Tuned Mass Vibration Damper for Poles

[Dinosaur]

I work at a DOT and we have thousands of poles supporting lights and signs. When I was in Grad School, we talked about using tuned mass vibration dampers to reduce vibration forces on structures. Our aluminum poles come with a device that sounds as if it may be one of these devices. However, our steel poles do not. I do not know why this is so.

I would like to do my homework first, and then propose that we install tuned mass vibration dampers on some of our larger steel structures to reduce the amount of loading on these structures due to wind. So far my research indicates we can resonably expect to reduct the base moments by 33-40% with this technology. It is extremely simple, until you have to do the math. Eigenvectors send a chill down my spine, but with the help of a well documented example, I could likely handle a two or three DOF model.

Is there anyone among you that can steer me in the right direction so I may master the mathmatics of this problem? Thanks in advance for any help you may be able to provide.

 

[Denial]

I recently had my first encounter with tuned mass dampers. It was for a bridge. The reference that I found the most useful was "Vibration Problems in Structures — Practical Guidelines", by Hugo Bachmann, Walter Ammann, et 13 als. Published by Birkhäuser Verlag, in 1995 I think. Its Appendix D is excellent. Note however that the emphasis is most definitely practical, and the book will not give you much mathematical theory.

The standard idealisation for TMDs is as a two-degree-of-freedom problem. The mathematics is quite tricky, but no more so than for any other 2-dof problem. Once I had designed my system on the basis of the above book, I checked the result by done a full FE analysis on the structure (using an FE program that offered damper elements). It checked out fine. Even more important, the actual bridge when built also checked out fine.

 

[GregLocock]

I'm a bit surprised. Tuned absorbers don't work at DC, so the static moment due to wind loading would not be affected.

So, I'd talk to your test people to find what data they have on the fatigue life of the poles, before getting too enthusiastic, and also see if they have any accelerometer data for the vibration at the top of the poles.

I can't see why it would be worse than a 2DOF problem, and with a bit of malarkey we can just pretend that the pole is a cantilever in bending.

So I would work out, or measure the modal mass at the top of the pole, and then set up a 2 dof spring mass damper model to estimate the reduction in amplitude. You can do that in Excel. So far as I am aware there is no analytical solution to a discrete SMD on the tip of a distributed cantilever beam.





Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[rob768]

Tuned dampers work at the natural frequency of a system. You'll need to add a mass and a spring with a natural frequency corresponding to that of the structure you want to detune. The effect is that you will have 2 natural frequencies, and higher and one lower than the orignal one. if this works with wind loads, I don't know.

 

[GregLocock]

Sorry, no. If the excitation is at a non natural frequency you can tune the TMD to that.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[rob768]

Agreed, this method works only at resonance conditions, snice it detunes natural frequencies.

 

[electricpete]

Den Hartog pages 93-102 discusses a damped dynamic absorber (under the assumption the pole could be treated as an undamped SDOF mass spring system).

From some of the figures given, it looks like you can get pretty dramatic reduction in peak amplitude at any frequency, even if the mass ratio (auxiliary mass over main mass) is small.

For a given mass ratio, in the optimum tuning, he adjust the natural frequency ratio f of damping system to main system to get equal heights of the two sidebands. Then he adjusts the damping to determine the value of damping which minimizes the magnitude of those two sidebands. At least that's what it looks like to me.

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[electricpete]

To back up a little
My assumption (right or wrong?) is that the excitation should be viewed as broadband or random from flow turbulence. Perhaps one could attempt to predict vortex shedding frequencies, but those would change with wind velocity, direction, and maybe profile. So it seems the design objective would not be to shift the resonant frequency, but to reduce the magnitude of the highest resonant peaks within the credible region of excitation. I think the damped dynamic vibration absorber is capable of that.

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[electricpete]

As I-10 goes through Lake Charles, Louisiana there is a bridge where the lightpoles have these strange gadgets that look like a rod with masses on each end supported at the middle of the rod.

Here is a photo:

http://home.houston.rr.com/electricpete/eng-tips/PICT1117.JPG

I tried to take a picture but the quality is understandably bad (I was driving at the time).
I heard second-hand that these are some kind of vibration device and I’m curious if that’s what they are.

Is this similar to the ones you have seen on aluminum poles Dinosaur?

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[MikeHalloran]

The excitation is random, but you only want to suppress (or more correctly offset) the part of it that happens to be at the structure's natural frequency. You don't care about excitation at other frequencies, because they won't bother the structure.

When a TMD is excited at the design frequency, the damper buzzes, but the protected structure hardly moves.

