## 3 Results
### Measurements on Ceramic Test-Objects
Useful information derived from that research provide, among other evidence, the measured frequencies of the most relevant peaks of the vibration velocity (fundamental mode), when the test objects were exposed to an external acoustic pressure field in the audio frequency interval. These data are reported in Table 3, and they were also in a good agreement with the theoretical vibration frequency of the fundamental mode for a rectangular plate, with a boundary condition that is not properly clamped (mainly due to the presence of the epoxy glue), calculated using [PERSON]'s formulas [25; 26]. Figure 11: Tile models with artificial delamination. The measurements performed with the system described in this paper are shown in Figure 12. About 200 points were acquired on each tile and a colored visualization scale was used, before only using audio data (Figure 12a) and then using only impact time data (Figure 12b). As can be easily seen in the figure, the delamination modeled by the tiles T1 and T11 are easily highlighted using audio data, while that of the tile T13 is not evident. In fact, the latter has a first mode frequency of over 11 kHz, as can be seen from Table 3, which is beyond the frequency limit detectable by the audio section of the instrument. The upper limit of the frequency detectable with this electronics is less than 10 kHz, so we can also conclude that delamination up to thicknesses of about 0.8 mm of equivalent circular area of about 40 mm in diameter can be easily highlighted. To obtain valid measurements relative to defects of a lower area (or due to delamination of lesser thickness) by the audio data, it is necessary to use a slightly more sophisticated electronics, together with a microphone that extends its reception band at a frequency up to 20 kHz, of good quality. Therefore, the system can detect a wide variety of defects even of small dimensions; using components of better quality and obviously higher cost, the characteristics of the system can be improved, allowing the detection of ever smaller defects. In conclusion we preferred to use commercial components, so as not to affect the total cost of the instrument, which was one of the objectives set in this research work. The result of the measurement carried out using the force sensor is different. The data relating to the impact-time confirm the result relating to the samples T1 and T11, while in the case of the sample T13, which cannot be measured by means of the audio data, the measurement of the force pulse allows the detection of this type of defect, as it is not involved the free resonant frequency of the equivalent plate, but it is simply the measure of the stiffness of the surface under examination. This result is very encouraging and allows us to affirm that the fusion of the data obtainable from the two measurement methods allows to cover a large dimensional variety of defects, of various kinds and arranged in a different way with respect to the surface. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**ID** & **Materials and Size (mm3)** & **Cavity (mm3)** & **Notes** \\ \hline \multirow{2}{*}{T1} & clay substrate and glass & \multirow{2}{*}{42 \(\times\) 42 \(\times\) 1.3} & 0.8 1 st layer glass \\  & 68.0 \(\times\) 68.0 \(\times\) 11.6 substrate + glass & & 0.7 cap layer glass \\  & & & 2 layers of glue \\ \hline \multirow{2}{*}{T11} & clay substrate and glass & \multirow{2}{*}{34 \(\times\) 37 \(\times\) 0.8} & 0.7 cap layer glass \\  & 70.0 \(\times\) 72.0 \(\times\) 11.9 substrate + glass & & 2 layers of glue \\ \hline \multirow{2}{*}{T13} & clay substrate and glass & \multirow{2}{*}{35 \(\times\) 28 \(\times\) 0.6} & 0.7 cap layer glass \\  & 72.6 \(\times\) 70.8 \(\times\) 12.2 substrate + glass & & 2 layers of glue \\ \hline \hline \end{tabular}
\end{table} 
Table 2: List and details of the tile models under study.