Reformulation of the Stochastic BEM to improve the computational efficiency in the prediction of the vibro-acoustic behaviour of structures with uncertainties

Non-determinism plays a crucial role in the prediction of the vibro-acoustic behaviour of structures. The Stochastic Boundary Element Method (SBEM) allows computing the average response of systems with geometrical uncertainties. The method consists in including such perturbations in the standard BEM formulation and adding a set of equations representative of the energetic behaviour. Due to the presence of unknown cross-products, the addition of a set of auxiliary equation is necessary to solve the problem. As a consequence, the system dimension becomes very large and the application of the methodology is limited to small models. This paper deals with a reformulation of the SBEM approach such that the system dimension is drastically decreased and the methodology can be applied to more complex cases. Moreover, the approach is extended to predict the variance of the field variable at no additional computational cost. After a theoretical introduction, the SBEM is applied to two-dimensional examples with pressure and velocity boundary conditions. The comparison with Monte Carlo simulations shows a good agreement of the results and a reduction in the computational load is achieved.