Gaussian and non-Gaussian stochastic sensitivity analysis of discrete structural system

Abstract

The derivatives of the response of a structural system with respect to the system parameters are termed sensitivities. They play an important role in assessing the effect of uncertainties in the mathematical model of the system and in predicting changes of the response due to changes of the design parameters. In this paper, a time domain approach for evaluating the sensitivity of discrete structural systems to deterministic, as well as to Gaussian or non-Gaussian stochastic input is presented. In particular, in the latter case, the stochastic input has been assumed to be a delta-correlated process and, by using Kronecker algebra extensively, cumulant sensitivities of order higher than two have been obtained by solving sets of algebraic or differential equations for stationary and non-stationary input, respectively. The theoretical background is developed for the general case of multi-degrees-of-freedom (MDOF) primary system with an attached secondary single-degree-of-freedom (SDOF) structure. However, numerical examples for the simple case of an SDOF primary-secondary structure, in order to explore how variations of the system parameters influence the system, are presented. Finally, it should be noted that a study of the optimal placement of the secondary system within the primary one should be conducted on an MDOF structure.