# Physics:Fatigue damage spectrum

The **Fatigue Damage Spectrum** (FDS) of a vibration is obtained by tracing the fatigue damage experienced by a linear Single Degree of Freedom System (SDOF) according to its natural frequency, for given damping ratio and for a given value of parameter b (this parameter comes from the Basquin law representing the Wöhler curve of the material constituting the structure).

Regardless of the vibratory signal studied (sinusoidal vibration, shock, random or composite vibration); the FDS can be obtained directly from the time history signal. The method consists of :

- numerically calculating relative response displacement of the mass in relation to its support;
- establishing a peak histogram, giving the number ni of peaks according to their amplitude;
- using Miner’s damage accumulation law.

In the case of stationary random vibration, the Power spectral density (PSD) of the vibration can be directly used for the FDS calculation.

## Note

Vibrations can damage a mechanical system as a result of several processes, among which are:

- the exceeding of characteristic instantaneous stress limits (yield stress, ultimate stress etc.);
- the damage by fatigue following the application of a large number of cycles.

FDS is used according to the second criterion. The first criterion is considered with the *Extreme response spectrum* (ERS).

## See also

## References

- Lalanne, C.,
*Mechanical Vibration and Shock Analysis. Volume 5: Specification Development*, Second Edition, ISTE - Wiley, 2009.