In the interval response analysis of structural-acoustic systems, the traditional interval perturbation finite element method exhibits significantly increasing errors under rising uncertainty levels, owing to the omission of higher-order terms of the Taylor series. To address this limitation, a univariate dimension-reduction interval finite element method (UDIM) is proposed to enhance the traditional interval finite element method for structural-acoustic systems. Compared with the first-order Taylor expansion, the proposed method preserves the higher-order terms of Taylor when approximating the interval dynamic stiffness matrix and load vector, thus more accurately estimating the nominal midpoint and radius. Subsequently, the Neumann series is enhanced using the geometric series summation theory, where the inclusion of higher-order terms improves the accuracy of the matrix inversion process. As a result, the proposed method achieves higher accuracy, especially under relatively large uncertainty levels. The accuracy and effectiveness of the proposed method are demonstrated through three numerical examples.
Li et al. (Thu,) studied this question.