Efficient modal analysis of systems with local stiffness uncertainties

Abstract

The characterization of the uncertainty in modal quantities of an uncertain linear structural system is essential to the rapid determination of its response to arbitrary loadings. Although the size of many computational structural models used is extremely large, i.e. thousands of equations, the uncertainty to be analyzed is oftentimes localized to very small regions of the model. This paper addresses the development of an efficient, computational methodology for the modal analysis of linear structural systems with local stiffness uncertainties. The newly developed methodology utilizes an enriched basis that consists of the sub-spectrum of a nominal structural system augmented with additional basis vectors generated from a knowledge of the structure of the stiffness uncertainty. In addition, methods for determining bounds on the approximate modal frequencies and mode shapes are discussed. Numerical results demonstrate that the algorithm produces highly accurate results with greatly reduced computational effort. © 2009 John Wiley & Sons, Ltd.