## 3 Results and Discussions  
### Verification by Finite Element Simulation  
Taking the most complex composite structure of PCMCPC for example, the simulation model for preliminary verification of the optimal dimensional parameters was constructed in the software of Virtual Lab Acoustics based on the finite element method [30; 31], as shown in Figure 5. With respect to the other four composite structures, the simulation was realized by adjusting parameters of the porous metal 1, porous metal 2, cavity 1, cavity 2, cavity 3, and the microperforated panel in the constructed model according to the optimal parameters in the Tables 3-5 respectively. Size of each element in this simulation model was 5 mm, and it was a triangular mesh in the thickness direction, which indicated that it utilized 897 points in the calculation process. The plane wave was loaded in the acoustic source inlet and used as the sound source input. Effect of the microperforated panel was represented by the transfer relation admittance between two surfaces, which was calculated according to the structural parameters in the Tables 3-5. Through testing peak sound level and valley sound level at the microphone 1 and microphone 2 respectively, sound absorption coefficient of the detected sound absorber at a certain frequency could be calculated. By this method, sound absorption coefficients of the investigated composite structures were simulated.  
Comparisons of the sound absorption coefficient of the theoretical result and that of the simulation result are shown in Figure 6. It can be observed that the distributions of sound absorption coefficients of the composite structures in the simulation results were in accordance with those in the theoretical results. Especially for the composite structure of MC, the simulation result was almost same with the theoretical result, which indicated that the constructed model for the microperforated panel based on [PERSON]'s theory was accurate. With respect to the other four composite structures, the differences between the simulation result and the theoretical result were generated in constructing model of the porous material according to the Johnson--Champoux-Allard model, which has been used in studying the relationship between sound absorption performance of the porous material and its structural parameters [8; 9]. With an increase of the limited total thickness, deviations between the simulation results and the theoretical results were reduced, because sound absorption coefficients in the frequency range (2000 Hz, 6000 Hz) were close to 100% both in the theoretical result and in the simulation result. Meanwhile, the absolute deviation of corresponding average sound absorption coefficient was smaller than 1% between the simulation results and the theoretical results. Therefore, it was preliminarily concluded that the optimal structural parameters obtained by the cuckoo search algorithm were reasonable and accurate.  
Figure 5: Simulation model for the sound absorption coefficient of the composite sound absorbing structure.  
Figure 6: Comparison of the sound absorption coefficient in theory and that obtained by simulation. (**a**) Composite structures with limited total thickness 30 mm corresponding to parameters in Table 3; (**b**) composite structures with limited total thickness 50 mm corresponding to parameters in Table 4; (**c**) composite structures with limited total thickness 100 mm corresponding to parameters in Table 5.