Assume that input and response acceleration PSDs have been measured. The corresponding displacement PSDs can be readily calculated.
But the relative displacement cannot be calculated accurately because the phase angles are discarded in the PSD calculation.
The best method is to perform the relative displacement calculation in the time domain. The relative displacement PSD can then be calculated if desired.
The first step is to calculate the relative acceleration in the time domain. Then integrations are performed to calculate the relative velocity and the relative displacement. Highpass filtering and trend removal are optional steps in this process.
A function for calculating the relative displacement from two accelerometer time histories is given in:
Matlab script: Vibrationdata Signal Analysis Package
The function can be accessed via:
>> vibrationdata > Time History > Integrate or Differentiate > Relative Displacement from Two Acceleration Time Histories
Typically, a highpass filter from 5 to 10 Hz is needed.
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– Tom Irvine