Tuned Mass Dampers 1

[abusementpark]

I am looking to get some fundamental information on tuned mass dampers. Can anyone recommend a good article/reference as a good introduction? I just want to get a good grasp of how they are typically used and what the general process is.

 

[rob768]

I don't have any articles or references to articles, but we have used it a couple of times with good result.
The idea is to use a mass-spring system with a mass of about 10% of the active mass of the object you want to dampen. Steel springs are best, as you don't want damping in your damper. Furthermore, the effect is based on the 90 degrees phase lag you see during resonance. It only works when resonance is the source of your problems, and you need to have the damper to have the same natural frequency as the construction you want to dampen.
The idea: at resonance you get a reaction force/movement with a phase lag of 90 degrees to the original force (the force you want to dampen). So the force exciting you damper (which is the vibration you want to damp) occurs 90 degrees later, but causes resonance in your damper. The reaction force from that also lags 90 degrees, but to the excitating force of the damper, and thus 180 degrees to the original exciting force of the construction. So, the construction is excited in one directio by whatever it is that excites it, but also experience a reaction force from the damper that is excactly opposite of the orinal force. Hance the damping effect.
This should be described in good books such as Den Hartog, but I hope this helps you on the way.

 

[271828]

TMD design comes in two flavors: the easy SDOF way and "others."

First start off with the thesis by a young lady named Cheryl Rottmann at Virginia Tech, circa 1996. It has the best examples I've ever seen for how to actually design a TMD using simplified SDOF methods.

For deeper stuff, look for papers by Setareh and Hanson.

One thing to be aware of: The success of a TMD is HIGHLY dependent on tuning to the structure's modal properties. They can work very well if you have a structure with isolated modes. If you have 5 modes in a 1 Hz bandwidth, which is somewhat typical for floors, you might have trouble. In buildings, they also have a way of becoming "un-tuned" when the occupant changes the mass and therefore shifting a natural frequency.

 

[VibeAC]

I partially agree with 271828. The actual mass, stiffness and damping of the structure is critical when designing the TMD. The amount of mass and its distribution in the building can change over time depending on occupants.

To properly design a TMD, you really should really have the measured frequency response function (FRF) for the structure. From there you can use parameter estimation techniques to determine the modal mass, modal stiffness and inherent damping of the structure.

For lateral building modes I would agree that many modes can occur within a narrow frequency range; however vertical ("trampoline") modes of floors are typically spaced far apart.

I have some papers on this topic, but do not have them at my fingertips now. Let me know if you would like them.

Andrew Gorton, MSc
Noise & Vibration Consultant

http://www.PapadimosGroup.com

 

[271828]

"however vertical ("trampoline") modes of floors are typically spaced far apart."

Andrew, I respectfully disagree but am interested in your viewpoint on this matter.

I've personally done experimental modal analyses of two building floors. I also know of one dissertation in which the author did EMA on two building floors (Barrett 2006, Va. Tech) and a journal paper (Pavic & colleagues 2007) that included EMA of a composite floor.

One of my floors had 5 modes in a 1.5 Hz bandwidth and the other had 3 in a 0.5 Hz bandwidth. The other references had even closer spaced modes than that IIRC.

However, I am always interested in more info, so if you have other references, I'd love to run 'em down.

 

[271828]

I just remembered a couple of other studies also. One of them had a 4 bay lab specimen arranged like a hotel wing--4 square bays with a corridor. It had 4 modes in 0.5 Hz. When partitions were added, it had 4 modes in 0.1 Hz--they were not even visible without very detailed post-processing of the FRFs.

I've seen one lab footbridge that was 3 spans. It had three modes in about 0.7 Hz.

That's all I have, LOL.

I think this makes perfect sense. Say I have a 3 span footbridge for simplicity's sake.

Mode 1 has Bay 1 up, Bay 2, down, and Bay 3 up.

Mode 2 has Bay 1 up, Bay 2 almost flat, and Bay 3 down.

Mode 3 has all three bays up with the middle bay up more.

All three modes are very similar frequency. THis is what the classical solution would predict and what I've actually seen measured.

Building floors do the same thing except there are bays up and down in a checkerboard-like pattern, so there are even more modes.

 

[VibeAC]

I think you are correct if you are talking about global modes for an entire floor plate; I was speaking to local modes within a single bay.

I'm wondering though if these global modes will truly participate in the response once "sees" within a single bay (i.e. a driving point response).

It seems like you definitely have spent some time looking at these things. Alex Pavic and his colleagues are a great resource; I met them all last year at the IMAC conference.

I'm pretty much focused in the area of floor and building vibrations currently, and always welcome healthy discussion. Please give me a call sometime. You can find my info on the Papadimos Group website.

