Resumen de Numerical modelling of sound transmission in lightweight structures
Jordi Poblet Puig
The thesis deals with the numerical modelling of sound transmission, All the analyses are done in the frequency domain and assuming that the structures are linear and elastic. Linear acoustics is considered for the fluid domains. Thus, the fluid-structure interaction problems analysed here are governed by the vibroacoustic equations. The models are applied to the field of building acoustics, with especial interest on lightweight structures. A set of one-dimensional models for single and layered partitions considering finite acoustic domains is developed. Preliminary parametric analyses are done, considering aspects like the acoustic absorption, the structural damping, the separation between layers, the quality of absorbing material, or the influence of the eigenfrequencies of the problem in the isolation capacity. The analytical solution of these situations is available and it is used to test two and three-dimensional models. Numerical-based models for vibroacoustic problems lead to large system of linear equations. This is an important drawback for mid and high-frequencies where the computational costs become unaffordable. The block Gauss-Seidel algorithm has been applied for sound transmission problems. Its performance has been analysed by means of analytical expressions of the spectral radius obtained in one-dimensional situations. Moreover, a selective coupling strategy is developed in order to efficiently iii solve problems where some acoustic domains are strongly coupled (i.e. double walls). In building acoustics, the acoustic domains are often cuboid-shaped rooms. Analytical expressions of the eigenfunctions are well known and can be used in order to obtain the pressure field by means of a modal analysis. A model that combines this with a more general finite element (FEM) description of the structure is presented. This mixed approach is more efficient (time and memory requirements) than a FEMFEM model. The most relevant aspects of the modal-FEM approach are a
