A dual modal formulation for multiple flexural subsystems connected at a junction in energy-based models. (15th March 2019) - Maxit, Laurent; Guasch, Oriol
Highlights: Revision of the modal coupling scheme of statistical energy analysis like models. The modal coupling is not straightforward for multiple connected subsystems. A displacement-stress dual formulation is proposed to tackle that situation. A test case of a floor coupled to two walls at right angle is examined. The dual formulation works fine for strong impedance mismatch between subsystems. Abstract: Statistical energy methods in vibroacoustics, like the statistical energy analysis (SEA) or the statistical modal energy distribution analysis (SmEdA), rely on specific modal coupling assumptions (MCAs) between subsystem modes. These methods assume that the behavior of subsystem mode amplitudes mimic that of oscillators, that the modes within a subsystem are uncoupled, and that the coupling between two different subsystems only takes place through the interaction of resonant modes. In the case of more than two subsystems being connected at a junction, however, it becomes difficult to establish a modal interaction scheme for them. In SEA, the problem is avoided by resorting to the travelling wave approach instead of the modal one. Nevertheless, there is a need for other energy-based methods, like SmEdA, to deal with such a situation. In this work it is proposed to extend the displacement-stress dual formulation, originally intended for two subsystems, to the case of multiple flexural waveguides connected at a junction. Numerical results are presented for a test case consisting of a floor coupled to two walls at right angle. The fulfillment of the MCAs by the dual modal formulation is examined in terms of the impedance mismatch between the floor and the walls.