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. 2025 Jun 29;18(13):3087.
doi: 10.3390/ma18133087.

Structural Optimization and Performance Analysis of Acoustic Metamaterials with Parallel Unequal Cavities

Tengyue Pan  1 , Fei Yang  1 , Chengming Jiang  1 , Xinmin Shen  1 , Xiaocui Yang  2   3 , Wenqiang Peng  4 , Zhidan Sun  1 , Enshuai Wang  3 , Juying Dai  1 , Jingwei Zhu  1
Affiliations

Structural Optimization and Performance Analysis of Acoustic Metamaterials with Parallel Unequal Cavities

Tengyue Pan et al. Materials (Basel). .

Abstract

Noise reduction for manufacturing enterprises is favorable for workers because it relieves occupational diseases and improves productivity. An acoustic metamaterial with parallel, unequal cavities is proposed and optimized, aiming to achieve an optimal broadband sound absorber in the low-frequency range with a limited total thickness. A theoretical model for the acoustic metamaterial of a hexagonal column with 6 triangular cavities and 12 right-angled trapezoidal cavities was established. The lengths of these embedded apertures were optimized using the particle swarm optimization algorithm, with initial parameters obtained from acoustic finite element simulation. Additionally, the impacts of manufacturing errors on different regions were analyzed. The experimental results prove that the proposed acoustic metamaterials can achieve an average absorption coefficient of 0.87 from 384 Hz to 667 Hz with a thickness of 50 mm, 0.83 from 265 Hz to 525 Hz with a thickness of 70 mm, and 0.82 from 156 Hz to 250 Hz with a thickness of 100 mm. The experimental validation demonstrates the accuracy of the finite element model and the effectiveness of the optimization algorithm. This extensible acoustic metamaterial, with excellent sound absorption performance in the low-frequency range, can be mass-produced and widely applied for noise control in industries.

Keywords: acoustic finite element simulation; acoustic metamaterial; particle swarm optimization; sound-absorbing capacity; theoretical model.

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Conflict of interest statement

The authors declare that they have no conflicts of interest.

Figures

Figure 1
Figure 1
A structural representation of the presented acoustic metamaterial with parallel unequal cavities. (a) The overall structure; (b) the triangular Helmholtz resonator; and (c) the right-angle trapezoidal Helmholtz resonator.
Figure 2
Figure 2
The regional division of the overall structure.
Figure 3
Figure 3
Triangular and right-angled trapezoidal single cavities. (a) FEM of the triangular and right-angled trapezoidal single cavities; (b) meshed models.
Figure 4
Figure 4
Sound-absorbing capacity of the initial acoustic metamaterial. (a) Scenario 1; (b) Scenario 2; (c) Scenario 3; and (d) Scenario 4.
Figure 5
Figure 5
The flow diagram of the PSO algorithm.
Figure 6
Figure 6
Sound absorption coefficients of the optimized metamaterials. (a) Scenario 1; (b) Scenario 2; (c) Scenario 3; and (d) Scenario 4.
Figure 6
Figure 6
Sound absorption coefficients of the optimized metamaterials. (a) Scenario 1; (b) Scenario 2; (c) Scenario 3; and (d) Scenario 4.
Figure 7
Figure 7
The distribution of sound pressure of optimized acoustic metamaterial for Scenario 1. (a) 361 Hz; (b) 391 Hz; (c) 402 Hz; (d) 428 Hz; (e) 460 Hz; (f) 571 Hz; (g) 615 Hz; (h) 663 Hz; and (i) 692 Hz.
Figure 7
Figure 7
The distribution of sound pressure of optimized acoustic metamaterial for Scenario 1. (a) 361 Hz; (b) 391 Hz; (c) 402 Hz; (d) 428 Hz; (e) 460 Hz; (f) 571 Hz; (g) 615 Hz; (h) 663 Hz; and (i) 692 Hz.
Figure 8
Figure 8
The experimental testing process of acoustic metamaterials.
Figure 9
Figure 9
Sound-absorbing curves of the acoustic metamaterial samples. (a) Scenario 1; (b) Scenario 2; (c) Scenario 3; and (d) Scenario 4.
Figure 10
Figure 10
The impact of the diameter of apertures in Region 1 on the sound-absorbing capacity.
Figure 11
Figure 11
The impact of the diameter of apertures in Region 2 on the sound-absorbing capacity.
Figure 12
Figure 12
The impact of the diameter of apertures in Region 3 on the sound-absorbing capacity.
Figure 13
Figure 13
The impact of the diameter of apertures in Region 4 on the sound-absorbing capacity.
Figure 14
Figure 14
The impact of the length of the embedded aperture in Region 1 on the sound-absorbing capacity.
Figure 15
Figure 15
The impact of the length of the embedded aperture in Region 2 on the sound-absorbing capacity.
Figure 16
Figure 16
Impact of the length of the embedded aperture in Region 3 on the sound-absorbing capacity.
Figure 17
Figure 17
The impact of the length of the embedded aperture in Region 4 on the sound-absorbing capacity.
Figure 18
Figure 18
The impact of the depth of the rear cavity on the sound-absorbing capacity.
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