Response of Systems with Uncertain Parameters to Stochastic Excitation

Abstract

This paper presents a method for the dynamic analysis of linear systems with uncertain parameters to stochastic excitation. The applied forcing function is modeled as a modulated Gaussian white‐noise process in time. A procedure to derive the random state‐space equation for the response covariance matrix of the system is presented. The covariance equation is then integrated in time and the response variability is computed. The proposed method is applied to the random response of a five‐degree‐of‐freedom primary‐secondary system. Five different values of the ratio of the fundamental natural frequency of the primary to secondary system are considered along with two different ratios of primary‐ to secondary‐system mass. Two types of uncertainty are considered: uncertain primary‐system stiffness and damping, and uncertain secondary‐system stiffness and damping. Results are reported for the effect of system uncertainty on both the relative displacement and absolute acceleration response of the secondary system. It is concluded that uncertainty in the stiffness of the primary and secondary systems has a very strong influence on the response of the secondary system and its reliability, and must be properly accounted for in the analysis of such systems.