Issue 78

F. Veschi et alii, Fracture and Structural Integrity, 78 (2026) 44-73; DOI: 10.3221/IGF-ESIS.78.04

 This work reviews the theoretical notions regarding random vibration fatigue and statistics of Sine on Random signals, which are considered necessary for the understanding of the presented Sine on Random fatigue assessment approaches.  The paper concretely gathers in a single manuscript all the available fatigue assessment methodologies for SoR environments, providing a unified review and classifying them according to their characteristics.  The presented approaches are subjected to a systematic numerical comparison based on identical benchmark loading configurations, which go from simple single-sinusoid profiles with rectangular PSDs, where the sinusoidal frequency is shifted relative to the random background, to a real MIL-STD SoR profile, consisting of a broadband random PSD and four sinusoidal signals with different frequencies and different amplitudes.  The paper concludes with a discussion concerning the practical applicability and main limitations of each approach, providing engineers with pragmatic guidelines for selecting the most fitting method based on the loading scenario.

R ANDOM FATIGUE

T

his section outlines the established analytical approaches for the fatigue life assessment of components subjected to purely random Gaussian loadings.

Spectral methods for fatigue life estimation Under the assumption of Gaussian distribution, any random process   x t can be described in the frequency domain by its statistical properties, namely its PSD   ω xx S , which is defined as the Fourier transform of the autocorrelation function       τ τ xx R E x t x t       [18]:

1



  ω

  ωτ τ i R e d 

2 π  



S

(1)

xx

xx





  xx S f and the single-sided

  xx G f , and the relation is provided in Eqn.

Two definitions of PSD exist, the double-sided

(2):

 

 

2 S f  xx

xx G f

(2)

The spectral moments n m are important characteristics of a random process; they are defined as:



  ω G d xx

 

n



m

ω

(3)

n

0

where the subscript n represents the order. Spectral moments represent some important properties of the signal; for example, the moment of order zero, denoted as 0 m , coincides with the variance of the random signal [19]. Combinations of spectral moments of higher order are used to characterize some statistical properties of the random signal that are of interest in fatigue analysis. For a Gaussian process, the number of zero-upcrossings per second ( 0 ν  ) and the peak rate ( ν p ) are defined in Eqns. (4) and (5):

m m

1

 

2



(4)

0



2

0

m m

1

4 2





(5)

p



2

46