Variance of fatigue damage in stationary random loadings: comparison between time- and frequency-domain results

In this paper, the variance of fatigue damage under stationary random loadings is investigated by means of different case studies (linear oscillator system, random process with ideal unimodal or bimodal power spectral density). Monte Carlo method is used to evaluate the variance of fatigue damage in time-domain and frequency-domain approach. The variance from simulations is compared with analytical methods (e.g. Mark and Crandall’s method, Bendat’s method and Low’s method). Furthermore, for each case study, the paper investigates the relationship between the variance of fatigue damage and the bandwidth parameters. The purpose is to provide a simple closed-form solution for the case of ideal unimodal power spectral density. The closed-form solution has been compared with Monte Carlo simulation in time-domain. The results show good agreement not only for narrow- band but also for wide-band process.