Response spectrum method for random fatigue assessment and its engineering applications

To address efficient prediction of structural fatigue life under random excitation, a Fatigue Response Spectrum Method (FRSM), a high-efficiency algorithm, is established and organized. In the proposed method, a Fatigue Damage Response Spectrum (FDRS) is constructed to quantify the contribution of modal response to the total fatigue damage of the structure, and an explicit relationship is deduced to connect the fatigue life of the structure with its structural characteristics, such as the natural frequency and the stress mode shape. Firstly, based on the theory of random vibration, the establishment of the FRSM is discussed in terms of the single moment method and the Power Spectral Density (PSD) decomposition strategy of the fatigue life assessment in the frequency domain. Then, the dimensionless FDRS is constructed, with the spatial characteristics of the structure, such as the stress mode and the modal participation coefficient, separated from the modal contribution to the total fatigue damage, and a feasible database establishment strategy is proposed. Finally, analysis of numerical examples is carried out based on engineering application of the FRSM to vibration and acoustic fatigue problems, demonstrating the advantage of the method in dealing with large-scale engineering problems. The results show that the accuracy of the FRSM is consistent with that of classical methods such as the rainflow counting method, Dirlik method, and T-B method, and the efficiency can be improved by 2–3 orders of magnitude due to avoidance of calculation of intermediate variables such as PSD function and spectral moment.