Keywords: airborne sound insulation, impact sound pressure level, flanking transmission, structural joints, boundary element method.

In this paper three models using the boundary element method (BEM) are implemented and used to study the airborne and impact sound insulation, between acoustic spaces, provided by single panels. The first one consists of two acoustic quadrangular spaces separated by a single wall, surrounded by an elastic infinite medium. The second one assumes four two-dimensional acoustic closed spaces separated by slabs and walls. The walls and slabs are modelled as single partitions and are connected by a cross joint. In the third model three two-dimensional acoustic closed spaces separated by single slabs and walls are defined. The walls and slabs are here connected using a T joint.

A BEM algorithm, formulated in the frequency domain, is used to predict the acoustic behaviour provided by three geometries. The algorithm used here makes use of Green functions for the full fluid and elastic medium [1]. The integrations needed are carried out analytically for the loaded element [2,3] and when the element to be integrated is not the loaded element, a Gaussian quadrature scheme is used.

When the load acts in the acoustic medium, the sound pressure level reduction between adjacent rooms provided by both Models 2 and 3 show differences in relation to the result obtained using Model 1. These differences are due to a flanking transmission provided by the slab and due to the different stiffness of the structures of Models 2 and 3. It was also found that in the majority of the frequency range, the differences provided by Model 3 are slightly greater then those provided by Model 2. The structure with a cross junction that connects the walls and the slabs allows a more pronounced reduction in the energy that is transmitted by these elements than the T junction of Model 2, which is more flexible. When the thickness of the structure increases the differences tend to decrease.

When the load acts in the elastic medium, the impact sound pressure level curves obtained using Models 2 and 3 shows an increase at certain frequency ranges when the vibration modes of the structure are excited. As the frequency increases the increase in the sound level with the excitation of the vibration modes of the structure tends to decrease. Although both models have these similar features, they provide quite different curves because the structure natural modes of vibration are excited at different eigenfrequencies. Model 3 provides higher sound pressure levels at low frequency ranges than that obtained using Model 2, resulting from the lower stiffness of the structure.

1

A. Tadeu, E. Kausel, "Green's functions for two-and-a half dimensional elastodynamic problems", Journal of Engineering Mechanics ASCE, 126(10), 1093-1097, 2000. doi:10.1061/(ASCE)0733-9399(2000)126:10(1093)

2

A. Tadeu, P. Santos, E. Kausel, "Closed-form integration of singular terms for constant, linear and quadratic boundary elements - Part I: SH Wave Propagation", Engineering Analysis with Boundary Elements, 23(8), 671-681, 1999. doi:10.1016/S0955-7997(99)00016-8

3

A. Tadeu, P. Santos, E. Kausel, "Closed-form integration of singular terms for constant, linear and quadratic boundary elements - Part II: SV-P Wave Propagation", Engineering Analysis with Boundary Elements, 23(9), 757-768, 1999. doi:10.1016/S0955-7997(99)00017-X

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