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# FFT and IFFT of PSD acceleration and stress

## FFT and IFFT of PSD acceleration and stress

(OP)
Hello,

given a test request which specifies a random vibration profile as a PSD and after running a simulation to get a PSD stress, is it possible to simply carry out inverse fft of the responce (nm^2)^2/Hz to get the stress in the time domain (nm^2/s) and then carry out rainflow counting to estimate fatigue?

The simulation uses modal and linear dynamics to get PSD repsonse.

### RE: FFT and IFFT of PSD acceleration and stress

ifft of a PSD does not make sense.

Fe

### RE: FFT and IFFT of PSD acceleration and stress

(OP)
Sorry, Inverse fourier transformation? reading this paper 'a frequency domain approach for fatigue life estimation from finite element analysis' by Andrew Halfpenny (ncode) suggest that you can regenerate the time signal via an inverse fourier transformation assuming the PSD was created from time history data, but also contunies to say that you may assume the PSD data to have come from time history data in which case (if it actually hadnt or was unknown) would generate a statisically equivilant time history signal anyway.

im not questioning your responces, just desporatly trying to clarify what is essentially a complex subject that i for one have been going in circles with.

(OP)

### RE: FFT and IFFT of PSD acceleration and stress

to reconstruct the time signal you need magnitude and phase.
when you form the psd, the phase information is lost

now you can make assumptions about the system response and construct a phase response per your reference, then reconstruct the time series from the data, but it is no longer the actual data but a guestimate...

### RE: FFT and IFFT of PSD acceleration and stress

Did you actually read the paper in detail?

I suggest that you re-read page 3, which explains exactly what the author meant.

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