1. Introduction
The sound absorption and noise reduction are mainly applications of the porous metal because it has the advantages of excellent absorption performance, a wide absorption band, outstanding flame resistance, extraordinary light weight, satisfactory cost-effective ratio, and so on [
1,
2,
3,
4,
5]. Hakamada et al. [
1] had produced the porous aluminum with a density of 0.27 g/cm
3 by the spacer method, and a sound absorption coefficient near unity was achieved by inserting an air gap back to the sample. The porous copper was prepared by Ru et al. [
2] through a novel rosin curing and foaming method, and influences of resin content on the micropore structure and its sound absorption were investigated. The nickel-based superalloy open-cell foam with the controllable porosity (92–98%) and cell size (300–900 µm) was prepared by Zhai et al. [
3] the through template replication process, which achieved sound absorption coefficient >0.9 at the frequency >1500 Hz with a thickness of 50 mm. Geometrical and dimensional optimization of the sound-absorbing porous copper with cavity was conducted by Yang et al. [
4], which obtained a sound absorption coefficient >0.7 at the frequency range 2000–5000 Hz with a thickness of 28.8 mm. Liu et al. [
5] investigated the sound absorption performance of the highly porous titanium foams, and it was concluded that the main sound absorption mechanism was the interference silencing due to the surface reflection at low-frequency range and viscous dissipation at a high-frequency range. Therefore, the porous metal is considered as one of the research focuses on the fields of sound absorption and noise reduction.
Besides these common porous sound-absorbing materials [
1,
2,
3,
4,
5], some novel sound absorbers have already been developed from the standard porous metal [
6,
7,
8,
9,
10,
11,
12,
13,
14,
15]. Bai et al. [
6] had attempted to improve sound absorption efficiency of the porous metal by compression, and further promote the sound absorption performance by microperforation [
7]. The gradient compressed porous metal had been proposed by Yang et al. [
8], which obtained the average sound absorption coefficient of 0.6033 in the 100–6000 Hz range with a total thickness of 11 mm. The thin acoustic absorber of multilayer compressed porous metal with rear cavity was investigated by Shen et al. [
9], and its average sound absorption coefficient of the optimal four-layer compressed porous metal with the total thickness of 5 mm reached 0.5105 in the 100–6000 Hz. Otaru et al. [
10] proposed and optimized the porous metal with a bottleneck-type structure, which obtained the the optimal sound absorption performance when its porosity was 0.68. Meanwhile, the composite structures consisted of porous metal and the other sound-absorbing materials are treated as an effective method to develop the practical acoustic absorbers for some normal or special applications [
11,
12,
13,
14,
15]. Lu et al. [
11] had investigated influences of the microperforated panel combination on the sound absorption performance of the nickel foam, which indicated that the sound absorption coefficient was controlled by adjusting the thickness of the composite layer and location of the perforated panel. High-performance aluminum foam sandwich was prepared by Peng et al. [
12] through the friction stir welding, which could obtain outstanding sound absorption property. Shen et al. [
13] had fabricated the low-frequency sound absorber by the combination of porous metal and microperforated panel, which could achieve the average sound absorption coefficients of 0.6296 and 0.7359 in the 100–1800 Hz with limited total thicknesses of 30 mm and 50 mm, respectively. A simple two-dimensional microstructural model of the perforated closed-cell metallic foam was presented by Chevillotte et al. [
14,
15], which attempted to understand how perforation interacted with the closed-cell foam microstructure and how it modified the sound absorption of the foam. Therefore, porous metal and its derivatives are widely utilized in sound absorption and attract worldwide research enthusiasm.
Normally, no matter for the common porous metal or for composite sound-absorbing structure, the structural parameters must be optimized to achieve the satisfactory sound absorption performance under certain constraint conditions [
16,
17,
18,
19,
20,
21]. Acoustic topology optimization of porous material distribution based on the adjoint variable fast multipole boundary element method was conducted by Zhao et al. [
16], and its ability to handle the large-scale problems was validated through numerical examples of acoustic scattering over a single cylinder and multiple cylinders. Zhu et al. [
17] investigated the effects of gradient pore structure on the sound absorption performance of the metal fiber porous material, and the sound absorption coefficient was improved due to repeated reflection of the sound wave in the porous media between gradient interfaces. A ten-layer gradient compressed porous metal with a thickness of 20 mm was optimized to obtain an excellent sound absorption performance by Yang et al. [
18], and its average sound absorption coefficients could reach 0.3325, 0.5412, 0.7461, and 0.7617 when the frequency ranges were 100–1000 Hz, 100–2000 Hz, 100–4000 Hz, and 100–6000 Hz, respectively. Takezawa et al. [
19] proposed new topology optimization by the solid isotropic material with the penalization method for optimizing a sound-absorbing material layout, which obtained the appropriate solutions and generated the optimal result for each selected sample. Parametric optimization and analysis of a metallic porous material were conducted by Barbosa and Lenzi [
20], who aimed to reduce the gas pulsation noise in the household refrigerators. Park et al. [
21] carried out multistage numerical analysis of the polyurethane foam, and it could be proved that reduction of the mean cell diameter could enhance acoustic damping efficiency in low-frequency ranges. Therefore, parameter optimization is the critical step to develop the novel sound absorber, and it is extremely important to obtain acoustic characteristic parameters of the porous metal.
