## 4 Embedded Battery Tile Modal Testing
### Results and Discussion
In the case of the outer skin (Figure 16b), the experimental data show much noise below 50 Hz. The amplitudes for modes 1 and 2 are much higher than for the numerical data obtained with the experimental voltage input. For the PCBs (Figure 16c,d), the results exhibit considerable noise below 100 Hz. The Inner PCB spectra (Figure 16c) reflect the discrepancy between the experimental and numerical eigenfrequencies of the third mode (Table 4). Similarly, the outer PCB spectra (Figure 16d) reflect the discrepancy between the first experimental and the first numerical eigenfrequency, as shown in Table 4. This is due to the absence of the tailor's tread in the SOL 111 simulation. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Component** & **Mode** & \multicolumn{2}{c}{**Frequency**} & \(\Delta\) \\ \hline  & & **Experimental** & **SOL 103** & \\  & **(-)** & **(Hz)** & **(\%)** \\ \hline  & 1 & 61.13 & 64.09 & 4.9 \\ Inner & 2 & 80.50 & 81.02 & 0.6 \\ skin & 3 & 160.75 & 166.03 & 3.3 \\ \hline  & 1 & 58.25 & 55.42 & 5.1 \\  & 2 & 69.50 & 72.29 & 4.0 \\ Outer & U1 & 84.25 & - & - \\ skin & 3 & 163.88 & 166.32 & 1.5 \\  & 4 & 195.63 & - & - \\ \hline  & 1 & 271.00 & 298.52 & 10.2 \\  & 2 & 428.38 & 397.12 & 7.9 \\ Inner & 3 & 675.00 & 544.92 & 23.9 \\ PCB & 4 & 762.63 & 754.32 & 1.1 \\  & 5 & 772.13 & 766.83 & 0.7 \\ \hline  & 1 & 168.75 & 219.47 & 30.1 \\  & 2 & 292.25 & 293.71 & 0.5 \\ Outer & 3 & 484.13 & 438.24 & 10.5 \\ PCB & 4 & 500.00 & 535.04 & 7.0 \\  & 5 & 585.13 & 607.28 & 3.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Eigenfrequencies for tile components: comparison between experimental and numerical SOL 103 results. Figure 16: Mean frequency response spectra for the tile prototype components: (**a**) inner skin; (**b**) outer skin; (**c**) inner PCB; and (**d**) outer PCB. Figure 15: Modal assurance criterion (crossMAC) for the tile prototype components: (**a**) inner skin; (**b**) outer skin; (**c**) inner PCB; and (**d**) outer PCB. The structural modes for the complete tile prototype are shown in Figure 17. The upper row shows the experimental modes and the lower row shows the correspondent SOL 103 modes. The FEM eigenfrequencies (Table 5) have a good compatibility with the experimental frequencies, up to the third mode. The discrepancies for the fourth and fifth modes can be due to inaccuracies in the assembly procedure and approximations in the FEM model; however, the FEM model is considered acceptable. The crossMAC between the experimental and numerical data (Figure 18a) gives an acceptable match just for the first and the second mode. Thus, the eigenfrequency match for the third mode (Table 5) should be considered with caution. The mean spectra (Figure 18b) show good correspondence just for the first and the second mode. There is a remarkable component of experimental noise below 200 Hz. In conclusion, although just the first and the second mode have acceptable results, the results of the complete tile analysis are considered acceptable. In fact, usually the launch vehicle requirements are given just on the first eigenfrequencies. The modal characteristics of the tile prototype are compatible with the Vega [26] (pp. 4-3, 4-4), Ariane 6 [27] (p. 4-4), Falcon 9 and Heavy [28] (p. 17) launch vehicle requirements. Figure 17: Structural mode visualizations for the complete tile prototype. Left: mode 7; center: mode 8; right: mode 9. Upper row: experimental modes; lower row: FEM modes. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Mode** & \multicolumn{2}{c}{**Frequency**} & \(\boldsymbol{\Delta}\) \\ \hline  & **Experimental** & **SOL 103** & \\
**(-)** & & **(Hz)** & **(\%)** \\ \hline
1 & 460.78 & 507.94 & 10.2 \\
2 & 814.53 & 748.68 & 8.8 \\
3 & 953.13 & 1015.80 & 6.6 \\
4 & 1319.22 & 1080.20 & 22.1 \\
5 & 1439.22 & 1138.00 & 26.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Eigenfrequencies for the complete tile prototype: comparison between experimental and numerical results.