Vibration fatigue analysis using spectral methods is a frequency-domain approach used to estimate the fatigue life of structures subjected to random, stationary Gaussian loads. This method is significantly more efficient than time-domain analysis, often reducing computational time by over 80%. Theoretical Framework
$$E[D] = T \int_0^\infty \fracp(S) \cdot v_pN(S) ds$$
offer an alternative by operating in the frequency domain . Instead of analyzing a time-history stress signal, these methods utilize the Power Spectral Density (PSD) function of the stress response. The primary advantage is computational efficiency: a frequency-domain analysis takes seconds compared to the hours required for transient dynamic simulations.