Damping ratio from Transmissibiltiy curves 1

[vibract]

Hello dear members,
I am bit newbie to the Exp Modal Analysis. Recently, we conducted several experiments and we were with certain transmissibility ratio data along with the frequency. After maknig transmissibility ratio vs frequency charts, I was able to determine peaks in the chart. Now, the problem is the determination of damping ratios for the peaks.
My questions are:
-->How can we determine damping ratios from the transmissibiltiy data?
-->Will the damping ratio increase with the increase of frequency?

Regards,
vibract

 

[GregLocock]

-->How can we determine damping ratios from the transmissibiltiy data?


You can measure the half power bandwidth of each peak, or perform some sort of modal parameter extraction (ie fit an array of SDOF modes to your data), or you can use the rate of change of phase near the peak. There are other methods.


-->Will the damping ratio increase with the increase of frequency?

Depends on what you are measuring. On a welded steel structure, for example, the damping ratio doesn't change much from 10 to 1000 Hz.




Cheers

Greg Locock

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

 

[vibract]

Hello Greg,
Thanks for the response. I came across certain formula to calculate damping ratio from the transmissibility curves and it's
T=1/(2/*D)
Where T is the transmissibility ratio and
D is the damping ratio
and this formula is appplicable if D<0.1.

Please someone confirm whether I can use this or not?

Regards

 

[electricpete]

I don't see how you'd use that formula.
T varies with frequency, but D is a constant.

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[GregLocock]

Agreed. Looks irrelevant to me.

Cheers

Greg Locock

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

 

[vibract]

Thanks for the responses.
Theoretically, D ( damping ratio) has to increase with the increase of modes. This is deduced from D=C/Cc.
Where Cc is the Critical Damping and is proportial to
Sqrt(mk). Here m is the modal mass pariticipation. This decreases with the increase of modes. Consequently, Cc also decreases. With the decrease of Cc, D increases with the increase of modes.
In short, D,the damping ratio, has to increase with the increase of modal frequencies.

Regarding, damping ratio from Transmissibility curves..
yes, in literature it's given like that. Here, transmissibility ratio is the ratio of accelration at the response points over the structure to the acceleration at the shaker.

As we are doing this kind of experiments for the first time, we need some suggestions from the experts like you.

Suggestions are most welcome.

Regards

 

[GregLocock]

No it doesn't. I don't know what gave you that idea.

For instance, consider a wing mirror on a car.

The first few modes are of the suspension. The shock absorbers will ensure that they are heavily damped.

On the other hand by the time we hit the resonant frequency of the wing mirror, at say 30 or 40 Hz, it will be almost undamped.







Cheers

Greg Locock

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

 

[vibract]

Hello dear members,
Thank you very much for suggestions. As we can't proceed again with experiments, we have to use this transmissibility ratio data,(acceleration of the structure/accelration of the shaker)to determine damping ratios.
--> Calculation of Damping ratios from the transmissibility curves.
Your suggestions are highly appreciated in this regard.
Regards

 

[spongebob007]

You are on the right track. The equation you cited above is only valid at resonance. That is when f=fn, your transmissibility is equal to 1/2D. This is only valid for lightly damped systems (typically less than 5%)

 

[vibract]

Hello spongebob,
Thanks for your reply. Yeah, literature suggests that. As its known that damping ratio should be constant for particulary mode ( irrespecitve of the measurement points). That means, at all measurement points we should have same damping ratio.

If we use the formula, D=1/2T, then I am with different damping ratio values at various measurement points. This is due to different T values at different points.

If I use halfpower bandwidth method, I am getting constant damping ratio at all the measurement points.

Can any one explain this contradictory?
regards.

 

[spongebob007]

They should be the same since:

1/2D=fn/(f2-f1)

where f1 and f2 are the frequencies that correspond to the half power points.