# Damping Assessment of Lightweight Timber Floors Under Human Walking Excitations
## 3 Results and Discussion
### Fundamental Vertical Vibration Frequencies and Modal Shapes  
Table 5 shows the fundamental vibration frequencies (first resonant frequency) for all floors, obtained through the EFDD and SSI-UPC methods.  
From Table 5, it can be observed that all floors can be classified as high frequency according to [24], since their fundamental vibration frequencies were always greater than 10 Hz. Concerning modal identification methods, both EFDD and SSI-UPC were able to determine very similar fundamental frequencies. The percentage differences between the methods did not exceed 4%. In addition, the frequency measurements were stable, since the coefficients of variation did not exceed 6%. These low values of the coefficients of variation also suggest that the floors had a predominantly linear elastic behavior. If the nonlinearity had been high, the vibration frequencies would have a more significant dispersion for the 36 person walks executed. Therefore, if there was incursion in the non-linear range, it was very slight, and mainly related to the activation of minor friction mechanisms between timber joints. From the above, it follows that the assumption of the floor's linear behavior is still reasonably valid.  
Similarly, it can be observed that for laboratory floors, as the span length decreases, the vertical frequency and, therefore their stiffness, increases. Besides, the floors that had steel-based supports achieved higher frequencies than those that were wood-based supported. This effect was more evident in the floors of shorter span lengths, and disappeared as the span lengths increased.  
For the in-situ floors, the effect of the presence of a ceiling and partition walls in the vibration frequency could be observed. Both the Field-2.4-W and Field-3.1-W floors had fundamental frequencies that were 20% lower than the laboratory floors with similar lengths. Therefore, it was observed that both the ceiling and partition walls increased the floors' mass, but not their vertical stiffness.  
In order to confirm that the vibration frequencies found with the EFDD and SSI-UPC methods correspond to the fundamental vibrational mode of the floors, it was necessary to graph their modal shapes. Figures 11 and 12 show some examples of the fundamental vibration modes found for both laboratory and in-situ floors.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Series**} & \multicolumn{2}{c}{**EFDD**} & \multicolumn{2}{c}{**SSI-UPC**} & \multirow{2}{*}{**Difference (\%)**} \\ \cline{2-2} \cline{4-6}  & **Mean Value** & **Coef. of** & **Mean Value** & **Coef. of** & **SSI–EFDD** \\  & **(Hz)** & **Variation (\%)** & **(Hz)** & **Variation (\%)** & **EFDD** \\ \hline Lab-2.1-W & 39.35 & 0.63 & 39.87 & 1.12 & 1.32 \\ Lab-2.1-S & 43.60 & 0.70 & 44.12 & 0.78 & 1.19 \\ Lab-2.4-W & 33.72 & 0.43 & 33.63 & 0.87 & \(-\)0.27 \\ Lab-2.4-S & 34.67 & 0.58 & 34.79 & 0.28 & 0.35 \\ Lab-2.7-W & 25.99 & 0.63 & 26.79 & 1.68 & 3.08 \\ Lab-2.7-S & 26.34 & 0.63 & 26.59 & 0.58 & 0.95 \\ Lab-3.0-W & 20.32 & 0.50 & 20.40 & 0.33 & 0.39 \\ Lab-3.0-S & 20.34 & 0.77 & 20.39 & 0.68 & 0.25 \\ Field-2.4-W & 26.45 & 4.59 & 25.70 & 5.79 & \(-\)2.84 \\ Field-3.1-W & 16.38 & 4.39 & 16.99 & 4.38 & 3.72 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Fundamental frequencies for laboratory and in-situ timber floors.  
From Figures 11 and 12, it can be deduced that the detected vibration modes corresponded to the fundamental vibration modes in the vertical direction. When these modes of vibration are excited by people walking, they can generate relevant levels of vertical accelerations in the floors and, therefore, user discomfort.