I'm trying to find the damping values of a specimen, based on sweeping the forcing frequency from 0-10 kHz. As shown in the diagram, I measure the input force from the shaker, and the subsequent response using an accelerometer on top. (The steel plate in the diagram has known properties and was used to isolate my system from sources of noise).

Using the force sensor and accelerometer, I have time-series and frequency responses of input force and output acceleration.

enter image description here

This is where my question arises. Can I extract damping from just the response (acceleration), or do I need to do it using the transfer function (output/input)? These give quite different peaks, and damping values. I've attached a picture showing the frequency response of the accelerometer on top, the force sensor on the bottom, and the transfer function. (The thick black lines represent the average of multiple runs, the red dots are automatically-detected peaks in the transfer function).

enter image description here

Most resources I've seen online use the transfer function, but from what I understand, the response by itself should also be usable (?).

If it's just the transfer function, then is it sufficient to present data in acceleration/force units, or should I convert both to force/both to acceleration such that the transfer function is dimensionless?

Thanks in advance!

  • $\begingroup$ You have measured the transfer function, so use it! The only reason not to use it is because in some situation you can't measure the force, for example. The transfer function plot shows 4 (or maybe 5) clear modes below 2 kHz. Also, look at the phase difference between the force and response, to see if there are any identifiable modes above 2kHz - most of the red dots on your plot are unlikely to be modes. $\endgroup$
    – alephzero
    Aug 21, 2020 at 11:58
  • $\begingroup$ Thanks for the tip @alephzero. Was wondering what your thoughts are on the dimensionality of the transfer function? Is it appropriate to leave it in g/N? Thanks1 $\endgroup$
    – hopper19
    Aug 21, 2020 at 15:44


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