The exact extreme response and the confidence extreme response analysis of structures subjected to uncertain-but-bounded excitations

Abstract

In this study, the methods for computing the exact bounds and the confidence bounds of the dynamic response of structures subjected to uncertain-but-bounded excitations are discussed. Here the Euclidean norm of the nodal displacement is considered as the measurement of the structural response. The problem of calculating the exact lower bound, the confidence (outer) approximation and the inner approximation of the exact upper bound, and the exact upper bound of the dynamic response are modeled as three convex QB (quadratic programming with box constraints) problems and a problem of quadratic programming with bivalent constraints at each time point, respectively. Accordingly, the DCA (difference of convex functions algorithm) and the vertex method are adopted to solve the above convex QB problems and the quadratic programming problem with bivalent constraints, respectively. Based on the inner approximation and the outer approximation of the exact upper bound, the error between the confidence upper bound and the exact upper bound of dynamic response could be yielded. Specially, we also investigate how to obtain the confidence bound of the dynamic response of structures subjected to harmonic excitations with uncertain-but-bounded excitation frequencies. Four examples are given to show the efficiency and accuracy of the proposed method.