# Development of a Vibroacoustic Stochastic Finite Element Prediction Tool for a CLT Floor
## 6 Results and Discussion
### Calibration of the CLT Panel  
In this section, the best combination of elastic constants of CLT should be identified by selecting the best NRFDs and MACs among 100 simulations. To select the best combination of mechanical constants, the NRFDs of the first four resonances at point 11, point 13, point 17, and point 24 were calculated. The simulations with the smallest NRFDs of the first four resonances at each point were selected from 100 simulations at each point. The NRFDs of the simulated and measured eigen-frequencies at four excitation positions are shown in Figure 15. It can be seen from the NRFDs of each excitation position that the NRFDs of the first four resonances are lower than 5%. However, the NRFDs of the 5 th and 6 th resonances are relatively high when compared to the first four resonances. This result emphasizes that more structural details should be involved in the FE model to calibrate the dynamic behavior of CLT in the frequency range higher than 100 Hz. However, only NRFD values are not enough to justify the best combination of elastic constants. Since the NRFDs can only represent the simulated eigen-frequency shifts when compared with the experimental results, the mode order can be different even with a low NRFD. Therefore, MAC numbers are needed to validate the model by ensuring the modes in the same order with reference even if there are low NRFDs. The simulated eigen-frequencies and mode shape are reported in Table 1 and Figure 17. The corresponding material properties of CLT are reported in Table 3. Figure 18 shows that the first six simulated modes are in the same order with the measured ones. However, there exist two extra modes in the simulation results. Figure 14: (**a**) Air gaps in the laminate layers of CLT. (**b**) No edge-bonding of CLT. Figure 13: Measured (blue) and simulated (red) FRFs at point 11, 13, 17, and 24. Figure 16: _Cont._  
Figure 15: NRFDs of the first six resonances at points 11, 13, 17, and 24. Figure 17: _Cont._  
Figure 17: Measured and simulated modes. Figure 18: Cross-MAC. The same results can also be seen in the mobility of different excitation points of the lowest NRFD values (c.f. Figure 19). The simulated FRFs at these four different excitation points correlate better with the measured ones, while there are extra peaks and eigen-frequency shifts in the simulated FRFs in the frequency range from 110 Hz to 170 Hz. We suspect that these discrepancies are higher than the 110 Hz result from the over-simplified homogenous laminated FE model, which ignores the geometrical details contained in the real CLT panel. Yet, the boundary condition set-up in the model could not describe the real measurement boundary conditions. The dynamic properties of wooden structures highly depend on the material properties of the structure, the geometry details, and the workmanship. Consequently, the deterministic model may not be able to represent the dynamic response of the wooden structures in a realistic way. A calibrated model may not be able to accurately predict the dynamic behavior of the theoretical identical wooden structure due to the uncertainties. The stochastic method is applied in this case to quantify the uncertainties induced by material properties so that this model can estimate the dynamic response of a class of wooden structures, instead of only one structure. Moreover, the influence of material properties on the vibration of CLT is the coupling effect of Young's moduli and shear moduli in all directions, so that calibration is always time consuming and tedious work to find the appropriate combination of elastic constants in different directions. The calibration employing the stochastic approach could start from the material properties collected from the literature and set the mathematical and physical constraints to generate the input data to find the best combination of the mechanical constants of the under investigated structure. This method could automate the calibration step to avoid the repetitive manual calibrations.