Damping measurement with Logarithmic decrement method - Excitation in both axis

[Canada580]

I am trying to measure structural damping value (For the First mode of vibration) of a steel pole (pipe Section) with Logarithmic decrement method. When I excited the pole, the excitation axis is changing. It is mainly because the circular section have same stiffness about all axis passing through center. Saying that, I got significant acceleration values in both X and Y axis. Now the question is: how do I combine the X and Y values of acceleration to get resultant acieration time history diagram accounting both positive and negative values so that I can use logarithmic decrement method to calculate damping?

As a way, probably I can calculate resultant acceleration and provide positive or negative sign to it base on predominant axis of vibration as in the attached file ? But little doubt as the axis of vibration is changing with time.

Any methodology for such resultant acceleration time history and find damping from that or any literature ? any reference ?

Much appreciate for any help.

Thank you.

 

[JoshPlumSE]

I am trying to measure structural damping value of a steel pole with Logarithmic decrement method. When I excited the pole, the excitation axis is changing. It is mainly because the circular section have same stiffness about all axis passing through center.

I dealt with a nearly identical issue 25 years ago, or so. We were doing dynamic testing on composite tubular shafts for sporting equipment. Perfectly symmetrical. We'd excite it in one direction and the direction of excitation would slowly "drift" until it was 90 degrees to the direction we originally excited it.

Unfortunately, I don't remember the exact solution we used to work around the problem. I think it may have been one of the following:

1) We added an extra mass at the top of one end, which helped to force it to vibrate in the vertical direction... If it started vibrating in a different direction that have needed to include a torsion mode which was much stiffer.

2) We added some kind of a kicker brace towards the base (in only one direction). Just enough to change the stiffness so that the motion would stay at the direction of excitation.

 

[JoshPlumSE]

I just thought of another one. If you have the response in both directions recorded, then only look at the SRSS (square root sum of the squares) of the two displacement values. That's actually probably the simplest solution.

 

[Canada580]

Thank you Josh. much appreciated! yes both direction recorded. In the attached excel file, I did the SRSS of two acceleration values. But the confusion is in sign (-ve or +ve) because SRSS will always be positive.

 

[ATSE]

I might be able to answer only part of your question.
For a welded steel-only system, we know the damping ratio will be very low (between 0.5% and 1.5%).
As an estimate, the log decrement = delta ~ 2*pi*(zeta), where zeta = damping ratio.
zeta = 0.11 / (number of cycles for acceleration to reduce 50%).
As an example, if your system takes 11 cycles to reduce the initial acceleration (or amplitude) by 50%, then you have a system zeta = 0.01 = 1.0 %.
This will be true, even if the axis of shaking is changing.

The decrement is evaluated for cycles (crest to crest), so you do not need to consider positive and negative values for acceleration (or displacement).
Either the Chopra text or Clough & Penzien are one of many structural dynamics textbooks.

It may be easier and only slightly more conservative to just analyze your system as undamped.

[Friendly note: For future posts, your attached Excel file is more than a scratch pad with digital ramblings, and not ready to share with outside observers. It needs labels, comments, units... for the rest of us to easily understand.]

 

[WARose]

I don't think I've ever seen a decrement method that considered more than one direction at the same time.

The question I would have is: for a steel pole....do you really need to get that precise? We are talking very low damping here that (I think) could be approximated very easily. Out of curiosity: what is the application?