Rainflow fatigue cycles can be easily calculated for a single-degree-of-freedom subjected to a sine or sine sweep base input. The reason is that each pair of consecutive positive and negative response peaks forms a half-cycle.
The relative fatigue damage can then be calculated from the rainflow cycles.
Here are Matlab scripts for performing the rainflow and damage calculations. rainflow_sine.zip
rainflow_sine.m is for the case where the natural frequency is known.
rainflow_sine_fds.m gives the fatigue damage spectrum for a family of natural frequencies.
The remaining scripts are supporting functions.
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– Tom Irvine