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Explicit solution of Rice/Lalanne peak probability distribution for statistical fatigue assessment in the frequency domain

A closed-form explicit solution for statistical fatigue life assessment under broad-band stochastic loading is proposed herein. Obtained solution is valid for stationary, random and ergodic zero mean Gaussian stress process. It is based on Rice/Lalanne peak stress probability distribution function. The solution is given in terms of special Gaussian HyperGeometric function which accurately describes the transcendent error weighting function between the Rayleigh (i.e. narrow-band) and Gaussian (i.e. broad-band) contribution of the random vibration fatigue model. HyperGeometric-based solution is more accurate compared to other approximate methods based on the peak distribution from literature. Fatigue benchmark test comparison is performed in time and frequency domains with very good match-up reported.

Spectral fatigue ; Probability density function ; Rice/Lalanne distribution ; HyperGeometric function

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