Influence of Structural Periodicity on Vibration Transmission in a Multi-Storey Wooden Building

Noise is a nuisance to people, and buildings should therefore be designed to prevent propagation of sound and vibration in the audible frequency range as well as the range of frequencies relevant to whole-body vibrations of humans. In heavy structures made of concrete and masonry, a source with high energy content is required to mobilise the inertia. However, for lightweight building structures made of wood, less energy is required to produce vibrations since the mass is smaller. This leads to a high risk of sound and vibration propagation in terms of direct as well as flanking transmission. However, lightweight structures are typically periodic in the sense that joists and studs are placed with a repetition of the same distance along each panel. Further, in a multi-storey building the geometry of entire rooms may be repeated along the horizontal and vertical directions.
Such periodicity is known to result in pass bands and stop bands regarding wave propagation. The paper focuses on analysing and quantifying the effects that a change in the structure, especially regarding the periodicity, has on the overall dynamic performance in the low to mid frequency range up to 250 Hz. The analysis is performed by means of a finite-element model. Firstly, a rigorous solid finite-element model is made for each wall and floor panel. Secondly, reduced models with significantly fewer degrees of freedom are obtained by component mode synthesis, augmenting Guyan reduction with a number of internal Eigen modes. Using a substructure approach, the panels are then combined to a global model of a multi-storey building. Example Eigen modes of a single floor panel and the global building are presented. Vibration caused by point force excitation is finally analysed in the frequency domain as well as the time domain.