A hybrid boundary element-statistical energy analysis for the mid-frequency vibration of vibro-acoustic systems

Based on the concept of hybrid Finite Element (FE) analysis and Statistical Energy Analysis (SEA), a new hybrid method is developed for the mid-frequency vibration of vibro-acoustic systems. The Boundary Element (BE) method is used to describe the motion of a deterministic acoustic cavity. By enforcing the continuity conditions of displacement and velocity at the coupling interface, the dynamic coupling between the deterministic acoustic cavity and the statistical structure described by SEA is established. Then, a hybrid BE-SEA method for the mid-frequency vibration of vibro-acoustic systems is proposed. Post-processing provides formulations for calculating the sound pressure at points inside the acoustic cavity. Due to the nature of the BE method for acoustics, the proposed method not only has few degrees of freedom, but also automatically satisfies the Sommerfeld radiation condition at infinity for exterior acoustics problems. A numerical example compares results from the proposed hybrid BE-SEA method with those from the hybrid FE-SEA method and Monte Carlo simulation. The comparison illustrates that the proposed method gives good predictions for the mid-frequency behavior of vibro-acoustic systems and has the fewest degrees of freedom