According to the classical Johnson-Champoux-Allard model [
22,
23,
24], major acoustic characteristic parameters for the porous material were porosity and static flow resistivity. Although the porosity is easy to obtain, it is difficult to accurately measure the static flow resistivity [
3,
8,
25,
26,
27]. Therefore, identification of the acoustic characteristic parameters, which included the porosity and static flow resistivity, were conducted through the cuckoo search algorithm [
28,
29] based on the experimental data of the sound absorption coefficient of the porous metal in this study. Afterward, the sound absorption performance of the porous metal was improved through adding the microperforated metal panel in front of it to form a composite sound-absorbing structure. After that, the theoretical sound absorption model of the composite structure was constructed by the transfer matrix method [
9,
13,
30,
31,
32]. Then, parameters of the composite structures were optimized by the cuckoo search algorithm [
8,
18,
28,
29] to achieve maximum average sound absorption coefficient in a certain frequency range. Moreover, the effectiveness and practicability of the optimal composite sound-absorbing structures were verified through the finite element simulation in the virtual acoustic laboratory [
33,
34,
35]. Finally, accuracy and reliability of theoretical sound absorption model, cuckoo search identification and optimization algorithm, and finite element simulation method were testified by the experimental validation, and experimental data of sound absorption coefficients of the porous metal and those of the composite sound-absorbing structures were obtained by the standing wave tube measurement [
36,
37,
38]. By this method, identification of acoustic characteristic parameters and improvement of the sound absorption performance for porous metal were conducted, which aimed to promote its practical application.
6. Conclusions
The identification of acoustic characteristic parameters and improvement of the sound absorption performance for the porous metal were conducted in this research. Through the theoretical sound absorption modeling, parameter identification and optimization, finite element simulation analysis, and standing wave tube measurement, the following conclusions were obtained in this study.
(1) Acoustic characteristic parameters of the porous metal were identified through the cuckoo search identification algorithm based on the theoretical sound absorption model and experimental data of its sound absorption coefficients. These identified acoustic characteristic parameters were close to the labeled porosity and static flow resistivity. Meanwhile, through the standing wave tube measurement of sound absorption coefficients of the porous metal with the different thickness, excellent consistencies between the experimental data and theoretical predictions proved the reliability of the cuckoo search algorithm, which provided a foundation for the following improvement.
(2) The sound absorption performance of the porous metal with different target frequency range was improved through adding microperforated metal panel to form a composite sound-absorbing structure, and optimal parameters of the added microperforated metal panel were obtained by the cuckoo search optimization algorithm based on the constructed theoretical model. Average sound absorption coefficients of these optimal composite sound-absorbing structures were 0.5393, 0.6533, 0.7159, 0.7562, 0.7830, and 0.7949 when the target frequency ranges were 100–1000 Hz, 100–2000 Hz, 100–3000 Hz, 100–4000 Hz, 100–5000 Hz, and 100–6000 Hz, respectively, which increased by 240%, 131%, 85%, 61%, 48%, and 41%, respectively, relative to the original porous metal with a thickness of 20 mm. The sound absorption performance of the porous metal was significantly improved.
(3) Finite element simulation analysis in the virtual acoustic laboratory and standing wave tube measurement by the AWA6128A detector were conducted to verify the effectiveness and practicability of the optimal composite sound-absorbing structures. Excellent consistencies among the theoretical predictions, simulation results, and experimental data proved the accuracies and effectiveness of the constructed theoretical sound absorption model, the selected cuckoo search identification and optimization algorithm, and the adopted finite element simulation method.
(4) When the target frequency ranges were 100–1000 Hz, 100–2000 Hz, 100–3000 Hz, and 100–4000 Hz, corresponding actual average sound absorption coefficients of the optimal composite sound-absorbing structures were 0.5154, 0.6369, 0.6770, and 0.7378, respectively, and those of the original porous metal with thickness of 20 mm were 0.1575, 0.2791, 0.3804, and 0.4644, respectively, which exhibited the obvious improvement of the sound absorption performance with a tiny increase in the occupied space and a small addition in weight. Judging from the actual improvements of 227.24%, 128.20%, 77.97%, and 58.87%, respectively, it could be concluded that these improvements were more effective for the low-frequency range, which was consistent with common views that the microperforated panel had superiority in the low-to-middle-frequency sound absorption and the porous metal was good at the middle-to-high-frequency period.
In this study, acoustic characteristic parameters of the porous metal were precisely identified and its sound absorption performances were significantly improved, which would be favorable to promote its practical application in the fields of sound absorption and noise reduction.
