This paper provides a new formula to take into account phase differences in the determination of an equivalent von Mises stress power spectral density (PSD) from multiple random inputs. The obtained von Mises PSD can subsequently be used for fatigue analysis. The formula was derived for use in the commercial vehicle business and was implemented in combination with Finite Element software to predict and analyse fatigue failure in the frequency domain.
Bonte, M. H. A., de Boer, A., & Liebregts, R. (2007). Determining the von Mises stress power spectral density for frequency domain fatigue analysis including out-of-phase stress components. Journal of sound and vibration, 302(1-2), 379-386. https://doi.org/10.1016/j.jsv.2006.11.025