## 5 Results and Discussion
### Summary of Lamb-Wave Attenuation
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Test** & & \(\alpha_{\text{L}}\) & \(\alpha_{\text{T}}\) & **Thickness** & \multicolumn{3}{c}{**Symmetric**} & \multicolumn{3}{c}{**Asymmetric**} \\ \hline \multirow{3}{*}{**No.**} & \multirow{3}{*}{**Material**} & & **Feq. kHz** & \(\alpha\)**–S\({}_{\text{o}}\) (dB/m)** & **Feq. kHz** & \(\alpha\)**–A\({}_{\text{o}}\) (dB/m)** & **Notes** \\  & & & **Theory** & **Exp.** & & & **Theory** & **Exp.** & \\ \hline G1 & PS & 39 & 113 & 1.38 & 300 & 19.7 & 16.4 & 350 & 37.4 & 34.3 & Average of two. \\ G2a & Al-1100-H18 & 15.7 & 26.5 & 2.06 & 350 & 5.77 & 5.6 & 250 & 7.44 & 7 & \\ G2b & Al-1100-H18 & 15.7 & 26.5 & 6.38 & 300 & 6.71 & 7.9 & 250 & 6.71 & 6.6 & \\ G3 & Al-601-T6 & 2.7 & 6.38 & 12.7 & 150 & 1.27 & 1.9 & 450 & 4.84 & 4.3 & \\ G6a & Soda-mite glass & 8.7 & 16.2 & 1.98 & 525 & 5.15 & 3.7 & 450 & 7.42 & 6.8 & \\ G6b & Soda-mite glass & 8.7 & 16.2 & 4.72 & 300 & 3.15 & 1.5 & 500 & 8.12 & 7.8 & \\ G7a & PMMA & 131 & 420 & 1.76 & 200 & 44.6 & 47.8 & 250 & 98.2 & 117 & \\ G7b & PMMA & 106 & 216 & 6.3 & 200 & 67.5 & 68.7 & 250 & 55.5 & 56.6 & \\ G8 & PVC & 239 & 990 & 4.3 & 70 & 33.5 & 43.9 & 70 & 58.5 & 71.7 & \\ G9 & HDPE & 222 & 1010 & 7.09 & 60 & 33.1 & 43.8 & 60 & 55.1 & 54.1 & \\ G10 & XP-GRP & 117 & 445 & 2.3 & 300 & 35.3\({}^{\star}\) & 43.6 & 80 & 36.7 & 40.5 & \({}^{\star}\)\(\alpha_{\text{L}}\) value used. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of Lamb wave attenuation values at approximate center frequencies. Note that sufficient signal qualities were obtained, allowing WT spectral analyses even with the peak displacements of 10-15 pm. In order to examine the noise level of the KRN sensor, it was set on a GFRP sheet (G10) and produced 1.0 mV peak-to-peak output of a 10-cycle, 200-kHz wavelet at 300 mm from a transmitter (V101, excited by 275 mV peak-to-peak tone-burst signal). The output signal of 1.0 mV peak-to-peak has rms output voltage of 371 \(\upmu\)V\({}_{\text{rms}}\), and the noise was 41.5 \(\upmu\)V\({}_{\text{rms}}\), giving a signal-to-noise (SN) ratio of 19.0 dB. This corresponds to better than 100 fm resolution. When the same signal is averaged, output and noise voltages were 365 \(\upmu\)V\({}_{\text{rms}}\) and 2.67 \(\upmu\)V\({}_{\text{rms}}\), respectively, resulting in an SN ratio of 42.7 dB and 10 fm resolution or better. Note that the resolution is conservatively estimated, but it cannot be verified at present. These results are tabulated below. As the present test set-up always uses signal averaging, the KRN sensor can detect 1 pm displacement, yielding 1 mV output with an SN ratio of better than 40 dB. Using this conversion factor of 1.0 pm/mV, the equivalent noise in displacement measurement is 4.3 fm/\(\surd\)Hz because the bandwidth was 400 kHz. This result shows that Lamb-wave signals with 10-pm peak can be adequately detected and recorded. The use of laser interferometry/vibrometry allows non-contact sensing, but with high equipment cost. Some of the units have scanning capability, but a vibrometer head can be combined with a mechanical X-Y scanning system to scan a large area. With precision scanning, a positional accuracy of better than \(\pm\)0.1 mm can be obtained. Non-contact and scanning features are positive attributes. In regard to the displacement sensitivity, careful technical evaluation is needed before getting a vibrometer for ultrasonic studies. PicoScale vibrometer (SmarAct, Oldenburg, Germany) has 1-pm resolution and 2.5-MHz bandwidth, while Polytec PSV-500 vibrometer (Polytec, Waldbronn, Germany) has 30-fm resolution (at 200 kHz) and 6-MHz bandwidth according to respective technical specifications. Since the resolution is the amplitude of the smallest signal above noise level, the displacement amplitude has to exceed at least 100 times the resolution in order to obtain a signal-to-noise (SN) ratio of 40 dB or higher. In the present Lamb-wave tests, signals below 100 pm were commonly observed (cf. Figure 3b and Table 3).