## 5 Conclusions  
Based on the above, it can be hypothesized that for resonators with a wrap-around electrode in the shape and dimensions according to the scheme in Figure 2 there will be a decrease in the electromechanical coupling coefficient compared to a fully electroded resonator of identical dimensions. The hypothesis is based on the comparison of the results obtained by the same method, which is the FEM model calculation for both the resonators with a wrap-around electrode and the fully electroded resonator. The reasons that lead to the decrease in the electromechanical coupling coefficient are likely to lie in the differences between the fully electroded resonator and the resonators with a wrap-around electrode; in particular, the uneven polarization of the resonator due to the shape and placement of the electrodes in resonators with wrap-around electrodes.  
In the available literature, the author has not found a study of the effect of partial electroding, asymmetrical along the resonator axis, on the electromechanical coupling coefficient. Mention may be made of the works of [8; 12; 14; 15; 21]. Here, however, the cases of partial electroding symmetrical along the axis of symmetry of the disc and for the case of radial oscillations are studied.  
It can be concluded that the claim of a decrease in the electromechanical coupling coefficient during partial electrode position is consistent with the results published in [12]. In this work, the graph in Figure 10 shows the dependence of the electromechanical coupling coefficient on the size of the electrodes. However, these findings apply to a symmetrically electroded disc and radial type of oscillation. Thus, the hypothesis made in the present paper cannot be based on the results published in [12].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Fully Electroded** & **Wrap-Around (a)** & **Wrap-Around (b)** \\ \hline \(k_{t}\) & 0.5013 & 0.4867 & 0.4858 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Calculated values \(k_{t}\).  
The results presented here can be verified experimentally; for the reasons given in Section 1 it is not possible to determine an analytical solution. The experimental determination of the frequency spectra of thickness oscillating resonators with a wrap-around electrode is the subject of the technical report of [22]. The report contains the values of the electromechanical coupling coefficient calculated from the measured resonance and antiresonance frequencies of resonators with double-sided electroding and resonators with a wrap-around electrode. The electromechanical coupling coefficient of the thickness oscillation is determined here to be lower in most cases for resonators with a wrap-around electrode than for the fully electroded resonators. Although the measurements were carried out on a small number of samples, this result supports the proposed hypothesis of a decrease in the electromechanical coupling coefficient of resonators with a wrap-around electrode.  
This research was funded by the Technical University of Liberec.  
The data presented in this study are available on request from the author. The data are not publicly available.  
The author declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.  
The following abbreviations are used in this manuscript.