A Novel Method for Fatigue Damage Assessment in Bimodal Processes Considering High- and Low-Frequency Reduction Effects

Abstract

Due to inherent nonlinearities within floating systems and the second-order wave forces affecting them, the dynamic responses of floating systems manifest as bimodal Gaussian processes. Consequently, the classical spectral fatigue assessment method grounded in the Rayleigh distribution cannot be applied. This paper introduces the double frequency coupled (DFC) method as a spectral fatigue assessment approach, providing an accurate estimation of fatigue damage originating from bimodal Gaussian processes. Within the DFC method, the bimodal Gaussian process is partitioned into two components: low-frequency (LF) and high-frequency (HF) processes. A Gaussian distribution is employed to describe the probability distribution function (PDF) of the amplitude reduction induced by the interaction between LF and HF processes. The PDF of small-cycle fatigue can be computed by convoluting the PDF of HF amplitudes and the reduction amplitude between LF and HF. Similarly, the PDF of large-cycle fatigue can be determined through convolution, which involves the PDF of LF amplitudes and small-cycle fatigue. The overall fatigue damage arising from the bimodal Gaussian process is obtained by directly summing the contributions of small-cycle and large-cycle fatigue. Numerical investigations of the DFC method’s effectiveness are presented through a series of parametric studies, demonstrating its robustness, efficiency, and accuracy within engineering expectations. Furthermore, the DFC method is found to be applicable to both single-slope and two-slope S-N curves.