Fatigue Damage Spectrum, Time Domain

Consider a single-degree-of-freedom system subjected to base excitation where the input is an arbitrary time history.

The response of the system can be calculated via a digital recursive filtering relationship, which is the numerical engine embedded in the SRS calculation.   This is done for each natural frequency and amplification factor Q of interest.

Next, a rainflow cycle count can be performed for each time history response permutation.

Then a relative damage index can be calculated for each fatigue exponent b case of interest using a Miners-type summation.

The damage index can then be plotted as a function of natural frequency, with separate curves for each Q and b pairs.  This is a Fatigue Damage Spectrum (FDS).

The fatigue damage spectrum is useful for comparing the relative damage potential between two different base inputs, particularly for the case of a nonstationary input.

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An FDS program in C/C++ is:

fds.cpp
fds.exe

Note that C/C++ is the optimum language to use for speed because the rainflow calculation requires deleting intermediate rows from the amplitude array.

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An alternative would be to use a Matlab MEX script that calls a C/C++ program. A script set is posted at: Matlab MEX

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The following presentation gives further information on Fatigue Damage Spectra:  SAVE_conference_2013_Irvine_fatigue

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See also:

Rainflow Cycle Counting

Dirlik Rainflow Counting Method from Response PSD

Fatigue Damage Spectra, Frequency Domain

Shock Response Spectrum

Sine Vibration Rainflow & Fatigue Damage

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– Tom Irvine