Response analysis of uncertain structural-acoustic system based on multi-convex set model. (November 2016) - Yin, Hui; Yu, Dejie; Yin, Shengwen; Xia, Baizhan
Abstract: This paper presents the convex perturbation method (CPM) and a new non-probabilistic convex analysis method named Chebyshev convex method (CCM) for uncertain analysis of structural-acoustic system based on multi-convex set model. The uncertain properties of the structure domain and the acoustic domain are uncorrelated, thus it is reasonable to describe the uncertainties of the structural-acoustic system as a multi-convex set model rather than a single one. The well-known CPM with lower-order Taylor series expansions is limited to handle small convex uncertainties. To handle large convex uncertainties, the Chebyshev convex method (CCM) is proposed. In CCM, the Chebyshev polynomials for approximating the original function are obtained by treating the uncertain parameters described by the multi-convex set model as the corresponding marginal interval parameters; the bounds of the original function are calculated by applying the convex Monte Carlo simulation (CMCS) to the approximate function. Numerical results on two structural-acoustic systems verify that the accuracy of CCM is higher than that of CPM, and large convex uncertainties can be effectively handled by using the higher-order CCM with reasonable computational costs. Graphical abstract: Highlights: Uncertain structural-acoustic analysis based on multi-convex set model is targeted. CCM is proposed for handling the convex uncertainty. The accuracy of CCM is higher than that of CPM. Large convex uncertainty can be handled by CCM with reasonable computational costs.