Response of uncertain dynamic systems. I (Q1819597)

This paper and its sequel deal with the characterization of the response of a structure modeled by a single-degree-of-freedom system in which the mass, stiffness, and damping parameters are only imprecisely known. Using an information theoretic framework, closed form expressions are developed for the probability densities of the parameters that control the characteristics of the dynamic response, namely, the natural frequency of vibration, the damped natural frequency, and the percentage of critical damping. The manner in which these closed form expressions depend on the extent and nature of our knowledge about the uncertain parameters is highlighted. Some comparisons with perturbation solutions are also presented.