A hybrid numerical approach in the medium frequency range for vibroacoustic analysis

In linear dynamical analysis of complex systems the use of a deterministic method faces difficulties in the high frequency range due to the requirement of excessive number of degrees of freedom and also the sensitivity to manufacturing imperfections at high frequencies. To overcome these difficulties statistical approaches are used, which take advantage of the statistical properties of the dynamic behavior at these ranges of frequency. But statistical approaches have low frequency limitations due to the underlying assumptions, leaving a range of mid-frequency computation with no definite methodology. In this paper we present a new hybrid approach for low and medium-frequency vibrational and vibroacoustic analysis of complex structures using a Finite Element Methodology (FEM) and Statistical Energy Analysis (SEA). The procedure presented is based on the Hybrid Analysis based on Component Mode Synthesis sub- structuring (HA-CMS) method. This method identifies the modes within the substructures that, in turn, will be modelled as subsystems by a sub-structuring procedure. The approach here presented consists of two steps: (a) Obtaining a sub-structuration of the system using a modified Craig-Bampton method, in which the frontier elements of the Craig- Bampton will be again sub-structured with the objective of obtain smaller subsystems of the interface elements between the mean subsystems of the Craig-Bampton partition. (b) Partitioning of the system degrees of freedom into a global and local set to take advantage of the statistical properties of the frequency response at higher frequencies. Thereby, a hybrid FE-SEA model can be obtained.