Interval Analysis of Vibro-Acoustic Systems by the Enclosing Interval Finite-Element Method

Abstract

Traditional interval analysis methods for interior vibro-acoustic system with uncertain-but-bounded parameters are based on interval perturbation theory. However, the solution sets by traditional interval finite-element methods are intrinsically not capable of reflecting the actual bounds of results, due to the non-conservative approximation for neglecting the high-order terms of both Taylor and Neumann series. In order to cope with this problem, this paper introduces the concept of unimodal components from structural mechanics to factorize the uncertainties, and a new enclosing interval-finite element method (enclosing-IFEM) is proposed to predict the uncertain vibro-acoustic response. In the enclosing-IFEM, the global matrix is assembled with the mixed-nodal-element strategy (MNE), which is different from the element-by-element assembly strategy. Thus, the vibro-acoustic coupling equation can be transformed into an iterative enclosure formula, and it avoids conflicts between the Lagrange multiplier matrix and the coupling sub-block matrix. The focus of this research is to reduce the overestimation caused by dependency phenomenon in the result of the enclosing-IFEM, therefore, both Rump’s and Neumaier–Pownuk methods are analyzed in residual convergence. Furthermore, taking the results of the Monte Carlo approach and other interval finite-element methods as the cross-references, both the efficiency and accuracy of the enclosing-IFEM are examined through two numerical validation examples.