Hello everybody,
I have performed a 'Transient Structural (TS) Analysis' of a simple 2D plate problem. I have the response as a function of time.
I have no material non-linearity, no discontinuity, no contacts and have also turned 'Large Deflection OFF' in Ansys WB. It is a simple homogeneous linear elastic 2D plate fixed at bottom and loaded in the top edge at a constant frequency of 50 Hz for 1 second.
I do a Fourier Transformation (FT) of the result to get the response in frequency domain. Can I compare this result with what I obtain from a 'Harmonic Analysis' of the same model where the frequency sweep range is from (0 - 50 Hz)? The problem is that, magnitude of stress at 50 Hz in the harmonic analysis does not match with the magnitude obtained after FT of results from a transient analysis.
Is it possible to compare the results of a linear analysis with that of a non-linear (with all possible non-linearities excluded)? If not, why? Am I missing something?
Thanks for your time.
Have a nice day.
Regards,
Shree
EDIT : Thanks for all inputs. Solved.. :)
Following may help:
1. Consider a linear system say e= L*didt +R * i
2. let e= vm*sin(wt) and z= sqrt((wL)^2 +R^2) thz = atan (wL/R)
3. The response i(t)= K*e^-L/R *t + vm/z *sin(wt -thz) that is natural + steady state response
4. When excited by e we must wait for transient to die down to access the steady state ie at least 5 or 6 times L/R time constant
5 Note if we take time wt0 = thz we obtain ss right away.
6. Now if we take FT of 3 clearly it will not be equal FS (ie steady state ) except in case 5 holds .
For the case given in question we may have a more complex circuit of parallel and series configuration of spring mass system (linear assumed), still we have natural and steady state response as above. Note however we can obtain the linear parameters L and R by an impulse response to a delta function or maybe a step function ,leading to system identification . We can then use this to obtain steady state harmonic response.
This might help explain your result.
Good Luck
Cheers
I think it is possible to compare the two responses in two ways:
1st way: Transform each of two load cases by FFT into equivalent spectral densities (square load versus frequency) to by spectral analysised to each of them, then compare their results
2nd way: Transform the results of transient analysis into spectral density (square displacement versus frequency) then estimate the root mean values (displacement versus frequency) to be compared with the results of frequency analysis directly.
Thank you all for the answers.
Q Narasim ramesh : I am not sure I completely followed your answer. Could you please explain it more? Or some reference material woudl help..
@ Ibrahim : I made sure I have the same constant damping ratio in both the analyses. I am more interested in knowing if the approach is correct?
@ Hatem Hadi : As mentioned in the question, I did the FT of the results of the transient analysis. I am not sure why I have to do FFT of the 2 load cases as you suggested (1st way). It would be great if you could please elaborate?
Regards,
Shree
Hello Shreeraman,
I am facing a problem similar to yours. My effort is to compare the results from my pre-stressed harmonic analysis of a cable vibration with the results obtained from nonlinear transient analysis.
My load in the transient case is a sinusoidal force applied at the same frequency as the harmonic analysis case. Theory states that if we wait for the transient simulation to reach SS, it should match the prestressed harmonic response results.
I have turned on large deflection in transient, and I am aware that I am attempting to compare a linear sim with a nonlinear sim. However, if the forced perturbation wrt equilibrium is small, the results should be comparable. I am nevertheless not getting a good match in ANSYS.
Note that I am applying forcing on a cable already sagging (large deformation) under self weight. In the harmonic case, ANSYS imports the stresses and conducts a pre-stressed analysis using the updated stiffness (hence linear). In the transient case, ANSYS captures the entire nonlinear results including the sag.
You said your doubt got solved. If so, would you please explain how it got solved and help provide me some insight into my problem.
Thank you,
Roshan
Hi Roshan,
If I understood it correctly,
I don't know if it helps, but my thoughts are
- 'However, if the forced perturbation wrt equilibrium is small, the results should be comparable.' - This is what I would expect as well (at least theoretically).
-- Check, double check and make sure damping is defined coherently in both the analyses.
-- Make sure your analysis is converged to the correct (steady state) solution. Cannot stress this enough.
- 'Note that I am applying forcing on a cable already sagging (large deformation) under self weight' - This I don't get. Now you say, you have large deformations and then you are bound to get different results.
- 'My effort is to compare the results from my pre-stressed harmonic analysis of a cable vibration with the results obtained from nonlinear transient analysis.' - I don't get this as well. For the sake of comparison, either both of them have to be pre-stressed or both should not. Corrections are welcome.
- I would suggest to verify the procedure with a simple linear model and get further with pre-stressed once that is done.
Just a tip. It is nicer to post a new question (as opposed to answering) to get better ideas from others as well
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