Dear researches
In general, the value of modal participating mass ratio (MPMR) for each vibration mode represents the participation of each mode in the structural responses.
when a structure equipped with TMD, a vibration mode is added to the others. MPMR value of the added vibration mode can be significant even when TMD mass is very small and as a result, TMD has no effect on the structural responses.
How can this contradiction be justified?
Majid Tavakolinia
I will give my inputs but I could be wrong. As MPMR indicates how much of the system's mass contributes to a particular mode, I would not really compare A2B as both the systems are different. Now, when you attach a TMD, it *detunes* the problematic frequency (or the frequency what you designed your TMD for) by causing a separation by +/- about that frequency. So, tbh you have changed your system by adding an auxiliary system now, which doesn't have that problematic frequency, and definitely your MPMR will show values corresponding to the *two* new frequencies. So, what you should do is check the MPMR for these two new modes and compare it with the original single value and try to see what trend do you observe. I would be interested to know that as well, so please update if you could do it. I do not think as of any contradiction, as that small mass split the original frequency into two nearby freqs, so definitely your response will have to shoot down at the problematic frequency. Since your new system doesn't have that problematic frequency, why to evaluate MPMR for that frequency?
Thanks,
Pranoy Nair
The answer is no. The effectiveness of a tuned mass damper is decided by its frequency tuning and its damping properties.
The topic of tuned mass dampers is comprehensively treated in my text book «Structural Dynamics», Chapter 9, Springer Verlag.
Dear Einar Strømmen
you are right. My question also confirms your answer but as I mentioned, although the value of MPMR describe the participation of each mode shape in structures but it is not true for structures equipped with systems such as TMD.
Now, what is the reason for this inconsistency from the point of view of modal analysis?
furthermore, Effectiveness of TMDs under seismic excitations depend on several factors, which is reviewed in my submitted paper.
I do not know why you are so hung up on this modal mass participating ratio. It may be helpful in evaluating how many modes should be included to obtain a sufficiently accurate solution, but in my opinon, it is a concept which is often more confusing than helpful. It looses its meaning when you include a tuned mass damper, because the tuned-in mode shape has been more or less eliminated by the additional tuned mass damper, that is its intension. Thus, there is no inconsistency.
Rather, any serious analysis should include a convergence investigation, i.e. a series of computational response calculations to ensure that the necessary number of modes are included.
I should also warn you that a tuned mass damper may be effective in quenching a resonant behaviour in a single mode, but rather limited in reducing a broad band or quasi-static type of structural behaviour, which most often is the case in an earthquake induced type of response. And, in a broad band response, it is the modal stiffness that is important.
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