that bridge broke.
Or made the oscillation simply continue at large amplitude
until the bridge weakened due to metal fatigue and broke.
All that would be my assumption.
But if you can extract a displacement-vs-time curve from the video,
and show it has some large deviations from a nice clean sine-wave,
maybe you could make the case that the aerodynamic component was a large part of
the in-phase or restoring forces.
Things that strange have happened in freak weather, I suppose.
And that would tip the balance towards "aeroelastic flutter".
Or you could do estimates, comparing the weight of half the width of the bridge
with the maximum lift that could occur at the wind velocity over the upwind edge of the bridge.
Regardless which you believe, having more designed-in mechanical lossiness
would have made that bridge more difficult to destroy.
So it's always fair to say the bridge was too resonant, as built.
It is also likely that more torsional stiffness and/or more aerodynamic baffling treatments
would have reduced the aerodynamic pumping forces.
What you are debating is whether there was more mass and momentum
in the fast swirl of air of a typical vortex behind the bridge
than in its slowly twisting solid mass.
Which may be of technical interest, but not a major controversy.
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Update: June 2012