FREQUENCY-RESPONSE OF LINEAR-SYSTEMS WITH PARAMETER UNCERTAINTIES

The primary objective of the present study is to develop a new analytical method for estimating the frequency response characteristics of a linear time-variant, discrete vibratory system when the mass, stiffness and damping parameters are uncertain. The excitation amplitude is also considered to be random but the frequency is deterministic. Given several simplifying assumptions, a direct product technique is proposed to estimate the mean and standard deviation of the steady state displacement response at the excitation frequency. Application of this theory is demonstrated by several single- and multi-degree-of-freedom examples. The distinction between off- and near-resonance regime characteristics is clearly pointed out. In order to verify the proposed analytical technique, predictions are compared with the results obtained by the Monte-Carlo simulation and/or perturbation methods. It is seen that, unlike the perturbation method, the proposed technique works well in the vicinity of a resonance. Our methodology can be implemented easily, and is reasonably accurate and computationally inexpensive, when compared with the existing methods. © 1993 Academic Press Limited.