SEA model of coupled structures by means of periodic Finite Element models of the subsystems

Statistical Energy Analysis (SEA) often relies on simplified analytical models to compute the parameters required to build the power balance equations of a coupled vibro-acoustic system. However, the vibro-acoustic of modern structural components, such as thick sandwich composites, ribbed panels, isogrids and metamaterials, is often too complex to be amenable to analytical developments without introducing further approximations. To overcome this limitation, a more general numerical approach is considered in this paper. Under the assumption that the structure is made of repetitions of a representative unit cell, a Finite Element (FE) model of the unit cell can be used to compute the parameters necessary to build the power balance equations. Following previous publications, the diffuse field reciprocity relationship is invoked to obtain closed formulas for the SEA parameters, leading to a more general power flow model. In this context, the direct field dynamic stiffness matrix of the SEA subsystems at the connection is needed to compute the SEA coupling coefficients. It is shown how such direct field operator can be computed from the FE model of the unit cell. Unit cells of different constructions are considered to demonstrate the effectiveness of the approach.