## 3 Results and Discussions
### Validation of the Optimal Composite Structures
(**a**) Optimal PCMC with limited total thickness of 30 mm; (**b**) optimal PCMCPC with limited total thickness of 30 mm; (**c**) optimal PCMC with limited total thickness of 50 mm; (**d**) optimal PCMCPC with limited total thickness of 50 mm. Uncertainties exist in the validation process, one of which is about material design of the composite structure and the other is about characterization of the sound absorption coefficient. Thickness of the utilized porous metal samples has fabrication error, especially those special blocks, which was measured by a vernier caliper. It can be found that uncertainty of thickness of the used porous metal sample was \(\pm\)0.01 mm and that of the microperforated panel was \(\pm\)0.004 mm. Meanwhile, length of the rear cavity in the optimal sound absorber was controlled through the sample holder, and its control accuracy was \(\pm\)0.01 mm. Thus, total uncertainty of the sound absorber was \(\pm\)0.024 mm. It had been proved by [PERSON] et al. [32; 43] that the fabrication error within the submillimeter range had few influences to sound absorption performance of the sound absorber. Meanwhile, there is uncertainty in measuring the sound absorption coefficients, and each sound absorber was measured by more than 10 times. For example, when the limited thickness was 30 mm, evolutions of experimental data of sound absorption coefficients of the PCMC in 10 measurements are shown in Figure 10. It can be observed that undulation of the experimental data was within \(\pm\)0.2%, which further showed that uncertainty in the measurement was tiny and it had little influence in the research results in this study. \begin{table}
\begin{tabular}{c c c c c} \hline
**Composite** & **Limited Total** & **Theoretical** & **Simulation** & **Experimental** \\
**Structure** & **Thickness** & **Result** & **Result** & **Result** \\ \hline \multirow{2}{*}{PCMC} & 30 mm & 98.15\% & 98.29\% & 96.51\% \\  & 50 mm & 99.09\% & 99.15\% & 96.76\% \\ \hline \multirow{2}{*}{PCMCPC} & 30 mm & 98.37\% & 98.80\% & 96.60\% \\  & 50 mm & 99.21\% & 99.35\% & 97.65\% \\ \hline \end{tabular}
\end{table} 
Table 6: Quantitative comparisons of average sound absorption coefficients in the frequency range (2000 Hz, 6000 Hz) in the theoretical result, the simulation result, and the experimental result. Figure 9: Comparisons of the sound absorption coefficients in theory and those in experiment. From the Table 3, Table 4 and Figure 9, it can be found that the actual total thickness of the optimal composite structure sometimes did not reach the presupposed limited total thickness, which indicated that the actual sound absorption efficiency of the investigated composite structure was even better. Therefore, comparisons of the actual total thickness with different presupposed limited total thickness are shown in the Table 7. When the presupposed limited total thickness was 50 mm, the actual total thickness for the composite structure of PCMCPC was 36.8 mm and lengths of all the 3 cavities were 0 mm, which indicated that this sandwich structure is a promising sound absorber with high absorption efficiency and low total thickness. Meanwhile, actual total thickness of the optimal composite structure of PCMC with the limited total thickness of 50 mm was 37.04 mm (including the cavity with length of 10.77 mm), and its average sound absorption coefficient of 96.76% was close to that 97.65% of corresponding optimal PCMCPC with thickness of 36.8 mm. Thus, taking complexity of the composite structure into account, the PCMC can also be treated as novel sound absorber with fewer utilized materials for reduction of the industrial noise.