Questing regarding the use of TMD dampers

[ThomasH]

Hi all

I have a project that involves the dynamic design of a slender beam. The structure is a pedestrian bridge and the span is ~ 90 m. In the figures below I have limited the geometry to the walkway.

The issue is that the vertical acceleration for the first mode shape has been to high for a while. Now there has been changes so the second mode shape is also in trouble.
I have assumed a damping of 1 % (of critical) and the idea was to use a TMD damper if the vibrations proved to be to high for the walkway. The vibrations will be measured after the bridge is completed. One option was originally, for practical reasons, to use two dampers at the same position (Position 1).That would be optimal for the performance of the TMD. Now since Mode 2 may also need some reduction my idea is to move one of the dampers towards position 2. The hope is that it will reduce the acceleration level for mode 2. I basically need to reduce the vibration level for mode 1 to half the original and mode 2 to 70 % of the original. I don't think I need optimal performance from the TMD. Just "good enough"

I have worked with dynamics on and of for years and occasionally had TMD'sd as possible solutions. But this situation is now for me. I will of course discuss it with the person that designs the TMD but for now, am I completely off here? Does anybody have experience from TMD's?

Best regards

Thomas

 

[centondollar]

Tuned mass dampers at the ends of the bridge will not prevent it from vibrating. The word "tuned" in "Tuned mass damper" is there for a reason: if you use any significant amount of damping (dedicated hydraulic pistons), the vibration will only be reduced (even at resonance), and the amplification compared to the static case will remain greater than or equal to approximately 4. This is not wanted to a bridge. TMD:s are more suited for balancing machinery (e.g., rotors) or tall buildings with one fundamental mode that dominates all others.

My suggestion is to increase the stiffness of the structure to increase the natural frequency, moving it far away from any regular excitation (e.g., pedestrian walking motion frequency) expected on the bridge, and to not rely on mechanical devices. If the structure is a plate girder, increase web depth and reduce flange thickness and maybe add some stiffeners. If it is a box section, add stiffeners to increase bending stiffness. If it is a truss, you should not be having this issue.

PS. Damping is notoriously difficult to model (in FEA software or otherwise) and apply accurately in practice.

 

[rb1957]

how did they fix that bridge in London (recently) ? the one that had a vibration problem from people walking over it.

another day in paradise, or is paradise one day closer ?

 

[271828]

I don't see any reason two TMDs couldn't be used. One at midspan and one at the maximum mode shape value for the second mode. They would be tuned to much different frequencies.

However, before getting into that...

The second modal frequency should be about 4x the fundamental frequency. Your mode 1 and 2 frequencies are pretty close together. What's up with that?

 

[ThomasH]

Hi and thanks for yor replies

Maybe my figures was unclear but Position 1 is at the midspan of the bridge. So if Mode 1 was the only issue Position 1 would be ideal. Unfortunatly Mode 2 has now become a problem as well. And Mode 2 does not move at midspan. That's the reason for moving one damper towards the 1/3 location.

Mode 2 became a problem when I included the piling in the model. What you see in the figures is the walkway in a cable stayed bridge. I wanted to keep the figures simple.

Let me put the question differently. For a TMD to be optimal it should have a mass x % of the modal mass. If the mass for the TMD is reduced to x/2 % of modal, how much does that "cost" in effeciency? It is a hypothetical question to give me an indication of how we can move forward in this.

 

[MotorCity]

I would add mass or stiffen the structure. I have not heard of TMD's being used on bridges. They are typically used in buildings to reduce the horizontal sway when the building acts like a giant cantilever. In your case, the "sway" is vertical, and not a cantilever. How would you propose attaching a TMD to a bridge, and where along the bridge to mitigate both modes?

 

[ThomasH]

Hi

I have seen examples where TMD's have been used on bridges to solve this specific type of issue. Even if it isn't common it is not new either.

The original concept was one (or two) devices at midspan but since I now have two difficult modes perhaps one device at midspan and another closer to the 1/3 point. I probably don't need optimal conditions, just good enough. But I am unsure regarding how much this modification will reduce the efficiency.

Thomas

 

[271828]

Your ideas and questions are valid, IMO.

I recommend contacting a TMD specialist such as Gerb. I've worked with them on a few projects. They could review this very quickly to get you going in the right direction.

 

[ThomasH]

@271828

Thank you for your reply.

I will contact a TMD specialist. They are actually already involved and I will talk to them soon. I just wanted a simple "sanity check" first .

Thank you.

Thomas

 

[FE_struct1]

@ThomasH

I assume this discussion is focusing on pedestrian comfort under walking/jogging alone ? If yes, then it's worth nothing that a TMD requires the structure to move before becoming really active. This will mean the structure will still achieve some accelerations under footfall before they get damped out by the TMDs, which may not satisfy the comfort criterion you're aiming for. Your damper specialist should be able to provide more info on this.

If accelerations are excessive at the point of proper 'damper activation', I'd recommend adding mass to your bridge deck as that is the quickest and easiest way to reduce accelerations (more mass inertia). Be aware though that if you do this, you'll reduce your natural frequency and so will need to be careful of not putting your bridge in a zone where the local wind gust frequencies end up close to your natural frequencies (see this link for an extreme case of what can go wrong: [URL unfurl="true"]https://engineering.jhu.edu/fsag/research/aeroelastic-flutter/[/url])

 

[blihpandgeorge]

TMD's in pedestrian bridges are very common, so this is a normal reply. I see no reason why having 2 locations is a problem either. Best to talk to a TMD supplier such as GERB. Without knowing much about the bridge construction, 1% seems high for critical damping of a pure structural element with little finishes / bolt on bits.

 

[centondollar]

If you do choose to use two or more TMD:s, remember that they are heavy. The more mass you add, the wider the range of the damper. A very small mass will have an extremely narrow range of adequate and optimal damping. A mass equal to 5, 10 or 20% of the primary mass (in this case the mass of the girder, the movement of which is to be damped) is not uncommon, and it may cause you issues with stability (LTB from longitudinal moments and torsion due to transverse offset of the TMD comes to mind), deflection or even strength.

 

[ThomasH]

Hi

The purpose for the discussion is pedestrian comfort, correct.

I think I have the feedback I was looking for. So thanks a lot for your time and interest .

Thomas

 

[GregLocock]

I agree with 271828, the second mode shape should have a much higher frequency relative to the first one shown, if it is basically a uniform beam with pinned ends, which it almost certainly isn't.

Equations 4 and 5 here

https://www.engineeringtoolbox.com/structures-vibration-frequency-d_1989.html

Again your estimate for damping could be a long way out, Tom Irvine measured 0.16% on a beam like pedestrian bridge

https://vibrationdata.wordpress.com/2016/07/28/huntsville-university-drive-bridge-vibration/

A TMD at location 2 will still be somewhat effective on mode 1, assuming it is tuned to both frequencies (not unheard of, for example the harmonic damper on an engine is tuned for two frequencies), but in effect you have two TMDs so just use one at each antinode.

An alternative to a TMD is an untuned damper, such as sand in a box, or long pipes with fluid in them sloshing about. These have the obvious advantage that they can deal with a broad range of frequencies.

Cheers

Greg Locock


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