STOCHASTIC BOUNDARY ELEMENT METHOD TO PREDICT THE EFFECTS OF GEOMETRICAL UNCERTAINTIES IN THE MID-FREQUENCY VIBRO-ACOUSTIC ANALYSIS

The Boundary Element Method (BEM) is a reliable technique to solve low-frequency acoustic problems. Nevertheless, when frequency increases, model uncertainties influence the response and a deterministic approach may become meaningless. In this paper, a Stochastic Boundary Element Method for the vibro-acoustic modelling over a wide frequency range is presented. Firstly, parametric geometrical uncertainties are introduced into the classic BEM equations. Secondly, under proper assumptions, auxiliary relations are added to describe the energetic behaviour of the system. As a result, the low-frequency response is characterised by the deterministic, resonant behaviour. When the wavelength becomes smaller, uncertainties influence the response and the numerical prediction starts being smoothened. Although the overall computational cost increases, if compared to the standard BEM, the average behaviour and its variance are predicted without massive Monte Carlo (MC) simulations of the structure. Moreover, because of its energetic nature, less elements per wavelength are required and smaller models are valid over a broad frequency range. Different conditions for the uncertainties on the model geometry are applied to practical cases to prove the capabilities and limitations of the methodology. Results are compared with MC simulations both in terms of solution accuracy and computational time.