Efficient models for building acoustics: combining deterministic and statistical methods

摘要

Modelling vibroacoustic problems in the field of building design is a challenging problem due to the large size of the domains and the wide frequency range required by regulations. Standard numerical techniques, for instance finite element methods (FEM), fail when trying to reach the highest frequencies. The required element size is too small compared to the problem dimensions and the computational cost becomes unaffordable for such an everyday calculation. Statistical energy analysis (SEA) is a framework of analysis for vibroacoustic problems, based on the wave behaviour at high frequencies. It works directly with averaged magnitudes, which is in fact what regulations require, and its computational cost is very low. However, this simplified approach presents several limitations when dealing with real-life structures. Experiments or other complementary data are often required to complete the definition of the SEA model. This thesis deals with the modelling of building acoustic problems with a reasonable computational cost. In this sense, two main research lines have been followed. In the first part of the thesis, the potential of numerical simulations for extending the SEA applicability is analysed. In particular, three main points are addressed: first, a systematic methodology for the estimation of coupling loss factors from numerical simulations is developed. These factors are estimated from small deterministic simulations, and then applied for solving larger problems with SEA. Then, an SEA-like model for non-conservative couplings is presented, and a strategy for obtaining conservative and non-conservative coupling loss factors from numerical simulations is developed. Finally, a methodology for identifying SEA subsystems with modal analysis is proposed. This technique consists in performing a cluster analysis based on the problem eigenmodes. It allows detecting optimal SEA subdivisions for complex domains, even when two subsystems coexist in the same region of the geometry. In the second part of the thesis, the sound transmission through double walls is analysed from different points of view, as a representative example of the complexities of vibroacoustic simulations. First, a compilation of classical approaches to this problem is presented. Then, the finite layer method is proposed as a new way of discretis-ing the pressure field in the cavity inside double walls, specially when it is partially filled with an absorbing material. This method combines a FEM-like discretisation in the direction perpendicular to the wall with trigonometric functions in the two in-plane directions. This approach has less computational cost than FEM but allows the enforcement of continuity and equilibrium between fluid layers. It is compared with experimental data and also with other prediction models in order to check the influence of commonly assumed simplifications. Finally, a combination of deterministic and statistical methods is presented as a possible solution for dealing with vibroacoustic problems consisting of double walls and other elements. The global analysis is performed with SEA, and numerical simulations of small parts of the problem are used to obtain the required parameters. Combining these techniques, a realistic simulation of the vibroacoustic problem can be performed with a reasonable computational cost.%La modelización de problemas vibroacústicos en el ámbito de la edificación supone un desafío debido al gran tamaño de los dominios y al amplio rango frecuencial requerido por las normativas. Las técnicas numéricas estándares, como por ejemplo el método de los elementos finitos (MEF), fallan al tratar de alcanzar las frecuencias más altas, puesto que el tamaño de elemento requerido es muy inferior a las dimensiones del problema y el coste computacional asociado es excesivo para tratarse de un cálculo tan cotidiano.