In this paper the basic methodology of the coupled response-degradation modelling of stochastic dynamical systems is presented along with the effective analysis of selected problems. First, the general formulation of the problems of stochastic dynamic s coupled with the evolution of deterioration process is given. Then same specific degrading oscillatory systems under random excitation are analyzed with a special attention on the systems with fatigue-induced stiffness degradation. Both, the general discussion and the analysis of seleeted exemplary problems indicate how the reliability of deteriorating stochastic dynamical systems can be assessed.
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