Keywords: boundary element method, wave propagation, vibrations, acoustics, noise transmission.

Nowadays there are various numerical procedures available that are very suitable for modelling wave propagation problems in acoustics and vibrations. Among them are the boundary element method (BEM) [1,2,3], the finite element method (FEM) [4], the finite difference method (FDM) and the statistical energy analyses (SEA) [5]. One of the most successful methods used to model acoustics and vibrations problems, particularly in unbounded media, is the Boundary Element Method, given the great suitability to model this kind of problems. Perhaps the biggest advantage of this method is that only requires the discretization of the problem surfaces (boundaries), which significantly reduces the number of elements needed, compared with other methods (FEM or FDM). This is possible given the automatic satisfaction of the far field conditions in the BEM formulation, rendering the discretization of the entire domain unnecessary.

In this work the Boundary Element Method is used to model several wave propagation acoustics and vibration problems. Five BEM models are presented in order to study some relevant engineering problems, including direct noise transmission, flanking noise transmission and the noise radiated by a vibrating wall excited by an impact load. These models avoid having to limit the panel thickness (wall or slab), which is required with the Kirchhoff and Mindlin theories, and takes the coupling between the solid wall and the fluid (air) fully into account. Another particularity of these BEM models algorithms lies in the analytical evaluation of singular integrals for the loaded element. The BEM responses are obtained in the frequency domain, but some time-domain results are also presented. The BEM responses allow the assessment of the importance of both acoustic and structural eigenmodes in the noise transmission between dwellings. The BEM results were compared with other methods, e.g. the theoretical mass law, the analytical method [6] and the SEA [7]. These simplified methods were not able to predict fluctuations in the insulation conferred by a wall, generated by acoustic eigenmodes and by the bending modes of the wall (structural eigenmodes), which appear to fully define its acoustic behaviour. Therefore, simplified models should be used with caution in the low frequency range.

1

R.D. Ciskowski, C.A. Brebbia, "Boundary element methods in acoustics", Computational Mechanics Publications, Southampton, 1991.

2

Ch. Provatidis, N. Zafiropoulos, "On the 'interior Helmoltz integral equation formulation' in sound radiation problems", Engineering Analyses with Boundary Elements, 26, 29-40, 2002. doi:10.1016/S0955-7997(01)00079-0

3

A. Tadeu, P. Santos, "Assessing the effect of a barrier between two rooms subjected to low frequency sound using the Boundary Element Method", Applied Acoustics, 64(3), 287-310, 2003. doi:10.1016/S0003-682X(02)00074-9

4

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

5

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

6

A. Tadeu, J. António, "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

7

E. Sarradj, FreeSEA v0.91 software, www.free-sea.de.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £145 +P&P)