Numerical probabilistic analysis of structural/acoustic systems

A methodology that accounts for structural variability in the acoustic response of structural/acoustic systems is presented. The new methodology integrates an advanced mean value first-order probabilistic method with finite element analysis (FEA) and boundary element analysis (BEA) in order to compute the probabilistic acoustic response of a structural/acoustic system subjected to a deterministic excitation. The advanced mean value (AMV) method is used to evaluate the probabilistic response from a linear response surface that is corrected for higher-order terms. FEA and BEA are combined for computing the performance function (i.e., acoustic response) each time that it is requested by the AMV algorithm. The AMV/FEA/BEA methodology is used to illustrate the difference between the probabilistic response of a system and the equivalent deterministic simulation through examples. The interaction between the distinct acoustic normal modes and the structural normal modes that shift due to structural variability constitutes the main source of the difference between the probabilistic and deterministic acoustic results. The non-monotonic nature of the structural/acoustic response is also considered in this development. Results are validated using a Monte Carlo simulation and a standard radius-based importance-sampling algorithm. On the basis of computational time and accuracy, the methodology is concluded to be a viable method of numerically calculating the probabilistic acoustic response of a structural/acoustic system due to structural variability.