Response of uncertain systems to stochastic excitation

The reliability of structural systems with time-invariant, uncertain parameters subjected to stochastic excitation is investigated. The properties of the system, such as stiffness, mass, and damping, are uncertain, and are modeled as continuous random variables. First- and second-order reliability methods are used to approximate the probability of a critical response exceeding a specified threshold. Measures of sensitivity of the probability with respect to the uncertain parameters are derived and examined for example systems. It is found that uncertainty in the parameters of certain systems may have significant influence on the irreliability, even when the input is a wideband stochastic process. Examples of such systems include composite systems, such as equipment-structure systems, in which the natural frequencies of individual subsystems are uncertain and are likely to coincide.