Coupling strength evaluation in vibro-acoustic systems

Statistical energy analysis (SEA) and related approaches to the high-frequency analysis of vibro-acoustic systems rely on a conceptual division of the system into subsystems that are assumed to carry a diffuse field and to be weakly coupled. Weak coupling in this context means that the exchange of energy between any two subsystems can be described in terms of their uncoupled free vibration modes. In this paper, a criterion is derived for assessing the coupling strength in the general case where the subsystems are rigidly coupled and/or via a deterministic linear dynamic component. First, the subsystems are taken to be deterministic and in a subsequent analysis they are taken to be diffuse subsystems in an SEA setting. The criterion is then elaborated such that it can be directly evaluated from quantities that appear in the SEA power balance. In this process, the hybrid deterministic-SEA approach is employed such that subsystems and connections of arbitrary complexity can be tackled in a rigorous way. In one of its approximate forms, the proposed general coupling strength criterion is shown to be identical to the γ criterion that has appeared in the literature for the coupling strength assessment of some special cases. The use of the criterion is illustrated with instructive validation examples involving two diffuse plate subsystems rigidly connected and/or via a deterministic beam, whose dynamic behaviour influences the coupling strength.