Author Contributions
Conceptualization, X.S.; software, X.Z.; validation, X.Y. and X.Z.; formal analysis, X.Y. and H.D.; investigation, Q.Y.; data curation, Q.Y. and X.Y.; writing—original draft preparation, X.Y. and X.S.; writing—review and editing, X.S. and H.D.; supervision, X.S.; funding acquisition, X.S. All authors have read and agreed to the published version of the manuscript.
Funding
This research was funded by the National Natural Science Foundation of China, grant number 51505498; the Natural Science Foundation of Jiangsu Province, grant number BK20150714; the National Key R&D Program of China, grant number 2016YFC0802900; the Hong Kong Scholars Program, grant number XJ2017025.
Acknowledgments
The authors wish to express their sincere thanks to Hangzhou Aihong Instruments Co., Ltd., China for the support with the AWA6128A detector.
Conflicts of Interest
The authors declare no conflicts of interest.
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Figure 1.
Structural morphologies of the porous metal obtained by the scanning electron microscope (a) with a low magnification of 20× and (b) with a high magnification of 100×.
Figure 2.
Schematic diagram of the standing wave tube measurement by AWA6128A detector.
Figure 3.
Flow chart of identification of the acoustic characteristic parameters through the cuckoo search algorithm.
Figure 4.
Optimization results of the cuckoo search identification algorithm.
Figure 5.
Distribution of the optional acoustic characteristic parameters of static flow resistivity and porosity.
Figure 6.
Comparisons of the theoretical predictions and the experimental data of sound absorption coefficients of the porous metal (a) with a thickness of 15 mm, (b) with a thickness of 20 mm, (c) with a thickness of 25 mm, and (d) with a thickness of 30 mm.
Figure 7.
Sound absorption coefficients of the porous metal with a thickness of 35 mm.
Figure 8.
Schematic diagram of the composite sound-absorbing structure.
Figure 9.
Comparisons of the theoretical sound absorption coefficients of the optimized composite sound-absorbing structures and those of the original porous metal.
Figure 10.
Finite element simulation model of the composite sound-absorbing structure.
Figure 11.
The composite sound-absorbing structures for improving the sound absorption performance of the porous metal with variable target frequency ranges. (a) Optimal structure for 100–1000 Hz; (b) optimal structure for 100–2000 Hz; (c) optimal structure for 100–3000 Hz; (d) optimal structure for 100–4000 Hz.
Figure 12.
Comparisons of sound absorption coefficients of the composite sound-absorbing structure with variable target frequency ranges. (a) Optimal structure for 100–1000 Hz; (b) optimal structure for 100–2000 Hz; (c) optimal structure for 100–3000 Hz; (d) optimal structure for 100–4000 Hz.
Table 1.
Optimal parameters of the microperforated panel for maximum improvement of sound absorption of the porous metal with different target frequency ranges.
Frequency Range (Hz) | Thickness of Panel (mm) | Diameter of the Hole (mm) | Distance of the Neighboring Holes (mm) | Average Sound Absorption Coefficient |
---|
100–1000 | 0.3 | 0.79 | 9.61 | 0.5393 |
100–2000 | 0.3 | 0.37 | 2.91 | 0.6533 |
100–3000 | 0.3 | 0.23 | 1.27 | 0.7159 |
100–4000 | 0.3 | 0.15 | 0.58 | 0.7562 |
100–5000 | 0.3 | 0.08 | 0.17 | 0.7830 |
100–6000 | 0.3 | 0.05 | 0.07 | 0.7949 |
Table 2.
Average sound absorption coefficients of the composite sound-absorbing structures.
Investigated Frequency Range | Average Sound Absorption Coefficient |
---|
in Actual | in Theory | in Simulation |
---|
100–1000 Hz | 0.5393 | 0.5493 | 0.5154 |
100–2000 Hz | 0.6533 | 0.6627 | 0.6369 |
100–3000 Hz | 0.7159 | 0.7195 | 0.6770 |
100–4000 Hz | 0.7562 | 0.7595 | 0.7378 |
Table 3.
Deviations among the theoretical predictions, simulation results, and experimental data.
Investigated Frequency Range | Total Departure of the Regressive Average Value Relative to Experimental Data |
---|
for Theoretical Predictions | for Simulation Results |
---|
100–1000 Hz | 0.9937 | 0.9914 |
100–2000 Hz | 0.9974 | 0.9949 |
100–3000 Hz | 0.9965 | 0.9943 |
100–4000 Hz | 0.9968 | 0.9964 |
Table 4.
Actual average sound absorption coefficients of the composite sound-absorbing structures and those of the original porous metals.
Investigated Frequency Range | Actual Average Sound Absorption Coefficients |
---|
for Composite Structure | for Original Porous Metal | Improvement |
---|
100–1000 Hz | 0.5154 | 0.1575 | 227.24% |
100–2000 Hz | 0.6369 | 0.2791 | 128.20% |
100–3000 Hz | 0.6770 | 0.3804 | 77.97% |
100–4000 Hz | 0.7378 | 0.4644 | 58.87% |
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