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Prediction of the Sound Insulation of Layered and Periodic Wall and Floor Systems while Accounting for Modal Behaviour
Book - Dissertation
Lightweight systems such as cross-laminated timber elements, sandwich panels, gypsum board walls,... are emerging in building construction. Because of their relatively low weight and complex vibro-acoustic behaviour, achieving a sufficient level of sound insulation with such systems is however challenging. The aim of this research is to develop a sound transmission loss prediction method, which exhibits similar accuracy as a comparable numerical tool so as to avoid the need of extensive experimental prototype testing in a transmission suite, but proves to be more efficient allowing it to be used as a design tool. The new method considers a model of the transmission suite, consisting of a source room, the wall or floor and the receiver room. As a result, two novel prediction tools were developed in this PhD project for two different applications: (1) thick and layered building elements and (2) periodic building elements.At high frequencies, the sound transmission loss through thick or layered structures can be computed with high accuracy in the frequency-wavenumber domain using the semi-analytical transfer matrix method, but it has important limitations. First, the system is assumed to be of infinite extent. At lower frequencies however, neglecting the modal behaviour of the wall can lead to large prediction errors. Second, only the mean of the sound transmission loss can be computed by the transfer matrix method, while the variance, inherent to the diffuse field assumption in the rooms, can not be obtained. Therefore, the transfer matrix approach is extended in two ways. The modal behaviour of rectangular walls and floors with simply supported boundary conditions is approximately accounted for by means of an approximate modal transfer matrix method. Using the diffuse reciprocity relationship, a hybrid approximate modal transfer matrix - statistical energy analysis method is then developed, enabling the rooms to carry a diffuse field (as in statistical energy analysis), while modelling the finite-sized wall deterministically with the modal transfer matrix method. The important advantage of the statistical room models is that the uncertainty on the transmission loss predictions due to the assumption of diffuse sound fields in the rooms, can be assessed. The approach is validated against alternative numerical prediction models and experimental data. The application of the proposed approach is however limited to thick and layered structures such as sandwich panels or laminated glazing. Therefore, the extension towards more complicated, finite-sized building elements which exhibit spatial periodicity, is considered in this work by invoking periodic structure theory. A hybridization between periodic finite element modelling and statistical energy analysis is achieved. Modal behaviour is accounted for within the periodic structure theory by combining the propagating waves resulting from the free wave propagation analysis of the periodic unit cell, into standing waves, which satisfy the simply supported boundary conditions. A spatial Fourier transformation of the system of equations allows for a fast conversion of the mode shapes of the unit cell to the entire finite-sized structure. The methodology is illustrated by verifying the predicted sound insulation for two orthotropic and two periodic structures with alternative predictions involving a full finite element model of the entire structure, and validating the results with experimental data.