This research is concerned with dynamical systems. Specifically, it deals with dynamical systems with inherent uncertainties, especially in the areas of random vibrations and multiphase flow and in the design of realistic and robust computational models for the stochastic analysis of engineering systems. It also addresses reliability-based design of structural and multiphase fluid systems, applicable to the study of vibrations, the investigation of cumulative damage, the treatment of waste, and the recovery of petroleum. It furthermore addresses the performance of dynamical systems which could be significantly affected by innate uncertainties. This awareness has tended to urge over-design and conservatism in predictions of system performance, rather than an organized study of the inherent uncertainties. It is herein proposed to conduct a program of interdisciplinary research to study the design of stochastic engineering models that are easily amenable to computational procedures. A fundamental objective lies in the construction of realistic and robust models for large classes of dynamical systems for the purpose of determining the effect of input uncertainties on the output.
