Improved Craig–Bampton stochastic method for spacecraft vibroacoustic analysis

Abstract

This paper addresses the susceptibility of finite element models to uncertainty in frequency ranges with relatively high modal density, particularly in the context of vibroacoustic analysis. The principal idea is based on a stochastic finite element method (FEM) technique called Craig–Bampton stochastic method (CBSM). It is a parametric Monte Carlo simulation (MCS) approach that can be performed at a fraction of the otherwise potentially impractical computational cost, due to the use of reduced rather than full system matrices. An enhanced formulation of the CBSM, significantly improving its efficiency by exploiting the block structure of the condensed model’s stiffness and mass matrices is derived. The improved method is adapted for use with distributed loads, such as diffuse sound field excitation. Its practical implementation is illustrated through a simple theoretical example followed by a high-complexity spacecraft structure case. In both cases solutions are compared to those for a classic MCS of the non-condensed models. Through an extensive parametric survey, recommendations are given on the ideal perturbation levels and underlying statistical distributions for the improved CBSM’s random variables. The proposed technique shows a very strong agreement with the benchmark MCS results. Computational time reductions of over 1 and 3 orders of magnitude against the original CBSM and the MCS, respectively, are demonstrated.