Keywords: boundary element method, wave propagation, structural vibrations, sound radiation, acoustics.

The increasing number of polluting sound sources and the growing need to improve people's standards of comfort have led to greater efforts being made to find noise reducing solutions. The experimental testing of structures is highly time-consuming and therefore several methods are used to predict the noise radiation from vibrating structures to evaluate the acoustic performance of a particular design. Among them are the finite element method (FEM) [1], the boundary element method (BEM) [2], the statistical energy analyses (SEA) [3] and also some hybrid methods [4].

Almost all noise events are caused by, or at least conducted through, vibrating bodies. This kind of noise generation is very complex and influenced by many variables [5]. In this work the BEM is formulated in the frequency domain and implemented in order to compute the sound transmission by a vibrating single structure excited by a steady state harmonic line load pressure source. This BEM model fully accounts for the air-solid interaction and makes it possible to compute and correlate the structural displacements and the sound pressure level (SPL) obtained. The BEM algorithm was verified by comparing the results for simple circular cylindrical geometries for which the solution is known in closed form. The main aim is to study how certain parameters may change the low frequency sound transmission by a single vibrating structure.

Two different BEM models were implemented. Using the first BEM model it was possible to identify only the panel's structural eigenmodes, and the second model revealed both the structural and the acoustic eigenmodes. These eigenmodes led to a significant increase in the panel's vibration level and the SPL radiated consequently increased. But it was possible to verify that not all acoustic eigenmodes cause an increment in the SPL radiated by the partition panel, given the proximity of some specific nodal lines to the panel. The correlation between the panel vibration velocity and the radiated SPL was confirmed, and a mathematical expression was used to predict the radiated SPL using the panel vibration velocity, with good results.

A set of experimental in situ measurements was taken in order to compare the measured data with the computed BEM results. Two different elastic partitions were tested experimentally, these being a light partition (plasterboard panel) and a heavy partition (ceramic brick wall). The experimental results showed lower oscillations in the level of vibration along the panel or wall for both partitions, compared with the response predicted by the BEM model.

1

S.P. Maluskia, B.M. Gibbs, "Application of a finite-element model to low-frequency sound insulation in dwellings", Journal of Acoustical Society of America, 108(4), 1741-1751, 2000. doi:10.1121/1.1310355

2

P. Santos, D. Mateus, "Modelling sound radiation using a vibrating wall excited by an impact load: a BEM approach", Proceedings of the 19th International Congress on Acoustics - ICA2007, Madrid, Spain, 2007.

3

R.J.M. Craik, "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

4

Z. Tong, Y. Zhang et al., "Dynamic behaviour and sound transmission analysis of a fluid-structure coupled system using the direct-BEM/FEM", Journal of Sound and Vibrations, 299, 645-655, 2007. doi:10.1016/j.jsv.2006.06.063

5

L. Cremer, M. Heckl, E.E. Ungar, "Structure-Borne Sound", Springer, Berlin, 1988.

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