Aerospace and military components must be designed and tested to withstand shock and vibration environments.
Some of this testing occurs as qualification, whereby a sample component is tested to levels much higher than those which it would otherwise encounter in the field. This is done to verify the design.
Now consider a launch vehicle component which must withstand random vibration and pyrotechnic shock. The random vibration specification is in the form of a power spectral density (PSD). The shock requirement is a shock response spectrum (SRS).
Pyrotechnic-type SRS tests are often more difficult to control and thus more expensive than shaker table PSD tests. Furthermore, some lower and even mid-level SRS specifications may not have the true damage potential to justify shock testing.
The fatigue damage spectrum (FDS) can be used to further determine whether the PSD specification covers the SRS requirement. If so, then shock testing can be omitted in some cases.
Here is a paper: random_cover_shock.pdf
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Matlab Mex – fds_main script
SDOF Response to an acceleration PSD Base Input – VRS script with FDS option
Matlab script: Vibrationdata Signal Analysis Package – SRS damped sine time history synthesis function
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– Tom Irvine