Transient Impacts, Summation of Forces and Transfer Fuctions

AI Thread Summary
The discussion focuses on calculating transfer functions for hammer impacts on a cylinder, specifically examining the accelerometer response. The user is unsure if the principle of superposition applies to transient impacts when forces F1 and F2 are applied at different times, questioning whether F3, defined as F1+F2, can be treated similarly. They seek clarification on whether the transfer functions from F1 to a1 and F2 to a2 can be summed to yield the same result as a single impact F3 at a different location. The inquiry highlights the complexities of linear system assumptions in transient scenarios. Understanding these principles is crucial for accurate modeling of dynamic responses.
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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