Stochastic response analysis of 3D vibro‐acoustic systems with geometrical uncertainties based on the extended finite element method

Abstract

Unlike uncertainties such as loads and material parameters, geometrical uncertainties caused by errors in the geometry and differences in equipment installation locations of the vibro‐acoustic system can significantly alter the solution domain, resulting in nominally identical vibro‐acoustic systems exhibiting large response dispersions. To solve such problems, this study introduces the extended finite element method/finite element method (XFEM/FEM) and the direct probability integration method (DPIM) to construct a novel stochastic response analysis scheme for 3D vibro‐acoustic systems. Furthermore, it examines the impact of geometric uncertainties on system responses. The XFEM/FEM can accurately capture the non‐smooth solution at the geometrical interface by constructing enriched functions without modifying the original mesh, and it allows the introduction of random parameters to describe the geometrical modifications. The input probability space of the parameters is partitioned, and the Dirac function is smoothed, yielding statistical properties like the probability density function of system responses, which are derived by summing responses from each representative point. The computational performance of the proposed scheme is validated with both single and multiple uncertain geometries, while also discussing the impact of these uncertain geometries on the responses of the vibro‐acoustic system.