# Ultrasonic Attenuation Characteristics of Glass-Fiber-Reinforced Polymer Hull Structure
## 5 Experimental Results  
### Effects of the Glass Fiber Weight Fraction on Attenuation  
Ultrasonic A-scanning was performed on all the hull plates, and the effect of the glass fiber weight fraction was analyzed based on the results for the hull plates in the \(Gc\) variation group with \(Gc\) = 30%, 40%, and 45%.  
Figure 5 provides an example of the A-scan analysis, showing multiple back reflections for the three aforementioned types of plates, and Table 3 presents the results, including the attenuation and attenuation coefficients according to Equation (1) at three random measurement points on each of the three plates. The results demonstrate that the attenuation coefficient increased with the increasing \(Gc\), and a variation in attenuation was also observed. However, because the thickness difference must be considered, the statistics of all the data needed be analyzed.  
The data obtained at the 150 measurement points on three hull plates in the \(Gc\) variation group are outlined above, and the attenuation variation was obtained as a function of the \(Gc\), as shown in Figure 6a. When the hull plate thickness was similar but the \(Gc\) was increased, the mean attenuation values of the plates with \(Gc\) = 30%, 40%, and 45% were 6.80 dB, 8.10 dB, and 8.78 dB, respectively. It was considered that increasing the \(Gc\) led to greater attenuation with ultrasonic wave propagation. In addition, a residual plot was prepared to test the regression model of attenuation as a function of the \(Gc\), and Figure 6b presents the results. A uniform distribution of residuals can be seen in the \(-2\)-\(2\) dB section, regardless of the fitted values; therefore, the regression model was determined to be suitable.  
Figure 5: Ultrasonic A-scan analysis results for each type of plate in the \(Gc\) variation group: (**a**) design \(Gc\) 30%; (**b**) design \(Gc\) 40%; and (**c**) design \(Gc\) 45%.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Items** & **Hull Plate 1** & **Hull Plate 2** & **Hull Plate 3** \\ \hline Design \(Gc\) (\%) & 30.00 & 40.00 & 45.00 \\ Thickness (\(T\), mm) & 9.89 & 8.89 & 7.50 \\ First echo pulse height (\(A_{A}\), \%) & 76 & 75 & 74 \\ Second echo pulse height (\(A\), \%) & 30 & 26 & 21 \\ Attenuation (\(Y\), dB) & 8.07 & 9.20 & 10.94 \\ Attenuation coefficient (\(\alpha\), dB/mm) & 0.41 & 0.52 & 0.73 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Characteristics of and attenuation analysis results for each plate in the \(Gc\) variation group.  
Figure 7(a) depicts the variation of the attenuation coefficient, which is defined as the attenuation per unit path length. The mean attenuation coefficients of the plates with \(Gc\) = 30%, 40%, and 45% were 0.35 dB/mm, 0.46 dB/mm, and 0.52 dB/mm, respectively. It can be concluded that during ultrasonic wave propagation, although E-glass fiber was the propagation medium, it increased the interference in the ultrasonic wave. In addition, it was assumed that the irregularity of the fiber chop, a characteristic of CSM, caused additional scattering. A uniform distribution of residuals can be seen between \(-\)0.1 and 0.1 dB/mm around 0, regardless of the fitted values; therefore, the regression model was determined to be suitable (Figure 7(b)).