Predicting the diffuse vibration transmission across finite junctions between thick plates

Predicting the sound insulation of an engineering system is a complex problem since both direct and flanking transmission can largely influence the sound insulation of the system. When conventionally analyzing flanking transmission, walls and floors are modelled as thin homogeneous plates and the junction is assumed to be of infinite extent. For thick walls or floors and junctions of finite length, it is not immediately obvious how this approach can be adapted. A new approach based on diffuse field reciprocity is proposed to overcome the limitations of the conventional approach. The diffuse field reciprocity relationship can be used to calculate the total energy in a vibrating subsystem based on the direct field dynamic stiffness matrix of the subsystem, i.e., the dynamic stiffness of the equivalent infinite subsystem as observed at the junction. The direct field dynamic stiffness matrix of a thin, isotropic, semi-infinite plate can be analytically derived. For thick or more complex walls or floors the direct field dynamic stiffness can be calculated using finite elements and perfectly matched layers. Using this new approach for calculating vibration transmission across junctions, practical design curves are determined.