# Evaluation of Dynamic Properties of Trees Subjected to Induced Vibrations
## 7 Conclusions  
Health monitoring of trees in urban and archeological areas is a topic of particular interest involving the specialist and diversified skills of professional figures.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Time** & **N** & \(\rho_{i}\) **(m)** & \(\xi_{i}\) & \(\omega_{0,i}\) **(rad/s)** & \(k_{1,i}\) & \(\mathbf{I_{1}}\) \\ \hline \multirow{4}{*}{0–60 s} & 1 & 0.0034 & 0.0153 & 7.59 & 0.5202 & \multirow{4}{*}{0–60 s} & \multirow{4}{*}{0.1578} \\  & 2 & 0.0027 & 0.0480 & 18.50 & 0.7995 & \\  & 3 & 0.0004 & 0.1578 & 33.94 & 0.7072 & \\  & 4 & 0.0008 & 0.1160 & 57.62 & 0.1347 & 0.0314 \\ \hline
0–8 s & 1 & 0.055 & 0.070 & 7.58 & - & 0.2587 \\ \hline
8–15 s & 1 & 0.055 & 0.045 & 7.50 & - & 0.2129 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Results deduced from the numerical approximation for the recorded response (r1_H2_TESO_SEO).  
Figure 11: Least square fitting of the whole recorded signal: (**a**) zoom of results on 0–8 s; (**b**) zoom of results on 8–60 s.  
The dynamic of trees is particularly complex because it is strictly related to its intricate architecture (i.e., configuration of trunk and branches) and the variability in the characteristics of wood material. Both these properties, moreover, change over time. Accelerations induced through pull-release tests or ambient excitations are strictly influenced by the characteristics of trees. The advances in the field of forest sciences together with modern instruments and approaches, some of which are carried out in engineering fields, allow for identifying important parameters, such as the frequency of vibrations and damping ratio, useful for studying the dynamic response of trees toward actions often responsible for their falling.  
In this paper, the dynamic identification of a tree case study has been presented by proposing an approach which combines a simple data-acquisition system, different sources of excitation, and elaboration approaches based on both common signal processing in the frequency domain and simplified numerical models.  
The following main outcomes have emerged from the study:  
* The results deduced from the approach have allowed to derive features characterizing the dynamic response of the tree toward the accounted sources of excitation by combining among them the adopted tools.
* The use of the power spectrum density has underlined the main frequencies governing the dynamic response of the tree, before and after removing one of the main branches and considering different positions of the accelerometer along the trunk. In particular, clearer identification in the case of the accelerometer located distant from the base of the trunk has been observed. Moreover, it has been observed that the removal of the branch placed near the base of the trunk did not induce significant variations in the frequencies.
* The schematization carried out by using the SDOF model and finite element model has allowed for deriving additional information concerning the level of damping and modal shapes, strictly correlated among them and playing a key role toward other types of excitations, such as wind actions. In particular, it has been observed that, while the lower modes involved a dynamic of the whole tree with a low value of the damping, the upper modes mainly involved the dynamic of branches that particularly increased the damping of the tree.
* The results obtained from the least square fitting pointed out levels of the modal damping ratio equal to 1.5% and 5%, respectively, for the first and second mode of vibration (in agreement with the values experimentally found and suggested by different authors [12; 21]) and equal to 12% and 16% for the third and fourth mode, respectively. The high values of the latter are probably influenced by the nonlinear nature of damping, its dependency on the amplitude of motion, and the approximation in using a pure viscous model [12].