Frequency-based analysis of random fatigue loads: Models, hypotheses, reality

Spectral methods use analytical expressions to estimate the fatigue damage in vibrating structures subjected to uniaxial or multiaxial random stresses. They exploit the random vibration theory which idealizes the random stress as a random process characterized by a power spectral density (PSD) in the frequency-domain. The random process is hypothesized to be stationary or non-stationary, Gaussian or non-Gaussian, and with narrow-band or wide-band power spectral density. The accuracy of analytical spectral solutions depends on whether such hypotheses are fulfilled by actual random time-histories encountered in practice. Knowing the range of applicability of each spectral method is then of utmost importance to avoid estimation errors. After a short account on the frequency-domain description of random processes, this paper presents a brief survey on selected spectral methods for uniaxial and multiaxial random loading. It then analyzes when the hypotheses behind each spectral method are not verified in reality, with the purpose to provide recommendations for a safe use of frequency-based methods.