PSI - Issue 19

Giovanni M. Teixeira et al. / Procedia Structural Integrity 19 (2019) 175–193 Author name / Structural Integrity Procedia 00 (2019) 000–000

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7

f

  n n m f G f df max 0   

(11)

The family of signals shown in Fig. 7 share, for instance, the 0 th spectral moment (m 0 =8138), which represents the variance of the variable being represented (in the present case stress) and corresponds to the area under the PSD curve in Fig. 6. In other words these signals carry the same “power” which roughly gives an idea of the damage they can cause to a certain material. Although an infinite number of spectral moments can be extracted from a PSD in practice just a small number of them are actually necessary for the purpose of fatigue analysis.

Fig. 6. Typical Stress PSD Curve.

Fig. 7. Stress histories that share the same PSD shown in Fig. 6.

In the frequency domain approach the PSDs of stresses mentioned above are obtained from the PSDs of loads (displacements, accelerations, forces, etc.), through a linear operation that employs transfer functions, also known as frequency response functions (FRF). It is easier to understand how FRF works by looking at a single degree of freedom