Physics:Fatigue damage spectrum

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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.


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

Fatigue (material)


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