Investigation for obtaining a modal coupling scheme in agreement with the SmEdA/SEA models for multi-subsystems connected at a junction

Statistical Energy Analysis (SEA) is commonly used for predicting the vibroacoustic behaviour of built-up structures in the high frequency range, for instance as a reference for the transmission loss regulation EN 12354-1 in the building sector. Statistical modal Energy distribution Analysis (SmEdA) has been developed the last decade as an extension of SEA to the mid-frequency range. The fundament of the two methods is however based on a particular coupling scheme between the subsystem modes. In the case of mechanical impedance mismatch like for two coupled panels with different stiffness, the dual modal formulation allows us obtaining the required modal equations and clearly defines the boundary conditions of the uncoupled-subsystem: the stiffest subsystem should be free at the junction and described by its displacements whereas the other one should be blocked and described by its stresses. This approach can however be difficultly applied to a junction of three or more subsystems having equivalent mechanical impedances. In the present paper, we investigate the possibility to obtain the required modal equations by the use of the Craig-Bampton component mode synthesis. Numerical results are presented for two test cases related to concrete masonry building and are composed by a floor coupled to two walls at right angle. For the first one, the walls and floor have different thickness and mechanical properties whereas for the second one, they have the same ones. It allows us studying the effect of the mechanical impedance mismatch.