Is a tuned damper effective in forced vibration? 5

[GMarsh]

Hi,

I have a structure on which a tuned damper is mounted, tuned for one of the resonant modes of structure. Now this structure is also being subjected to a forced vibration.

Now I am interested to know if the tuned damper will have effect on minimising forced vibration (because of added mass or some other effect)? If yes, how does the effect vary with amplitude of forced vibration?

I am also interested in simulating this through FE ? Any idea how to apply forced vibration with known frequency and amplitude in FE?

Thank you

Regards
Geoff

 

[Tmoose]

How close is the forced vibration frequency to the resonant frequency?

Is this structure you "have" actually built and in service?

 

[GMarsh]

Thanks for your reply.

They are few kHz apart.

I have not built this structure. A model similar to this is in service. My interest is to find out the effect of tuned damper in presence of forced vibration and if possible simulate it.

 

[Denial]

You don't say what type of structure you are dealing with, so I'll stick to generalities.

(1) Tuned mass dampers are effective under a lot of circumstances, but not under all circumstances. If your structure has a single (potentially) troublesome frequency, its response-versus-frequency curve will have a single peak that is sharp and high. Add a correctly tuned TMD to the structure and that single high peak turns into two lower peaks that are close to each other and are less sharp.

(2) Regarding modelling this with FE, it can certainly be done. You are looking for what is usually called "harmonic analysis".

 

[electricpete]

Is a tuned damper effective in forced vibration?

That is the typical application. There is nothing about "forced vibration" that suggests tuned damper will not work.

As others mentioned, the effectiveness of your particular installation depends in part on tuning (how close is absorber tuned to forcing frequency). And how closely it needs to be tuned depends on things like mass ratio.



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(2B)+(2B)' ?

 

[GregLocock]

Might be worth reading wiki on the suject. i wrote the non buidling bits. A typical use for a TMD on a car is on the driveline, to suppress the bending mode of the engine and gearbox, which is excited b combustion forces, or the crankshaft harmonic damper, which works torsionally.

The trick with TMDs is to mount them where the mode in question is very active, and to ensure you have enough mass, and, often, not too much damping. The maths is easy.

Cheers

Greg Locock


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[Denial]

An excellent, brief, practical, clear description of TMDs, how they work, when they work, how to optimise their performance, etc is given in Appendix D of the book "Vibration Problems in Structures", by Hugo Bachmann, Walter Ammann and others. Published by Birkhäuser-Verlag in 1994, second edition 1996.

The four pages of that Appendix are pretty much all you need (providing you know a fair bit about dynamics to begin with).

 

[GMarsh]

Thanks to all of you...

Now I will explain what I meant by forced vibration. Greg gave a very good example of forced vibration (combustion forces) exciting a 'resonant' mode (bending in the said example).

Now my problem is I am not targeting any resonant mode that is excited due to forced vibration. My interest is that forcing frequency itself ! Now this may sound stupid as I studied in some book that the very concept of 'damping' applies only to resonant modes (whether they are free or forced), but not for non-resonant modes.

Here in my case I am asking exactly same thing - damping a non-resonant frequency. One which is being externally applied.

Imagine a plate or drum being beaten by a rod at certain frequency AND amplitude. Now I am interested in knowing the effect of tuned damper (designed & mounted already for one of the resonant modes of plate or drum) on the vibration minimisation due to external frequency of beating rod. Also, if there is an effect, how does it vary with the amplitude of that external force?

My first guess is that the tuned damper would act only like an added mass (as far as external frequency is concerned) - no more effect. But I am not fully sure.

I am sorry if I am not clear still. I am willing to explain further.

I read most of tuned masses literature and designed one damper also. But this is off-shoot topic on which I am working.

Denial - Are you sure we can simulate forced vibration (the type which I mentioned above) using harmonic analysis ? I think it is used only for finding natural response of structure.

Many thanks.

 

[GregLocock]

A tuned damper by its nature will respond to any base excitation at its tuned frequency. So for example if you had a motor running at 50 Hz, with no modes below 90 hz, you might still have a 50 Hz problem, and you could try to improve it with a 50 Hz TMD.

It is not likely to be a convenient solution, and I can't think of an automotive example that is very clear.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[Denial]

Geoff,

Harmonic analysis, certainly when the term is used in structural engineering dynamics, calculates the sinusoidal response of a structure to a set of sinusoidal exciting actions. The exciting actions must all be acting at the same frequency. This frequency does NOT have to correspond with any of the structure's natural frequencies. When the structure has these exciting actions applied to it, it will respond sinusoidally at the same frequency as the exciting actions (once any transients have died out). Harmonic analysis directly calculates this sinusoidal response.

 

[rob768]

If vibrations due to the acting forces are too high, the construction is to compliant (you call it too weak if you want)

 

[GMarsh]

Thank you once again to all the comments.

Now I think the comments are answering my question - though we can design a damper for a forced (non-resonant) frequency such as the 50Hz example given by Greg, the performance may be not great if the structure is flimsy with heavy forced vibration.

Anyway, I will do a quick simulation in FE - as Denial suggested Harmonic should work and see what can be performance improvement in minimising the forced vibration.

Thank you.

 

[electricpete]

Sorry if I'm repeating stuff but I'm left wondering what it is you came away with.

Now this may sound stupid as I studied in some book that the very concept of 'damping' applies only to resonant modes (whether they are free or forced), but not for non-resonant modes.

