A SASM-PDD method for random vibration fatigue damage analysis of structures with uncertain parameters

This paper develops a semi-analytical spectral moment-polynomial dimensional decomposition (SASM-PDD) method for fatigue damage assessment of structures with uncertain parameters under random loading. First, within the framework of frequency-domain random vibration fatigue analysis, a closed-form solution for the modal spectral moments of linear stochastic structures is derived. By integrating this solution with the Dirlik model, a semi-analytical framework is established to characterize fatigue damage under an induction spectrum. Building on these derivations, component function decomposition is applied to the expected damage to achieve dimension reduction of the uncertain parameters, leading to an efficient SASM-PDD method. Numerical examples involving an L-shaped plate and a notched thin plate are presented to perform sensitivity analysis and uncertainty quantification of fatigue damage. The accuracy and efficiency of the SASM-PDD method are validated through comparisons with Monte Carlo simulations and experimental fatigue data from the literature. Furthermore, the engineering applicability of the proposed method is demonstrated through uncertainty analysis of fatigue damage at the hotspot locations of a complex industrial fan support frame.