If you look deep enough into old films of the Tacoma Narrows bridge, it would oscillate in pure bending modes at lower wind speeds. The ultimate failure occurred during exceptionally high storm winds, and did involve torsional modes as well.
I just travelled with a canoe on top of my car yesterday. Right when I started I noticed a loud flutter coming from the flat strap I used to strap it on the rack. After a little thought at the rest stop about killing the excitation I rolled the fluttering section into a circular profile with duck tape and that stopped it really effectively. I'm not sure if I reduced the the excitation or the torsional response by doing this but it worked.
Is that why when I see loads strapped to a flat bed trailer there always seems to be a half twist in the strap between the top of the load and the trailer?
davidbeach - I suppose it is - It's similar to the rotating spiral you see on fixed diameter metal chimneys - the idea is that there isn't a fixed diameter and hence not a fixed frequency.
Having a quick look it seems that yes it reduces flutter, especially when in a free air situation, but can fall foul of the DOT, if they interpret "twisted straps" a bit too far.
One half twist is OK, more than that and you reduce the tension strength.
Remember - More details = better answers
Also: If you get a response it's polite to respond to it.
The wind was 36 kph, which is nothing in the grand scheme, and the temporary barriers were an obvious point of issue. Having said that, it would be interesting to learn how the towers behaved as part of the oscillating system.
SparWeb,
I wonder if the rungs were at some critical spacing such that there was a reinforcing effect as air traveled down the ladder. I could easily see that being catastrophic at the right (i.e. wrong) speed.
(But what do I know; I bailed on the fluid mechanics option after taking one look at the Navier-Stokes equation... )
"Everyone is entitled to their own opinions, but they are not entitled to their own facts."
Once we had a substitute in either calc 3 or diffeq, it was the department chair. He was a great story teller, I heard he was a magician outside of his work at the community college. I think he had set up a system that could resonate or something like e^(bt)*sin t or something, and then he was like 'look at us here, all guys today. What do guys do together? They tell stories, and I've got one for ya. Well I was in the back yard, by the pool and I had just turned a fan on cause it was hot, and the fan was blowing JUST SO and these little waves started to form in the pool from the breeze, getting bigger and bigger, bit by bit. Then I went inside to answer a phone call and I made some iced tea and I came out and the waves were HUGE, the water was splashing out of the pool it was crazy! So what did I do? I turned the fan off and it all settled down.'
That was it. He left us to scratch our heads later and figure out why it was a fib (no damping in the system).
Vibration wise the Humen Bridge could be in pitching mode with one end dips while the other end rises. It could come from one of the six rigid body motions or the lowest natural frequencies (vertical, lateral, logitudinal, rocking, pitching and yawing. I say this because section between the two towers has a monolithic steel box girder structure supported by flexible vertical hangers. The two end approach spans are structurally seaparate as they are supported by short RC beams on columns (no vertcal hangers with the main cables). In a way the centre section is a simply supported beam on closely spaced spring supports. Had the system been relatively rigid the first mode should be the same shape as the deflection under its self weight. However if the structural system is relatively flexible the first natural frequencies would be the deck's free body movements.
The Engineer has since discovered couple of badly corroded hangers and one of them had totally severed. It is possible the spring supports were locally weakened when the vibration was observed.
To some including myself the vibration was set off by vortex shedding from the across wind effect. For slender structure the across wind effect is always more critical than the inline wind effect. I personally got involved with two steel chimenys that vibrated under modest wind. One actually had 40% of the base cleanly severed by fatque. I would say every steel chimney around 100m or about will have across wind vibration problem requiring mitigating measures like welding helical strakes at the upper one-third.
Tacoma Bridge was initially torsional along the longitudinal axis.
An excellent example of vortex shedding induced vibration is enclosed below.
That's a wild video Saikee119. I used to get light posts at the bus stop oscillating by pumping them in time. In a couple parking lots i've seen light posts connected to eachother by plastic line, I assume to damp vibration.
moon161,
Yep a vibrating pole can be damped down by using cable stays.
The other method is to use dampers. Some tall buildings use such technique to upset the vibration pattern making it difficult to sustain. We have in London the Millennium footbridge initially setting out excitations by the foot traffic. It was subsequently cured by dampers.
Normally for a robust structure a static design is all that is needed. For a slender structure, like a long suspension bridge, a dynamic analysis is often required. Structures subject to vibratory or repeated impact loads like machine foundations the design codes are invariably extended to cover the structure performance during dynamic conditions.
Saikee,
Thanks for the video.
On a number of occasions, at a local Costco parking lot, I have notice the light poles vibrating. I find it most interesting when they oscillate in the second mode, not the first. The lamp heads are moving a bit but the midpoint has much more amplitude and opposite in phase. This happens at wind speed about 30kph.
Thanks for letting us know. I have seen a few slender poles vibrating in first mode but your case is the first one in second mode. I suppose if the base and the top sections were strengthened leaving the middle section less stiff relatively then the second mode could be excited under certain wind speeds.
AFAIK if the environmental condition is favourable to sustain the mode shape the excitation doesn't have to be the first mode. Higher modes have more complicated mode shapes and are more difficult to sustain that is all.
If we idealise a cantileveer with one element (two nodes with bottom node fixed) we get one mode shape and one natural frequency. The same cantilever idealised with two elements gives us 1st and 2nd modes plus two natural frequencies. However if we idealise it with 1000 elements we get 1000 theoretical mode shapes and natural frequencies. The fundamental mode and frequency will not change materially in all cases. However the number of natural frequencies can be as many as we model it mathematically.
"I suppose if the base and the top sections were strengthened leaving the middle section less stiff relatively then the second mode could be excited under certain wind speeds."
I suggest you do some calculations. Sitffening the tip of a cantliever has very little effect on the low order modes.
Cheers
Greg Locock
New here? Try reading these, they might help FAQ731-376
Stiffening the structure is not always the answer. While excitation method is different, machinery vibration is essentially the same problem Spring - Mass - Damper system. Changing any of the variables can help. I have found setting a sandbag on top of vibrating machinery often damps the vibration to the point where it is no longer a problem. It is a good way to buy time while finding a better solution.
Some steel stacks use a tuned damper pendulum near the top
"AFAIK if the environmental condition is favourable to sustain the mode shape the excitation doesn't have to be the first mode. Higher modes have more complicated mode shapes and are more difficult to sustain that is all."
Vibration of cylinders subject to vortex shedding can be excited whenever the frequency of the vortices being shed coincides with a natural frequency of the cylinder. This most commonly occurs in the first sway mode, but higher modes can be excited if the conditions are right.
In the case of slender light masts, the first sway mode frequency may be low enough that the wind speed at which excitation is induced is low and you don't see much excitation in practice. Second-mode excitation can be developed at a higher wind speed, and you can see the lights swaying to the left while the middle third of the mast sways to the right. (I have only seen this on very slender masts.) In most practical circumstances, the wind speeds required to generate second- and higher-mode excitation tend to be gusty rather than steady, and the higher mode vibrations damp out quickly - the conditions have to be "just right" to maintain higher-mode excitation.