Here in my case I am asking exactly same thing - damping a non-resonant frequency. One which is being externally applied.

Tuned mass damper does not necessarily rely on damping. It can reduce vibration at a certain location using mass and springiness with no damping at all.

Tuned mass damper is not limited to a resonant system (as stated by Greg), the damper is tuned to the forcing frequency of interest.

My first guess is that the tuned damper would act only like an added mass (as far as external frequency is concerned) - no more effect. But I am not fully sure.

That would be incorrect. In theory, the vibration is forced to zero at location of attachment of the tuned mass damper. That assumes the damper is tuned to the forcing frequency. The larger the effective mass (*) of the damper compared to the effective mass of the system, the less critical is exact tuning (wider frequency band for reduction).

* Sorry to use the term "effective" mass. It is based on analysis of SDOF system corrected by SDOF TMD... then the mass is clear. For more complicated systems, if we have the system and absorber individually modeled, then we can replace each of them with SDOF system that gives similar frequency response in the frequency band of interest for purposes of determining the mass ratio. Modeling absorber should be easy as we have conceptualized it as sdof during the design.

Once again, sorry if I'm repeating what you already know.





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(2B)+(2B)' ?

 

[GMarsh]

electricpete - You need not say sorry. I should say thanks instead. You corrected my statements.

Though I know the concept and saw few tuned dampers with only mass and spring, I made a wrong statement to the effect that tuned mass damper relies on damping. I am sorry. It is just a slip. Yes the effect of adding damping in a tuned mass damper is only to minimise or level out those split modes formed on either side of the targeted frequency.

Now regarding the other concept only I posted this question - that is whether a tuned damper can be used to damp a 'non-resonant' mode? My understanding after above comments is: yes it can be done. But it may not be effective significantly if the structure is weak and vibration is very strong (which is what rob768 stated).

I am now posting another question - while designing a tuned damper for forced frequency (let us take Greg's example of 50Hz on a system which has no resonant modes nearby), can we say that increasing the mass ratio will help in minimising the forced vibration amplitude on the structure? I know you already stated that increasing mass ratio will make it less effective on tuned frequency. But just looking at compromise solution to improve the situation.

Many thanks.

 

[electricpete]

Based on analysis of undamped SDOF system corrected by undamped SDOF damper (which ends up being a 2DOF composite system):

The frequency response H(w) = X(w)/F(w) has a zero at the tuned damper frequency and a pole on each side. Obviously you want to get near the zero and far from the pole. If the TMD mass is small compared to the main mass, then the two poles on each side are very close to the zero... tuning is critical and sometimes practically impossible when the TMD mass is too small. If you have a larger TMD mass, you have a better chance of reaching a given target of vibration reduction with a given tuning error.

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(2B)+(2B)' ?

 

[electricpete]

Added clarification in bold below (no edit feature... kicks my butt every time)

Based on analysis of undamped SDOF system corrected by undamped SDOF damper (which ends up being a 2DOF composite system):

The frequency response H(w) = X(w)/F(w) has a zero at the tuned damper frequency and a pole on each side. Obviously you want to get near the zero and far from the pole. If the TMD mass is small compared to the main mass, then the two poles on each side are very close to the zero... tuning is critical and sometimes practically impossible when the TMD mass is too small. If you have a larger TMD mass, then the poles move farther away from the zero, and therefore you have a better chance of reaching a given target of vibration reduction with a given tuning error.

=====================================
(2B)+(2B)' ?

 

[electricpete]

Coping with tuning error is not the only advantage of larger tuning mass....also helps better cope with small changes in forcing frequency. (if the forcing frequency moves to close to your pole, you're in trouble... larger TMD gives more frequency separation between the poles and the zero).

=====================================
(2B)+(2B)' ?

 

[GMarsh]

electricpete, thanks for the info again.

I am writing a small code for studying response of 3-DOF system with tuned damper. I hope to study the effect of mass ratio, etc. I will get back to here if I have some doubts. Many thanks.

 

[GregLocock]

Handwavy sort of explanation - imagine a large strucure vibrating at 50 hz, with no nearby modes. Now add a small spring mass damper system tuned to the exact frequency. It will of course go off like billy-oh, and so the damping will start to extract energy from the total system. But if you add too much damping then the little mass won't shake much and so less energy is extracted. So there is an optimum 'ratio' of damping to TMD mass. Obviously if the TMD is too small it will have no noticeable effect. They can still be useful -it is not uncommon to mount TMDs near mounting points for the system in an attempt to minimise vibration transfereed through the mount. Theoretically this shouldn't help.

Cheers

Greg Locock


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[Denial]

Following on from Greg's most recent post.

The reference I gave above gives a formula for the optimum amount of damping, based on a 2-dof representation of the system. This is
Sqrt[3(mt/ms)/8/(1+(mt/ms))^3]
where mt is the mass of the TMD and ms is the mass of the structure being damped.
The text then says "This formula is, strictly speaking, only valid for an undamped primary system, but it can also be used for a damped system with good approximation".

When I was designing a damping system as part of the design for a very flexible pedestrian bridge I used this formula. As a check, I developed a spreadsheet that rigorously solved the dynamics of a 2-dof system. I used that spreadsheet to confirm (for my particular set of problem parameters) that this formula did in fact give the optimum damping. The formula passed the test.