# Damping Assessment of Lightweight Timber Floors Under Human Walking Excitations
## 2 Materials and Methods
### Operational Modal Analysis and Damping Ratio Estimations  
Operational Modal Analysis (OMA) is an engineering field that aims to identify the modal properties (modal frequencies, damping, and shapes) of dynamic systems based only on vibration response measurements. OMA provides a series of useful methods that can be classified as parametric and nonparametric. Usually, the parametric methods exhibit a better performance than the nonparametric methods. However, they use procedures that are more complex and computationally demanding. On the other hand, nonparametric methods are faster and easier to use in field tests, since they allow a quick view about the effectiveness of the measurements and the results of dynamic identification [15]. Therefore, it is always convenient to use these two types of methods when trying to identify modal properties as challenging as the damping ratios. In this study, only the frequency and damping ratio associated with the first resonant mode of the floors was estimated. This decision was based on the results obtained in previous theoretical studies, where a series of timber floors were modeled using the finite element method [16]. For most of the numerical models of the floors, it was found that the first resonant mode had an effective modal mass equivalent to 60% of the total mass. In contrast, the rest of the modes had effective modal masses less than 10% of the total floor mass. In this way, it was estimated that the first resonant mode of the floors would have a significant influence on their vibratory performance. Enhanced Frequency Domain Decomposition (EFDD) [17; 18] and Stochastic Subspace Identification (SSI) [19; 20] were selected as OMA techniques because they are widely used for modal parameter identification and are based on frequency domain (nonparametric) and time domain (parametric) approaches, respectively. The software package ARTeMIS Modal Pro [21] was used to determine modal frequencies, damping ratios, and shapes of the timber floors under operational-walking conditions for both EFDD and SSI methods. EFDD is a method based on the singular value decomposition (SVD) of the power spectral density (PSD) matrix and allows the identification of even closely spaced modes. This approach uses four main steps in order to estimate the damping ratio, as is illustrated in Figure 8. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Series** & **Span Length “L” (m)** & **Floor Width “B” (m)** & **Support Type** \\ \hline Field-2.4-W & 2.4 & 4.4 & Wood-based \\ Field-3.1-W & 3.1 & 2.7 & Wood-based \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Nomenclature, dimensions, and support details of in-situ timber floors. Figure 7: Walking paths and accelerometer locations on in-situ timber floors: (**a**) Field-2.4-W timber floor; (**b**) Field-3.1-W timber floor. [PERSON] et al. [22] have suggested some basic test and data processing rules in order to obtain reliable damping ratio estimations with the EFDD method. Firstly, a total record length equal to 1000-2000 times the first natural structural period is usually recommended. This record's lengths are needed to keep the PSD estimation errors low. According to some preliminary numerical simulations, it was estimated that the most flexible tested floors would have fundamental vibration periods of approximately 0.06 s. Therefore, it was decided that consecutive round-trip walks on the floors that had a total duration of at least 72 s would be conducted. In this way, it was possible to comply with the suggestions of the length records. Secondly, considerable attention must be paid when a frequency resolution is selected. Because the damping estimates improve with the frequency resolution [22], its value was set to 0.101 Hz. This resolution was adequate with respect to the values of resonant frequencies and the modal density found for the timber floors. More details of the EFDD method can be found in [15]. Figure 8: Logical diagram of damping ratio estimation based on the Enhanced Frequency Domain Decomposition (EFDD) method.