The 'rod' between the masses is often made of wire rope, which provides a little internal damping of its own, and I think spreads out the response a bit.




Mike Halloran
Pembroke Pines, FL, USA

 

[electricpete]

In the case of broadband excitation, you do care about the "sideband" peaks on each side of the original resonant frequency which would be created by the undamped dynamic absorber... that's why I think the damped dynamic aborber would be needed.

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[Dinosaur]

electricpete,

Yes, the mass dampers you have there in your photo are similar to those used on aluminum poles.

Several folks have correctly indicated that tuned mass dampers (TMDs) are used to reduce the response as the structure approaches the first natural frequency. This is important to our highway structures because they will sway in the wind at their first natural frequency even though the excitation is a random forcing function. Also, truck gusts will cause many to vibrate as well.

A properly tuned TMD will reduce the maximum response over 30% from the peak of the unmodified structures first mode. However, there are other things besides finding the original strusture's first mode that need to be considered. Also, I will need to be able to document the new response spectrum to a magnitude of about 1.5-2 x first freq in order to show some of our folks this is a positive thing.

Thanks for the help. Keep it coming. Dinosaur

 

[MikeHalloran]

Dinosaur, you have to go farther than documenting a reduced response with TMDs. You have to show that continued operation without TMDs is likely to break something. I.e. ...

Absent failure or foreboding incident not mentioned so far here, you have to prove that the problem you are proposing to spend resources to solve, actually is a problem.

It's entirely possible for a steel structure, even a large one, to flex noticeably over its entire service life, before it fails from fatigue. The odds are not so good for aluminum, hence (speculation on my part) the TMDs on/in the aluminum poles.

You may also have to prove that it's _your_ (or your outfit's) problem. I.e., if other parties engineered the structures in question, you need to review the contracts in before reviewing the design documents.

But you knew all that.

Since even just reviewing the contracts involves a lot of effort, you probably need to set up a crude 2DOF model as suggested, and evaluate it for deflection, _and_ for fatigue, with and without TMDs.



Mike Halloran
Pembroke Pines, FL, USA

 

[Dinosaur]

Mike,

You pretty much hit the highlights of proposing a change. As for the problem, well there definately is a problem. One of our structures fell due to a complete non-ductile mode failure at the pole base. This particular structure came down between the Cab and the Trailer of a truck traveling on the interstate. Think how amazing that is! We have had a few other non-ductile failures and these are occuring just above the base plate circumferential weld.

Now I say non-ductile failure mode, but what do I mean? Well these are steel structures of a grade between 36-50 ksi material. A material in this range should demonstrate a significant yielding where the maximim stress occurs before fracture. There is no such evidence of yielding, just a fairly straight grainy crack. This leads me to believe fatigue is a major contributer; however, I suspect there is a large residual stress built in due to the fabrication tolerances.

If I can reduce the free vibration deflection by 30%, there will be a substantial increase, possibly close to double, of the fatigue life, and more if we happen to drop below the CAFL. Regarding the premise that my organization needs to "Own" the problem ... well we are the DOT. Generally our customers want us to own problems like this. It is a legal matter whether we truly own it though; although, the structures are ours and the roadway below is also.

Does anyone else bear a greater responsibility such as the engineer? In this case I don't think so. If it can be shown the structures were designed to meet the code in effect when they were delivered, then I don't think the engineer will be considered negligent. The design code went through a substantial revision in the 90s I believe and I am unsure they have captured the essence of the vibration problem to this point. They included an entire new section with fatigue levels that need to be addressed but there still appears to be problems within the structural community about interpreting this.

For the cost of less than 5 new structures, I believe we could retrofit every cantilever sign support in our state, reducing the fatigue stress levels for free vibration by 30% and maybe more. It will take me years of paperwork to back that up because this is not a subject covered by my position responsibilities and I therefore have no resources to dedicate to pursuing. But I will continue to look for information to help me make the case. If I'm really lucky, the true problem will become known and fixed long before I'm ready to make my case.

 

[JJPellin]

