Variance of the fatigue damage due to a Gaussian narrowband process

Abstract

The fatigue life of a structure is inherently random when the loading is irregular. There is a vast body of literature on the analysis of the mean fatigue damage, but very few studies have been devoted to the variance. This paper presents an improved method for analyzing the variance of the damage for any narrowband Gaussian process. The field of application is not confined to the linear oscillator, unlike approaches in previous studies. The method is simple to apply; it involves a single summation for arbitrary processes, and closed form solutions are available for special cases (linear oscillator and bandpass process). The effectiveness of the method is demonstrated through case studies encompassing a variety of systems, including a realistic spectrum commonly seen in offshore engineering. Using rainflow counting of simulated time domain stresses as a benchmark, the proposed method is shown to yield a highly precise prediction of the variance. Moreover, it is significantly more accurate than an existing method for the linear oscillator system.