Transient Impacts, Summation of Forces and Transfer Fuctions

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SUMMARY

This discussion focuses on computing transfer functions for hammer impacts on a cylinder using accelerometer responses. The user is attempting to derive a transfer function from two separate hammer impacts, F1 and F2, to their respective accelerometer responses, a1 and a2. The main question revolves around the validity of summing the two transfer functions for a linear system when the impacts occur at different times. The user seeks confirmation on whether the principle of superposition applies in this transient case.

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  • Understanding of transfer functions in control systems
  • Knowledge of linear system theory
  • Familiarity with transient analysis in dynamics
  • Experience with accelerometer data interpretation
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  • Explore transient response analysis techniques
  • Study the computation of transfer functions using MATLAB or Python
  • Investigate the effects of time delays in impact responses
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MetalGearSemi
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So I have a question I am hoping someone can help me answer. I am trying to compute transfer functions for a hammer impact with an accelerometer response on a cylinder. Please see the attached photo.

http://imgur.com/F8DGwl2For some reason the picture did not attach but I have uploaded to Imgur: http://imgur.com/F8DGwl2
I have a transient impact of a hammer at F1 on a block protruding from the face of the cylinder. Then I can compute a transfer function from the hammer impact to the accelerometer response a1. I do the same then as a separate run for another hammer impact, this time of F2 at a different location. Because I am assuming it is a linear system, F3 can be defined as F1+F2 but I am unsure if this works for a transient case. I understand if both F1 and F2 were hit at the same time that F3=F1+F2 but I don't know if those holds true when they are hit at different times.

Ultimately, I would like to know if there is a way that I can sum up the two transfer functions (f1 to a1 and f2 to a2) and result in the same transfer function as if I were to hit with F3 at a different location to a1.
 
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