Efficient Frequency Response of Locally Uncertain Linear Structural Systems

The frequency response analysis of large, linear structural models subjected to deterministic, dynamic loads is oftentimes a computationally intensive task. The situation is only exacerbated when stiffness and damping uncertainties are present in the system’s description. However, this parametric uncertainty is often contained within a small number of localized features. These features involve only a small portion of the total degrees-of-freedom of the structural model. In this paper, this locality of uncertainty is exploited, and an exact method is presented for the frequency analysis of locally uncertain systems subjected to deterministic inputs based on the well-known Sherman-Morrison-Woodbury formula. The proposed method yields exact responses for the perturbed systems and is not affected by magnitude nor the type (e.g., normal, lognormal, etc.) of the uncertainties with the sole restriction that the system remains stable with probability one. A numerical example is presented to illustrate the significant gains in computational efficiency that can be attained using the proposed method.