Decomposed Interval Matrix Perturbation Finite Element Method for the Response Analysis of the Acoustic Field with Uncertain Parameters

Abstract

To further improve the computational accuracy and efficiency of the modified interval perturbation finite element method(MIPFEM),a decomposed interval matrix perturbation finite element method(DIMPFEM) is proposed. In the proposed method,the dynamic stiffness matrix of an acoustic system is decomposed into the sum of several sub-matrices whose perturbation matrix can be expressed as the products of perturbation factors and determine matrices,thus the errors arising from the first-order Taylor expansion can be avoided. To achieve a higher computational efficiency,the inverse perturbation matrix,approximated by the modified Neumann series expansion is calculated by the epsilon-algorithm. Numerical examples on a 2D acoustic tube and a 2D acoustic cavity of a multi-purpose vehicle(MPV) with interval parameters verify that the computational accuracy and efficiency of DIMPFEM are higher than those of MIPFEM.