Extension of SEA model to subsystems with non-uniform modal energy distribution

International audienceIn order to enlarge the application field of Statistical Energy Analysis (SEA), a reformulation is proposed. The model described here, Statistical modal Energy distribution Analysis (SmEdA), does not assume equipartition of modal energies contrary to classical SEA. Theoretical derivations are based on dual modal formulation described in [1,2] for the general case of coupled continuous elastic systems. Basic SEA relations describing power flow exchanged by two oscillators are used to obtain modal energy equations. They permit to determine modal energies of coupled subsystems from the knowledge of modes of uncoupled subsystems. The link between SEA and SmEdA is established and render possible to mix the two approaches: SmEdA for subsystems where equipartition is not verified and SEA for other subsystems. Three typical configurations of structural couplings are described for which SmEdA improves energy prediction compared to SEA: (a) coupling of subsystems with low modal overlap. (b) coupling of heterogeneous subsystems. (c) case of localised excitations. The application of the proposed method is not limited to academic structures, but could easily be applied to complex structures by using finite element method (FEM). In this case, FEM are used to calculate the modes of each uncoupled subsystems; these data are then used in a second step to determine modal coupling factors necessary to SmEdA to modelise the coupling