Keywords: boundary element method, flanking sound transmission, direct sound transmission, wave propagation, solid-fluid interaction.

Sound insulation between two contiguous rooms is a complex physical phenomenon that depends on direct and indirect airborne sound transmission. Although direct sound transmission can be found by means of laboratory experiments, flanking sound transmission is still very difficult to determine in the laboratory. In fact, a major difficulty, often encountered at the design stage, is related to predicting this second type of sound transmission. Several numerical schemes are available to predict the flanking sound transmission in buildings. statistical energy analysis (SEA) is one of those numerical techniques, suitable for studying sound transmission through complex structures, particularly at higher frequencies [1]. The finite elements method (FEM) is another numerical technique that can be used to model and predict flanking sound transmission in buildings [2]. Another numerical technique that can be used to model and predict the flanking sound transmission in buildings is the boundary elements method (BEM) [3].

In this paper the BEM is used to study the importance of room support conditions in the sound insulation conferred by a single partition wall dividing two contiguous rooms. The separating wall can be modelled with different mechanical properties from the surrounding elastic structure. The models assume concrete or ceramic material and the influence of the construction elements' support conditions is analysed. This model is then used to study the importance of the flanking or direct sound transmission for the sound pressure recorded in the second receiving room. The incident pressure field is generated by a cylindrical line load placed in one of the rooms. The BEM algorithm is formulated in the frequency domain and enables the sound pressure and the displacements in the separating element and surrounding structure to be determined. This method models the dwelling's surfaces and the separating wall completely, and takes full account of the coupling between the fluid (air) and the solid elastic medium. The structure is modelled with a number of boundary elements, defined according to the excitation frequency of the harmonic source. The sound insulation obtained is characterised, identifying the location of insulation dips in the frequency domain, with those dips related to both structural and acoustical natural dynamic vibration modes. The BEM results are compared with other methods, namely: the Law of Theoretical Mass [4], the Analytical Method [5], the European Simplified Method [6] and the Statistical Energy Analysis (SEA) [7].

The frequency results reveal that sound pressure levels, and therefore the sound transmission, appeared to be highly dependent on the room's structural and acoustic eigenmodes. The simplified methods (mass law, analytical method and SEA) were not able to predict localized oscillations in the sound reduction curve caused by these acoustic and structural eigenmodes. The analytical method can identify a dip in the sound reduction curve related to the coincidence effect, while the mass law and the SEA were not able to detect this acoustic phenomenon. The BEM method shows a tendency for lower predicted sound reduction in the vicinity of this critical frequency, however the numerous oscillations make this hard to observe. When the partition wall is made of ceramic instead of concrete material, the sound reduction falls and the oscillations are less pronounced.

The results obtained using the BEM models that allow the existence of flanking sound transmission show a significant decrease in the sound insulation, as expected. This was true also for the SEA results. Analysing the three different BEM models' results it was possible to confirm that the support conditions of the rooms surrounding structure play an important role, leading to significant variations in the flanking sound transmission. The SEA shows a general tendency to underestimate the flanking sound transmission when compared with the BEM results. When the partition wall is less stiff (ceramic wall) the oscillations in the flanking responses are much smaller, and therefore the BEM and the SEA results responses are closer.

1

Craik, R.J.M., "The contribution of long flanking paths to sound transmission in buildings", Applied Acoustics, 62, 29-46, 2001. doi:10.1016/S0003-682X(00)00020-7

2

Hopkins, C., "Vibration transmission between coupled plates using finite element methods and statistical energy analysis. Part 1: Comparison of measured and predicted data for masonry walls with and without apertures", Applied Acoustics, 64, 955-973, 2003. doi:10.1016/S0003-682X(03)00062-8

3

Santos, P., Mateus, D., Tadeu, A., "Predicting flanking sound transmission between two contiguous rooms", ICSV12 - Twelfth International Congress on Sound and Vibration, Lisbon, Portugal, July 2005.

4

Beranek, L.L., Vér, I.L., "Noise and Vibration Control Engineering", New York: Wiley, 1992.

5

Tadeu, A., António, J., "Acoustic insulation of single panel walls provided by analytical expressions versus the mass law", Journal of Sound and Vibration, 257(3), 457-475, 2002. doi:10.1006/jsvi.2002.5048

6

EN 12354-1:2000 Building Acoustics - Estimation of acoustic performance of buildings from the performance of elements - Part 1: Airborne sound insulation between rooms, European Standard, 2000.

7

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