Stochastic finite element method for vibroacoustic loads prediction.

Reliable and efficient vibroacoustic loads prediction is often critical in structural design, yet it remains a challenging task for many applications. Spacecraft structures are characterised by extensive use of composite materials, complex connections between components and various non-trivial geometrical features. Accurate treatment necessitates the construction of highly detailed numerical models, traditionally employing deterministic representations. Simultaneously, the broadband acoustic excitation due to the diffuse sound field experienced during launch requires modelling the fluid domain and solving the resulting elasto-acoustic interaction at = multiple frequencies. To alleviate the computational demand implications for large problem sizes, substructuring and reduction techniques for the structural domain are commonplace, component mode synthesis (CMS) being a framework widely adopted in the aerospace industry. Nevertheless, despite ongoing research, the topic still presents a range of difficulties when a universal, robust method of accounting for model uncertainties is sought. In this study, two CMS based approaches are proposed and evaluated. Firstly, the Craig-Bampton stochastic method (CBSM) is improved via a set of modifications enhancing its efficiency, and subsequently adapted for use in a vibroacoustic setting. Optimal perturbation levels and scope of validity of the technique are established against a probabilistic structural analysis (PSA) simulation for a spacecraft structure. Secondly, a novel stochastic finite element method (FEM) is presented. The underlying mathematical foundation is derived so that uncertainty can naturally be controlled at the subsystem level, in partitions of the corresponding condensed mass and stiffness matrices. This decomposition based approach ensures that realisations of the random matrices have key properties such as positive (semi)definiteness strictly preserved, guaranteeing complete robustness. The method is validated with a spacecraft test case, comparing its predictions against PSA, the improved CBSM and experimental data. A coupling scheme with a hierarchical matrix accelerated boundary element method is formulated, resulting in the construction of a complete stochastic vibroacoustic solver