The frequency domain approach in virtual fatigue estimation of non-linear systems: The problem of non-Gaussian states of stress

The use of the frequency domain approach in the virtual estimation of mechanical component fatigue life under random loads is related to two conditions regarding the dynamic behaviour of components and the state of stress. The mechanical system must have linear behaviour and the probability density function of stress must be Gaussian, respectively. Obviously, these conditions are not independent, because there is a close tie between the transformations induced by the system to the random inputs and stress distribution. The rigorous procedure for the extension of these hypotheses is not available and only approximated approaches can be used: normally these are based on a corrective coefficient to the narrow-band formula. The main goal of this report is to suggest a separation of the effects on the corrective coefficient. In this manner, the global coefficient can be seen as the product between a partial coefficient related only to the wide-band effects of stress power spectral density function and another one dependent on non-normality indices of stress probability density function. A meaningful application has been investigated to validate the practical employment of this approach. By this example the authors also defined an original analytical expression of a corrective coefficient for Gaussian damage; however, the formulation has to be improved by other applications, because its validity is tested only on a too much limited domain of Kurtosis values. Moreover, the authors suggest that a modal approach to the stress recovery procedure of a flexible body might be an interesting way to the rapid identification of non-Gaussianity indices in the analysis of frequency and time domain dynamics. For this reason, they believe that the investigation of tying the stress non-Gaussianity to the non-Gaussianity of the component modal coordinates to be useful.