Reduced order model-based uncertainty modeling of structures with localized response

This paper focuses on the introduction of uncertainty in reduced order models of structures exhibiting a localized static response in the neighborhood of the excitation. A straightforward application of the maximum entropy framework is first considered to carry out the stochastic modeling of the uncertainty. Quite consistently with the maximization of the entropy, it is found that this modeling may lead to a "globalization" of the response and thus an extension of the nonparametric stochastic modeling approach is sought. To this end, the eigenvalues and eigenvectors of the stiffness matrix of structures exhibiting this localization property are first studied. It is found that their lowest eigenvalues are closely spaced when the corresponding eigenvectors are extended to the entire structure. On this basis, a novel version of the nonparametric stochastic modeling approach is introduced to randomize the entire stiffness matrix while distorting only slightly the closely spaced eigenvalue structure. The above concepts are demonstrated on a thin annulus clamped at its inner radius and a localization of the uncertain response is indeed observed using the proposed approach.