## 4 Embedded Battery Tile Modal Testing
### Results and Discussion  
The application of the experimental procedure described above led to the materials' mechanical properties given in Table 3. These properties allow the correlation with the experimental data in terms of components and complete tile eigenfrequencies, modal shapes, and frequency response spectra, as shown in the present section. The properties for CFRP are in line with common woven CFRP materials [32; 33]. For the batteries, the mechanical properties are found by matching the modal analyses results with the experimental results and the entity of the [PERSON]'s modulus is compatible with previous studies [34] (p. 316). The comparison between experimental and SOL 103 eigenfrequencies for the tile components is given in Table 4, where the relative difference \(\Delta\) is given in percentage in the rightmost column. The corresponding crossMAC analysis results are given in Figure 15.  
For the inner skin, the correlation between the experimental and numerical eigenfrequencies is acceptable. The crossMAC analysis (Figure 15a) confirms the correspondence between the numerical and experimental mode shapes. For the outer skin, while experimental modes 1-3 have a good correspondence with the numerical modes in terms of eigenfrequencies, the experimental mode at 84.25 Hz has no clear correspondence with the numerical modes. This is due to the interference of the piezoelectric actuator cables (Figure 12a), which induce a constraint that is not considered in the free-free numerical analysis. The mode appears in the mean frequency response spectra (Figure 16b) that takes into account the constraint. The crossMAC analysis (Figure 15b) could find an acceptable match between the experimental and numerical mode shapes just for modes 1 and 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Material** & **E** & **\(\
u\)** & **G** & **\(\rho\)** \\  & **(GPa)** & **(-)** & **(GPa)** & **(g/cm\({}^{3}\))** \\ \hline Aluminum & 62.00 & 0.300 & 23.850 & 2.72 \\ \hline FR-4 & 7.50 & 0.300 & 2.880 & 1.80 \\ \hline Copper & 110.00 & 0.300 & 42.310 & 8.93 \\ \hline Equivalent battery material & 0.10 & 0.300 & 0.038 & 2.50 \\ \hline  & \(\mathbf{E_{11}=E_{22}}\) & \(\
u_{12}\) & \(\mathbf{G_{12}}\) & \(\rho\) \\  & **(GPa)** & **(-)** & **(GPa)** & **(g/cm\({}^{3}\))** \\ \hline CFRP & 28.00 & 0.044 & 2.000 & 1.54 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Materials’ mechanical properties used in the FEM analyses allow the correlation with the experimental results. For the inner PCB, the eigenfrequencies (Table 4) show a good correlation between experimental and numerical data, except for mode 3. This may be due to the fixing system of the experimental setup. The tailor's tread, in this case, exploits a through hole near the center of the PCB (Figure 12b), that is, the maximum displacement point of the third modal shape. The experimental mode frequency is then altered, although the correlation between the experimental and the numerical modal shapes is acceptable with a crossMAC of 98% (Figure 15c). For the outer PCB, the linear modal analysis reveals a good correlation between the eigenfrequencies with the experimental data, except for the first mode. This again may be due to the interference from the fixing system. The explanation is the same as in the inner PCB case. The fixing system has interfered with the first modal shape and thus the experimental eigenfrequency is rather different, although the modal shapes have a crossMAC of 99% (Figure 15d). The crossMAC (Figure 15d) reveals that there is no correlation between the experimental mode shape 3 and the numerical mode shape 3. The mean frequency response spectra for the tile prototype components are presented in Figure 16. For the inner skin (Figure 16a), the experimental data show a considerable noise below 20 Hz. The first mode is reproduced in the FEM result with acceptable precision. The second mode is visible in the experimental spectrum while it is not visible in the numerical analysis due to the piezoelectric actuator location.