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# Calculation of Response acceleration PSD in Random Vibration Analysis

## Calculation of Response acceleration PSD in Random Vibration Analysis

(OP)
Hello,

When I plot the response acceleration PSD vs Frequency curve, for each frequency there will be an acceleration PSD value. For example, if the frequency range is 1 to 1000 Hz, at 100 Hz, the PSD value is 0.5g^2/Hz. At 500 Hz, the psd value is 0.1 g^2/Hz, and so on. If we are talking about linear Random Vibration Analysis that based on modal superposition theory, how does the software calculate the response PSD at a specific frequency? Does this calculation involve all the mode shapes up to that specific frequency? In other words, for PSD value at 1000 Hz, was it computed based on the combination of all the modes up to 1000Hz? or was it computed based on just the mode shape at or nearest to 1000 Hz?

I hope my question is clear. Let me know if more clarification is needed. Any comments or resources would be much appreciated.

Thanks,

### RE: Calculation of Response acceleration PSD in Random Vibration Analysis

It should be using every mode at every frequency, using the damping dependent SDOF response of each mode. If it ignored the contribution from higher frequency modes you wouldn't see antiresonances.

Cheers

Greg Locock

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