This blog entry is a work-in-progress.
Fatigue analysis can be performed in the time domain using rainflow cycle counting. This is an elegant, brute-force approach. One advantage of the time domain approach is that it tends to highlight the occurrences of peaks above 3-sigma for the case of random vibration.
These higher peaks can also be accounted for in frequency domain methods, but the frequency domain approach requires a more thorough consideration of the Rayleigh distribution and other statistical theory.
Furthermore, the time domain method is better able to handle nonstationary and non-Gaussian time history inputs.
Here is a paper that gives a fatigue analysis example for a single-degree-of-freedom system subjected to a base input PSD using Rainflow cycle counting in the time domain: Miners_fatigue_rainflow.pdf
The method can readily be extended to the case of a multi-degree-of-freedom or a continuous system, as will be shown in future papers posted at this blog entry.
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A Matlab GUI version is included in: Vibrationdata Matlab Signal Analysis
A Matlab MEX version is given at: Matlab MEX Rainflow
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– Tom Irvine