# Ultrasonic Attenuation Characteristics of Glass-Fiber-Reinforced Polymer Hull Structure
## 5 Experimental Results
### Effects of the Laminate Thickness on Attenuation  
The effects of the thickness were analyzed based on the ultrasonic A-scan results of hull plate 2 (actual mean of 8.71 mm), hull plate 4 (actual mean of 14.10 mm), and hull plate 5 (actual mean of 18.34 mm) in the thickness variation group. Figure 8 provides an example of the analysis of the A-scan presentation, showing multiple back reflection results for each of the three plates, and Table 4 outlines the results, including the attenuation and attenuation coefficients according to Equation (1) at three random measurement points on the three plates. The attenuation increased significantly, whereas the attenuation coefficient showed no significant variation. Upon comparing these results with those shown in Figure 5  
Figure 6: Ultrasonic wave attenuation as a function of the \(Gc\). (**a**) Regression analysis results. (**b**) Residual analysis results.  
Figure 7: Ultrasonic wave attenuation as a function of the \(Gc\). (**a**) Regression analysis results. (**b**) Residual analysis results.  
(obtained by varying the _Gc_), we could infer that attenuation increased significantly. The polyester added to increase the thickness of the plate could have led to the increase in attenuation [13,14]. The discussion section explains in detail the effects of the varying _Gc_ and the thickness on attenuation and void formation.  
The data obtained at 150 measurement points were analyzed to obtain the results for hull plates 2, 4, and 5, which are shown in Figure 9. The _Gc_ was designed to be fixed at 40%. As the mean thickness increased from 8.71 mm to 14.10 mm and 18.34 mm, the mean attenuation also significantly increased from 8.10 dB to 12.45 dB and 17.38 dB, respectively (Figure 9a). Based on the residual analysis, the regression model was confirmed to be suitable.  
Figure 10a presents the attenuation coefficients of the three hull plates with different thicknesses. Although the plate thickness differed by more than two times, the actual mean  
\begin{table}
\begin{tabular}{c c c c} \hline
**Item** & **Hull Plate 2** & **Hull Plate 4** & **Hull Plate 5** \\ \hline Thickness (\(T\), mm) & 8.89 & 13.99 & 18.47 \\ First echo pulse height (\(A_{A}\), \%) & 75 & 78 & 79 \\ Second echo pulse height (\(A\), \%) & 26 & 18 & 8 \\ Attenuation (\(Y\), dB) & 9.20 & 12.74 & 19.89 \\ Attenuation coefficient (\(\alpha\), dB/mm) & 0.52 & 0.46 & 0.54 \\ \hline \end{tabular}
\end{table}
Table 4: Characteristics of and attenuation analysis results for each plate in the thickness variation group.  
Figure 8: Ultrasonic A-scan results for each type of plate in the thickness variation group. (**a**) Thickness = 8.89 mm. (**b**) Thickness = 13.99 mm. (**c**) Thickness = 18.47 mm.  
Figure 9: Ultrasonic wave attenuation as a function of thickness. (**a**) Regression analysis results. (**b**) Residual analysis results.  
\(Gc\) was similar, with values of 39.40%, 40.29%, and 43.39%. Accordingly, the attenuation coefficients of all three plates were similar, being 0.46 dB/mm, 0.44 dB/mm, and 0.48 dB/mm. The regression model was confirmed to be suitable by constructing a residual plot.