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

Spectral density

In statistical signal processing and physics, the spectral density, power spectral density , or energy spectral density , is a positive real function of a frequency variable associated with a stationary stochastic process, or a deterministic function of time, which has dimensions of power per hertz...

 (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

Extreme response spectrum

The Extreme Response Spectrum is defined as a curve giving the value of the highest peak of the response of a linear Single Degree of Freedom System to vibration, according to its natural frequency, for a given damping ratio...

(ERS).

Reference

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