This thesis examines the transmission of sound through lightweight parallel plates, (plasterboard double wall partitions and timber floors). Statistical energy analysis was used to assess the importance of individual transmission paths and to determine the overall performance. Several different theoretical models were developed, the choice depending on the frequency range of interest and method of attachment of the plates, whether point or line, to the structural frame. It was found that for a line connected double wall there was very good agreement between the measured and predicted results, where the dominant transmission path was through the frame and the cavity path was weak. The transition frequency where the coupling changes from a line to a point connection is when the first half wavelength is able to fit between the spacings of the nails. For point connected double walls, where the transmission through the frame was weaker than for line connection, the cavity path was dominant unless there was absorption present. When the cavity was sufficiently deep, such that it behaved more like a room, the agreement between the measured and predicted results was good. As the cavity depth decreases the plates of the double wall are closer together and the agreement between the measured and predicted results were not as good. Detailed experiments were carried out to determine the transmission into the double wall cavities and isolated cavities. It was found that the transmission into an isolated cavity could be predicted well. However, for transmission into double wall cavities the existing theories could not predict transmission accurately when the cavity depth was small. Extensive parametric surveys were undertaken to analyse changes to the sound transmission through these structures when the material or design parameters are altered. The SEA models are able to identify the dominant mechanisms of transmission and will be a useful design tool in the design of lightweight partitions and timber floors.

Multilayered structures have many application in industry and society: they have peculiar properties and serve a variety of purposes, like structural support, thermal insulation, vibrational and acoustic isolation. This thesis concerns the prediction of sound transmission in multilayered structures. Two problems are herein investigated: the transmission of energy through structures and the transmission of energy along structures. The focus of the analysis is on the mid to high frequency range. To predict sound transmission in these structures, statistical energy analysis (SEA) is used.SEA models are devised for the prediction of the sound reduction index for two kinds of multilayered structures, double-walls used in buildings and trim-panels in vehicles; the double-walls comprise an air cavity in between flat plasterboard or glass plates, whereas the trim-panels a porous layer in between curved aluminium and rubber layers. The SEA models are based upon the wave-types carrying energy. The novelty in these SEAs is an element describing the waves in the air cavity, or in the porous layer, fully coupled to the mass-impeded external layers. Compared to measurements, the proposed SEA performs well: for double-walls, it performs better than previous models; for trim-panels, it is an original result. The parameters of the new SEA element, such as modal density, are derived from the coupling equations describing the fully coupled waves. For double-walls, these equations are derived via Newton's laws. For trim-panels, a variational approach based upon a modified Hamilton's principle valid for non-conservative systems is preferred, because it is a powerful machinery for deriving equations of motion and coupling conditions of a medium as complex as the porous layer. The modified Hamilton's principle for non-conservative systems is based upon a self-adjoint functional analogous to the Lagrangian, inspired by Morse and Feshbach's construction. A self-adjoint variational principle for Biot's equations in the displacement formulation is devised. An equivalent mixed formulation is obtained changing the coordinates of the displacement formulation via Lagrange multipliers. From this mixed formulation, the Lagrangian for a porous material with a limp frame is derived, which yields the continuity of the total displacement of the porous layer. Lagrange multipliers help to obtain the correct coupling functionals between a porous material and a solid. The Lagrange multipliers introducing the continuity of the frame and the solid displacements equal the traction of the in-vacuo frame, thus disappearing if the latter is limp. Measurements to gather material parameters for a Biot model of the porous layer have been conducted.The effects of spatial energy decay in the transmission along structures predicted by SEA is studied: a major effect is the increased relevance of indirect coupling loss factors between SEA elements. This may jeopardize the usefulness of SEA at higher frequencies. / <p>QC 20130218</p>