# Development of a Vibroacoustic Stochastic Finite Element Prediction Tool for a CLT Floor
## 1 Introduction  
Multi-story wooden constructions have increased in the market during the last two decades. However, this kind of constructions still face the challenge coming from low-frequency sound insulation. Although these types of buildings comply with the present regulations, subjective ratings of inhabitants have shown complaints [1; 2; 3; 4; 5; 6] due to low-frequency impact noise. One of the important reasons resulting in this discrepancy between the subjective and objective evaluations is that the current standards are initially designed for heavy constructions, i.e., concrete constructions, but without an appropriate modification, they are directly applied to the wooden constructions. On the other hand, the low frequency impact noise is neglected in the standardized impact sound insulation evaluations. From recent research [3], it was shown that the subjective ratings are correlated better with the objective ratings with the help of the adaptation term \(C_{I,\,50-3000}\) following the standard ISO 717-2 [7]. But the correlation between the inhabitants' satisfaction (reported by means of questionnaires) and objective ratings can be further improved by taking the measurement from 20 Hz in comparison with the measurements performed from 50 Hz instead. Furthermore, the dynamic behavior of wood (as a natural material) is hard to predict due to its inhomogeneity. As a consequence, product development in the wooden industry is still based on empirical models and experimental tests, which could lead to an over-designed and expensive acoustical improvement solution. To end that, more knowledgeabout wooden construction is needed and accurate and handy prediction tools are called for in order to enable acoustic comfort in wooden constructions, especially in a low-frequency range. The finite element (FE) method is a widely employed approach to develop numerical prediction models in wooden industry. By performing numerical simulations, experimental acoustical tests can be reduced, and parametric studies can also be carried out to investigate the influence of specific geometrical changes in construction as well as the influence of the variations/uncertainties in material properties, which always have a markable influence on the results. In Reference [8], experimental tests were conducted on a full-scale cross-laminated timber (CLT) floor. The material properties of the CLT were collected from the literature and then put into the established FE model to compare the simulation results with the measured ones. A better correlation between the testing results and the modelling results was attained after tuning the collected material properties of CLT. The latter points out the importance of knowing the material properties if a proper calculation of dynamic properties needs to be achieved. A similar conclusion was drawn in References [9; 10; 11]. However, one should know that the variety of the wood species, the variation in theoretical identical wood structure, as well as the lack of material properties data base, make the reliable material properties of wood difficult to obtain. Consequently, the calibration of a model is always tedious and time-consuming. Moreover, even with the calibrated model to predict the theoretical identical wooden structure, the prediction results may be different from the realistic case due to the uncertainties induced by wooden material properties, workmanship and geometrical details in structures. As a result, the deterministic model may not be representative enough in a realistic situation. Therefore, it is a necessary step to quantify the variations in the model's outputs in order to ultimately establish an accurate prediction tool. To achieve that, uncertainties of the wood material properties can be addressed in a model by introducing probabilistic parameters [6]. In Reference [12], a generalized probabilistic model was constructed to take into account the statistical fluctuation associated with the elastic properties in the model.