# Theoretical doubt on Forced Response

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 April 2, 2022, 07:09 Theoretical doubt on Forced Response #1 Member   MC Join Date: Apr 2021 Posts: 43 Rep Power: 5 Dear all, I am performing a FSI using ANSYS Fluent and Mechanical on a flow in a channel. I solved for the unsteady pressure field and imported the pressure field at a certain number of time steps. Then, I found the frequency content of the system and I extract the Fourier excitation modes, in order to import them into Mechanical for the harmonic response. Using this procedure, the system shows very high amplitude of von Mises stresses around the first natural frequency. My question is: if I import the excitation at (for example) 100 Hz and the natural frequency is at 300 Hz, what I focus on is the amplitude/stress at 100 Hz in the frequency response right? At this point, what if the Fourier mode around 300 Hz (continuing the same example of before) has very low amplitude but then superposing it with the structural mode at 300 Hz, I get very high oscillating stress? What can we conclude about the system safety in this case? In reality, we are not exactly exciting the system at a sinusoidal oscillation at 300 Hz, but still the stress value might not be acceptable. Have you faced such an issue previously? Thanks a lot for helping Marco Last edited by MarcoC501; April 4, 2022 at 13:34.

 April 7, 2022, 00:44 #2 Senior Member   Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,677 Rep Power: 66 If you force at 100 Hz, you can and generally should still analyze the response over all frequencies. Of course, if you know what you're doing, you'll know that all the non-natural frequencies will be highly damped. And since the forcing isn't at 300 Hz, pretty much nothing will happen unless there is some system coupling. Do this analysis a few times and you'll acquire this experience.

 April 7, 2022, 03:07 #3 Member   MC Join Date: Apr 2021 Posts: 43 Rep Power: 5 Hello LuckyTran, thanks a lot for your reply. What do you mean when you say " pretty much nothing will happen unless there is some system coupling"? You mean that there could be a situation in which the excitation at 100 Hz can have a coupling with the natural frequency at 300 Hz? So I have to look at amplitudes at both frequencies? If the forcing is at 300 Hz, and I look at the value of stress in that point (which is the frequency response peak), I get a quite high value. My doubt is about the way a forced response is done in theory, since it assumes a sinusoidal excitation at 300 Hz, which is not exactly the case in the unsteady simulation (since I have a spectrum of frequencies for the wall pressure) Thanks a lot for your help and patience

 April 7, 2022, 16:29 #4 Senior Member   Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,677 Rep Power: 66 Yes forcing at 100 Hz can excite things at other frequencies but these are non-linear effects that you don't find from typical analysis methods. Next, the frequency response curve is a response curve at all frequencies. You looking at only the highest peak is simply you ignoring all the other useful data no the curve (and possibly even reading the curve wrong). The frequency response curve is the response to whatever is the forcing (that you apply). If you force at 100 Hz, then you have the response curve for an excitation at 100 Hz. If you force at 300 Hz, then you have the response curve. If the forcing is at multiple frequencies, then the response curve is for multiple frequencies. For small amplitude forcing (i.e. within the linear limit), the response curve isn't really affected by the type of forcing and they all produce the same output. That's why people don't even bother to check the response if they know the excitation isn't near the natural frequencies. Now I encourage you to do a case where you force it at 100 Hz and check the response at other frequencies. And then do a case where you force at 100 Hz and 101 Hz. A spectrum of frequencies of forcing is a superposition of a bunch of sinusoidal sources. And in the linear limit...

 April 7, 2022, 16:47 #5 Member   MC Join Date: Apr 2021 Posts: 43 Rep Power: 5 Hello Luckytran, thanks a lot, you clarified my ideas quite much! I believe that in my case the forcing is not changing so much the frequency response (i.e. all the frequency response curves show more or less the same output at various forcing frequencies), and the main issue is the response at the natural frequency (300 Hz) itself that has high amplitude. Therefore, if my frequency spectrum contains even a small amplitude at 300 Hz (continuing the example we are doing), the structure is in a risky situation right? What do you suggest me to look at in this case? Thanks, thanks, thanks!!

April 9, 2022, 05:23
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To elaborate more on the question, I will be more detailed with my case.

This is for example the forced response with excitation at 140 Hz: as you can see, the response is almost equivalent to the static response. Moreover, you can see the stress amplitude peak around 360 Hz (first natural frequency) is around 30 MPa. The Fourier component around 360 Hz has very low amplitude, but still the harmonic response is high. In my case, this value of oscillating stress is a bit too high considering also the mean component.

My question is very basic (and maybe a bit silly): can I conclude that the structure is not safe in that flow condition since the component has stress (mean + oscillating) higher than the yield stress? Because the forced response is in theory considering a sinusoidal oscillation at 360 Hz, while in reality that excitation has low amplitude and it is not exactly sinusoidal....
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