Modelling the sound insulation of corrugated roof structures : an extended transfer matrix approach

Over the course of this work, the transfer matrix method (TMM) was implemented and studied for its potential in predicting the sound insulation characteristics of corrugated dual leaf roof structures. A model of periodically connected plates, using Fourier expansions, was derived independently and extended in this work to include the stiffness of connectors and orthotropic plates, and intermediate beams in the framework of the structure. The same principles were applied in deriving the transmission loss through periodically stiffened plates, as a proxy for corrugated panels. At the same time, corrugated plates were modelled as equivalent orthotropic panels, a process which is compatible with the TMM without particular modifications. Infill materials were modelled using simple fluid representations and more complex poroelastic behaviour. The point-connected plate models were combined with the TMM to enable multiple layers of infill materials between the two plates, by using an effective fluid approach. The stiffness of typical roof connectors was obtained with numerical simulations, and used in predicting transmission loss. Corrections were introduced to simulate diffuse laboratory conditions and enable meaningful comparisons to available data. The limitations of a simple orthotropic plate model compared to laboratory measurements and the ribbed plate model were identified. A number of measurements of dual leaf partitions and full roof systems were compared to the TMM and point-connected plate models, finding typically good agreement at low to mid-frequency, and a strong dependence of high frequency transmission loss on connector stiffness