Robust estimation of the energy flow in timber structures

Within the context of efficient and sustainable design of buildings, a trend towards lightweight structures, e.g. timber structures, is recognizable. This trend implies the necessity of being able to predict serviceability and comfort as well as sound transmission in order to fulfill building requirements. To generate reliable prediction methods, the transfer of energy between building components has to be investigated. The Finite Element Method (FEM) is a convenient tool to predict the vibroacoustic behavior. However, without appropriate post-processing it is limited due to the sensitivity of the results at higher frequencies. In the mid-frequency range a sufficient number of modes per band enables the use of statistical methods like the Statistical Energy Analysis (SEA). It delivers averaged results and thus copes with the sensitivity. But the SEA is always limited to the governing partial differential equation related to wave types of the structures. E.g. through-thickness effects of plate-like structures at high frequencies are not modeled. As both techniques have a restricted validity regarding the frequency range, averaging techniques of the SEA are applied in the post-processing of the FEM to obtain an adapted hybrid approach. In case the load is unknown a robust estimation of the energy flow is needed for a general prognosis. The SEA delivers an ensemble average, but only within a limited frequency range, whereas one realization of the Energy Flow Analysis (EFA) simulates one specific load case. By averaging over varying random load cases, the EFA is able to predict the energy flow - which is robust regarding the load - inside a certain confidence interval. This contribution will focus on the statistical behavior of the energy flow due to variation of the number of loads and realizations. Furthermore, a comparison with a SEA model will be performed.