Regards,
Andrew

Andrew Gorton, MSc
Noise & Vibration Consultant

http://www.PapadimosGroup.com

 

[271828]

Andrew,

Within a given floor bay, there sometimes is only one very responsive mode, as defined by decent driving point FRF magnitude, but sometimes there can be several. For the floors I've tested and read about, the isolated mode usually happens in very simple structures, like single span footbridges.

The most extreme case had two modes literally right on top of each other, off by maybe 0.1 Hz. They looked like one mode with very slightly higher damping than normal in the FRF magnitude. The only way to separate them that I knew of was to look at the imaginary part of the FRF which can either have a min or a max at a natural frequency. One DOF had a min and a max in the same plot. Now THAT was cool, LOL.

I saw a really cool one a while back. It had a very responsive mode at 6 Hz +/- and 8 Hz +/- and little in between. Walking at 2 Hz excited both of them, so it looked like the walker was stepping on teh floor every third AND every fourth oscillation, which is obviously bogus.

It illustrated how the individual harmonics of the walking force really exist and are causing the response rather than individual steps hitting every 3rd or 4th oscillation.

 

[VibeAC]

Yes the walking harmonics are really there and do contribute to the actual response.

There are more advanced methods parameter estimation techniques for estimating the poles of the FRF function, but looking at the imaginary plot is a good start.

Andrew Gorton, MSc
Noise & Vibration Consultant

http://www.PapadimosGroup.com

 

[Denial]

As a good, practical, introductory reference, try "Vibration Problems in Structures", edited by Hugo Bachmann, published by Birkhauser-Verlag in 1997. Its Appendix D is excellent.

 

[hokie66]

Although interesting, I think the discussion of floor vibrations is a bit off the original topic. Tuned mass dampers are normally thought off as large masses hung in the top of high rise buildings to assist in controlling lateral movements. Am I correct or not?

 

[Denial]

Controlling lateral movements of high-rise buildings is one use. Another, the one I am more familiar with, is to control the vibration of slender, flexible, long-span bridges.

 

[rob768]

to hokie66: there are more applications for tuned mass dampers than just buildings.

 

[hokie66]

Fair enough, but because of the forum this is in and because I am familiar with the OP's usual interests, I assumed he was asking about buildings.

 

[GregLocock]

As a frequent user of the things - but not on buildings, a couple of comments.

Basically you split the SDOF mode of the main structure into two, one in which the mounting point and the TMD mass move in phase (the lower frequency), and one in which they move in antiphase.

The separation of these two new peaks is governed by the ratio of the inertia of the TMD to the modal mass at the mounting point.

Adding damping to the compliance joining the structure to the TMD inertia is how you control (a) the resonant response at each peak and (b) increasing the response on the shoulders of each peak, and between them. It also has some effect on the frequency split. Generally less damping is better than more, at least with rubber.

If you are just trying to add damping to a troublesome resonance then TMDs work well, if you can fit one at a point of high amplitude.

If your excitation is of a broadband (or impulsive) nature and you have a high modal density then you'll need lots of differently tuned TMDs, or a lot of damping. Some machines use untuned mass dampers in that case.

If you change the tune of the spring you can alter the relative height of the two peaks. This is useful if your excitation spectrum rolls off with frequency, which I imagine is quite common with structures (for instance vibrations from roads) - in that case you set the lower peak at a lower response than the upper one.

A simple 2dof excel model of this is the quickest way to study the various interactions, unless you have a great love for equations.

You can damp more than one mode at one location with the same damper - for instance the crankshaft damper on a car can be constructed so as to damp the first torsional and first bending mode of the crank.

I'd just emphasise that life is a lot easier if you can mount them at the point of maximum amplitude.

Cheers

Greg Locock

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

 

[abusementpark]

271828,
Do you perhaps have an electronic copy of the Rottmann paper? It sounds like a good introductory document, but I cannnot seem to find it online.

I was just interested in an introduction to TMD and how they are generally used in buildings. It seems like they are very useful in suppressing the dynamic response from both lateral loads and vertical excitation of floor system from service footfall??

Thanks for all the responses.

 

[271828]

See if you can download it here:

http://scholar.lib.vt.edu/theses/available/etd-09182008-063455/

 

[271828]

Crap, I just tried to download it and it's restricted. YOu might be able to contact the university and get a copy somehow.

 

[VibeAC]

Here's one paper on TMD applications.

Andrew Gorton, MSc
Noise & Vibration Consultant
www.PapadimosGroup.com

 

[VibeAC]

...and here's another.

Andrew Gorton, MSc
Noise & Vibration Consultant
www.PapadimosGroup.com