Uncertain linear systems in dynamics: Retrospective and recent developments by stochastic approaches

This paper provides an overview along with a critical appraisal of available methods for uncertainty propagation of linear systems subjected to dynamic loading. All uncertain structural properties are treated as random quantities by employing a stochastic approach. The loading can be either of deterministic or stochastic nature, described by white noise, filtered white noise, and more generally, by a Gaussian stochastic process.The assessment of the variability of the uncertain response in terms of the mean and variance is described by reviewing the random eigenvalue problem and procedures to evaluate the first two moments of the stochastic (uncertain) response. Computational procedures which are efficiently applicable for general FE-models are the focus of this work.Most recent developments for the reliability assessment–besides a retrospective review–are summarized, with particular emphasis on numerical Monte Carlo Simulation approaches. This review comprises methods to assess the first excursion probability directly by efficient numerical methods. General “black box” procedures and approaches applicable only for linear systems are critically discussed. Specific procedures applicable to linear systems subjected to general Gaussian excitation are subsequently addressed. Methods applicable for deterministic structural systems are introduced first. Finally, a procedure to exploit the solutions for deterministic linear systems for stochastic uncertain systems in an efficient manner is described.