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# How to rotate random PSD input to another coordinate system

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## How to rotate random PSD input to another coordinate system

(OP)
Suppose you have an assembly that will go on a launch vehicle and be subjected to random vibration. Also suppose the input random vibration PSD (acceleraton spectral density) is given in the launch vehicle coordinate system, with the X-axis aligning with the axial direction, and Y-axis aligning with lateral.

If the payload is mounted at some angle, suppose 10 degrees off from axial, how would you derive a new input to be inline with this new rotated coordinate system? If it were a static vector in axial and lateral, you could simply take the components of each vector in the new axis. But since the loads vary with time and vary over the frequency range, I don't think it's as simple as taking the components.

I'm wondering if I need to synthesize a time history in the axial and lateral directions from the respective PSD's, then combine the time histories in the new axis that accounts for phase differences, then calculate the PSD from the combined time history.

Thoughts on this? Thanks.

### RE: How to rotate random PSD input to another coordinate system

It still is as simple as that. For each frequency line just do the geometrical construction. There is a problem, you don't have phase information, so you may be overestimating the spectrum. Your other plan, resynthesising the time histories, is a fun and exciting idea, but faces the same issue. Just to see what I'm on about it might be worth taking a typical time history, psding it, and then resynthesising the time history. Use random phase for each frequency line.

Cheers

Greg Locock

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### RE: How to rotate random PSD input to another coordinate system

CamJPete,

I am not sure what you are doing here.

I was handed a file of vibration inputs in the form of XYZ data. I wanted to rotate this 45°, so I converted the coordinates to polar, I did the rotation, then I converted back to XYZ. I had suspicions. My analysis confirmed them.

--
JHG

### RE: How to rotate random PSD input to another coordinate system

(OP)
Thank you all for your input. Greg, I did just what you suggested. It is surely overestimating the input, but it is conservative. Overall, it was a minimal increase, something like 0.1 g-rms increase, so I'm not worried about it. I appreciate the time you spent to reply everybody.

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