Random vibration analysis of a single degree of freedom under imprecise proability assignments

The random vibration analysis of aircraft structural components is often performed with simplified techniques, such as Miles' Equation, which yields the root mean square of the acceleration response. The failure probability of the structural component is then established as the probability that the displacement exceeds a given threshold with a velocity in a certain period of time. Nonetheless, the dominant frequency of the system may be uncertain because of manufacturing variability, and because of variation in joints and connections of structural components. In this paper the conventional approach is extended in two ways: (i) firstly, the system parameters are taken to be uncertain rather than known, (ii) secondly, the uncertainty is modelled with an imprecise probability description, rather than with conventional pdfs (which usually are not known, due to a lack of empirical information). When the system parameters are modelled with a probability density function, the proposed approach yields: (a) the unconditional failure probability across an ensemble of Single Degree of Freedom (SDoF) systems; (b) the probability that the failure probability exceeds a specified target level across the ensemble of SDoFs. By introducing uncertainty in the probabilistic assignment of the system parameters, the bounds on these quantities are readily obtained. The feasibility of the proposed approaches are shown through their application to a structural panel of a spacecraft