Analysis of two-dimensional stochastic acoustic radiation problems with immersed media interface uncertainties

Unlike uncertainties stemming from loads and material properties, interface uncertainties arising from variations in immersed media within the acoustic field can significantly alter the solution domain, leading to substantial dispersion in radiated acoustic pressure. To address this issue, this study introduces the extended finite element method (XFEM), Dirichlet-to-Neumann (DtN), and direct probabilistic integration method to develop a two-dimensional stochastic acoustic radiation analysis approach for systems with immersed media interface uncertainties. The XFEM with DtN enables accurate capture of the non-smooth solutions at the interface by constructing enriched functions without modifying the original mesh and allows the introduction of random parameters to describe the interface modifications. The input probability space of the parameters is partitioned and the Dirac δ function is smoothed, and the statistical properties such as the probability density function of system responses are obtained by summing the response under each representative point, which can efficiently treat the propagation of interface uncertainties. The computational performance of the proposed scheme is validated using examples of infinite oscillating rigid cylinders and submarine acoustic radiation. Furthermore, the impact of parameters such as the position and thickness of porous material domains on the radiated acoustic pressure is discussed.