I probably should not be replying to this thread since this is outside of my area of expertise. But I might be able to jog some worthwhile comments from those who are experts. We deal with resonant vibration problems in our plant all the time. These problems can be solved in a number of ways. You can strengthen the structure such that it can take the stresses imposed on it and not fail from fatigue. But this tends to be expensive. You can try to control the response, with something like the tuned mass vibration damper that you describe. Or, you can try and reduce or eliminate the forcing function. We have a lot of heater stacks in the plant that are very tall and slender. To keep them from falling down, we do one of the following: We strengthen some of them by making the walls thick enough to withstand the loads. On others, we install guy wires for the same reason. But on most of them, we reduce the forcing function by installing spiral ribs on the OD of the stack to break up the vortices that generate the greatest forcing function. The loads on these stacks do not tend to be greatest from the pure force of the oncoming wind. The forces that will knock down a stack tend to be greatest in a direction perpendicular to the wind direction. The force comes from alternate vortex shedding on each side of the structure. Over the range of possible wind speeds and ambient temperatures, there will almost always be a condition that will produce alternating vortices that will come close to the resonant frequency of the stack. By installing spiral ribs on the outside, we produce stable vortices at regular intervals along the length of the stack. That is why the antenna on your new car has a spiral wire wrapped around it underneath the outer coating. Otherwise, at some driving speed, the antenna would whip back and forth violently when the wind excited the natural frequency. Could you do something similar to break up the forcing function? Or, do you believe that vortex shedding is not related to the problem?

Johnny Pellin

 

[GregLocock]

JP brings up an excellent point.

Back to TMDs, in this case you'd tune the damper to the problematical mode of the pole, and you probably need damping in the coupler, to pull energy out of the system. The problem is that the optimal damping is not very heavy tyically, certainly anything over 30% of critical seems to be too much for metal structures. If you use too much damping the TMD never really gets going, so it doesn't pull enough energy into the damper. I've rarely had much luck calculating these things, but in retrospect a phase angle of less than 10 degrees is too little, and 25-30 is typical, and 45 can be OK but is often too much.

Another alternative is to use an undamped tuned absorber, and just split the mode. I don't this will work in this case - in fact it would give you twice as many modes to worry about... but if vortex shedding is the problem then it could detune the problem away from the vortex frequency.


Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[MikeHalloran]

Now that you mention it, there have been recent changes here in Florida that might be of concern to ... someone, not me.

After Hurricane Wilma, there was a shortage of traffic signals. Wilma took them down and shredded them, and it took most of a year to catch up.

The 'old way' to suspend traffic signals above an intersection was with a cat's cradle of wires between four concrete poles. Wilma knocked the signal boxes off, but left the poles and the wires mostly intact.

The 'new way', now appearing, is two tapered tubular columns each supporting two very long tapered tubular beams at right angles to each other, with signals for four to six lanes attached to each beam. They have an interesting vibration mode that's excited at some wind speeds, with the column bending around an axis that's diagonal to the intersection, and the signals at the tip of each arm going up and down over a range of a couple of feet at about half a Hertz.

They sure look zoomy, and I guess they'll survive a hurricane, but I wonder how long they'll survive normal service. The poles flex quite a lot, and I swear you can see the column bend too.



Mike Halloran
Pembroke Pines, FL, USA

 

[Dinosaur]

Mike,

This is exactly what I am talking about. The design code has not captured this phenomena properly, in my opinion, and I am worried we will continue to get fatigue failures until we recognize this problem. The fact that these structures have no redundancy makes this a severe safety problem. However, in the civil engineering community, most folks act as if this sort of talk about vibrations is making this into a space shuttle design problem. Dynamic load, such as wind, in civil engineering has been handled by determining a safe magnified static load that will produce a structure stronger than the dynamic effect. It works in many cases, but I don't know if we could find a safe static load for the wind effects in this case because the problem is so dependent on the geometry of the problem.

Now picture that same cantilever signal support with a vibration absorber on the tip. Properly proportioned, the deflection of the pole should be reduced by approximately 30% and the pole will vibrate at a frequency near but not quite matching the original frequency. There would be a corresponding reduction in the maximum bending stress at the pole base, and that could be enough to save the pole.

This is my hypothesis and I am looking for some assistence in pursueing the mathmatics to show the potential benefit.

 

[electricpete]

Den Hartog damped model seems like a pretty good starting point to me (not that I have a lot of knowledge in this area).

It seems like estimating the damping in your original structure and in your damper will be the most challenging part of the calculation.

Where did you come up with the 30% number?

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[Dinosaur]

I have been doing some internet searches and found some stuff going on at other DOTs. One report shows a response spectra where the two new peaks were driven down as much as 44% and they said 30% should be achievable in non-labratory situations. However, another report discounted the use of TMDs as too complicated to adjust for every sort of structure that need them. This is my major point of disagreement because I believe a field adjustable device is practical.

Unfortunately, my DOT is not on-board with the problem statement and has some ways to go to catch up with the work going on at these other DOTs.

As for estimating the damping, I agree that would be a major challenge; however, I plan to circumvent the whole thing by simply measuring the response and back calculating the damping. There are any number of signal supports withing a half hours drive from the office I could study in the field but right now nobody sees any need to do that because they don't agree vibration can cause a failure.