Dynamic Transfer of Non-Gaussianity in SDOF Systems Using the Moment-Based Translation Model: From Excitation to Fatigue Damage

Engineering structures often experience non-Gaussian random vibrations, yet the propagation of non-Gaussianity through linear systems and its impact on fatigue are not fully understood. By numerical simulations, this study employs the moment-based Hermite translation model to generate non-Gaussian excitation and stress response time series. Time-domain fatigue damage analyses using the generated stress time series reveal that non-Gaussianity notably affects fatigue damage estimates: kurtosis [Formula: see text] 3 exacerbates fatigue damage, while kurtosis [Formula: see text] 3 mitigates it; skewness exerts a weaker impact but necessitates mean stress correction; and the fatigue-strength exponent in the S–N curve determines the extent of non-Gaussian effects. The non-Gaussian response of linear single-degree-of-freedom systems under non-Gaussian excitation is investigated through vibration analyses. The results demonstrate that damping ratio and excitation power spectral density (PSD) govern the non-Gaussianity transmission. For slowly varying PSDs encompassing the natural frequency, kurtosis transmissibility correlates with the ratio of the system’s bandwidth to PSD bandwidth and can be predicted by the proposed empirical model. PSDs offset from the natural frequency enhance kurtosis transfer. When both skewness and kurtosis are present, input skewness markedly modulates kurtosis transmissibility, indicating a need to account for skewness–kurtosis coupling. Overall, both skewness and kurtosis weaken during transmission. These findings underscore the complexity of fatigue analysis under non-Gaussian loads and highlight the importance of incorporating non-Gaussianity in random vibration fatigue assessments.