A Hybrid Method to Predict the Distribution of Vibro-Acoustic Energy in Complex Built-Up Structures

Predicting the distribution of vibro-acoustic energy in complex built-up structures in the mid-to-high frequency regime is often a difficult task because “numerically exact” results obtained by Finite Element Method (FEM) may be of little practical value; the vibro-acoustic response of “identical” structures assembled as part of a manufacturing process is very sensitive to small changes in material parameters and/or variability in the shape of the structure. These differences may lead to large changes in the resonance spectrum and a full (and time expensive) FEM calculation for an individual sample has at best statistical significance. This problem becomes severe in the mid-frequency regime where the high-frequency techniques, such as Statistical Energy Analysis (SEA), are not yet available. Mid-frequency problems usually occur in structures with large variation of local wavelengths and/or characteristic scales. One of the possible ways of solving them is to develop hybrid methods which incorporate both FEM and SEA. The method presented here is based on splitting the whole system into a number of subsystems, which can be treated with either FEM or an SEA approach depending on the local wavelength. The subsystems where the wavelength is of the same order as the characteristic scale are labeled “deterministic” and are treated with FEM. The other subsystems are labeled “stochastic”, and their averaged response can be reduced to a weighted random diffuse field correlation function. It is demonstrated that this approach results in an SEA-like set of linear equations which can be solved for the energies in the stochastic subsystems.