Analytical Solutions of Bimodal Gaussian Processes’ Fatigue Damages

Based on the rain-flow counting technique, a frequency domain method is developed for calculating the fatigue damages caused by the bimodal Gaussian loads. Firstly, by considering the reduction effect of low frequency loads on high frequency ones, the amplitudes of the small rain-flow cycles are obtained. Secondly, the amplitudes of the large rain-flow cycles are determined by means of Turkstra’s rule of load combination. Moreover, based on the numerical solutions developed, the two analytical formulas for the damage estimates of small and large cycles are developed. Both numerical and analytical solutions are benchmarked against the rain-flow damage estimates and compared with the existing ones. The numerical analyses show that the damages estimated by the new method are close to the rain-flow damages.