# A Novel Acoustic Ventilation Barrier Based on the Block-Shaped Space-Coiling Metamaterial
## 3 An Investigation of the Influence of the Design Parameters on the Transmission Loss  
This section investigates the influence of the design parameters on the TL of the proposed acoustic barrier. A total of five test groups are studied, which are listed as follows (shown in Table 2): (1) Group 1 studies the influence of the outer side length \(L\) on the TL, where the values of \(L\) are 60, 80, 100, and 120 mm; (2) Group 2 studies the influence of the inner side length \(l\) on the TL, where the values of \(l\) are 32, 36, 40, and 44 mm; (3) Group 3 studies the influence of the spacing of the first channel \(d_{1}\) on the TL, where the values of \(d_{1}\) are 8, 10, and 12 mm; (4) Group 4 studies the influence of the spacing of the second channel \(d_{2}\) on the TL, where the values of \(d_{2}\) are 8, 10, and 12 mm; and (5) Group 5 studies the influence of the spacing of the second channel \(d_{2}\) on the TL, where the values of \(d_{2}\) are 8, 10, and 12 mm. For the above five groups, except for the design parameter being studied, the rest of the design parameters are in accordance with the benchmark meta-unit (see Table 1).  
Figure 6 shows the simulated TLs of the above five test groups, where the simulations were performed on the pressure acoustic module of COMSOL Multiphysics. Figure 6a shows the influence of the outer side length \(L\) on the TLs. As shown in Figure 6a, the increase in \(L\) will shift the curves of the TLs to the left-hand side and simultaneously decrease the values of the TLs. Figure 6b shows the influence of the inner side length \(l\) on the TLs. From Figure 6b, it is seen that the increase in \(l\) will shift the curves of the TLs to the left-hand side and greatly decrease the values of the TLs. Figure 6c shows the influence of \(d_{1}\) on the TLs. It is seen from Figure 6c that the increase in \(d_{1}\) will shift the curve of the TL at the lower frequency part to the right-hand side, which will not greatly influence the curve of the TL at the higher frequency part. Figure 6d shows the influence of \(d_{2}\) on the TLs. Compared to Figure 6c, it is seen from Figure 6d that the increase in \(d_{2}\) will shift the curve of the TL at the higher frequency part to the left-hand side, which will not greatly influence the curve of the TL at the lower frequency part. Figure 6e shows the influence of \(d_{3}\) on the TLs, which indicates that the increase in \(d_{3}\) will stretch the curve of the TL, shifting the curve of the TL below and above 700 Hz to the left-hand side and right-hand side, respectively.  
Figure 5: The acoustic pressure fields of the benchmark acoustic barrier under different frequencies.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Group Number** & \(L\) & \(I\) & \(w\) & \(d_{1}\) & \(d_{2}\) & \(d_{3}\) \\ \hline
1 & 60 mm & 40 mm & 1 mm & 8 mm & 8 mm & 8 mm \\ \hline
1 & 80 mm & 40 mm & 1 mm & 8 mm & 8 mm \\ \hline
1 & 100 mm & 40 mm & 1 mm & 8 mm & 8 mm \\ \hline
1 & 120 mm & 40 mm & 1 mm & 8 mm & 8 mm \\ \hline
2 & 60 mm & 32 mm & 1 mm & 8 mm & 8 mm \\ \hline
2 & 60 mm & 36 mm & 1 mm & 8 mm & 8 mm \\ \hline
2 & 60 mm & 40 mm & 1 mm & 8 mm & 8 mm \\ \hline
2 & 60 mm & 44 mm & 1 mm & 8 mm & 8 mm \\ \hline
3 & 60 mm & 40 mm & 1 mm & 10 mm & 8 mm \\ \hline
3 & 60 mm & 40 mm & 1 mm & 12 mm & 8 mm \\ \hline
4 & 60 mm & 40 mm & 1 mm & 8 mm & 12 mm \\ \hline
5 & 60 mm & 40 mm & 1 mm & 8 mm & 10 mm \\ \hline
5 & 60 mm & 40 mm & 1 mm & 8 mm & 12 mm \\ \hline \end{tabular}
\end{table}
Table 2: The design parameters of the five test groups.  
Figure 6: Simulated transmission loss: (**a**) Group 1; (**b**) Group 2; (**c**) Group 3; (**d**) Group 4; (**e**) Group 5.