Fatigue Reliability of Multidimensional Vibratory Degrading Systems under Random Loading

Abstract

In this paper, the basic methodology for the fatigue reliability assessment of randomly vibrating multidegree-of-freedom systems is presented within the coupled response-degradation model. The fatigue process in the system components is quantified by the fatigue crack growth equations which—via the stress range—are coupled with the system response. Simultaneously, the system dynamics is affected by fatigue process via its stiffness degradation so that it provides the actual stress values to the fatigue growth equation. In addition to the general coupled response-degradation analysis, its special case of noncoupled fatigue crack growth is treated as well for the wide-band stationary applied stress by the use of its first four spectral moments and the approximate, empirically motivated, Dirlik’s probability distribution for the stress range. Both, the general analysis and the illustrating exemplary problems elaborated in the paper provide the route to the fatigue reliability estimation in complex–hierarchical vibratory systems under random loading.