基于神经网络的声学超材料板正反向设计方法

陈为谦; 郭辉; 傅伟; 孙裴; 王岩松

doi:10.12299/jsues.24-0163

基于神经网络的声学超材料板正反向设计方法

doi: 10.12299/jsues.24-0163

陈为谦^1,,
郭辉^1, ,,
傅伟²,
孙裴¹,
王岩松¹

1.
上海工程技术大学机械与汽车工程学院, 上海201620
2.
淄博市技师学院, 山东淄博 255000

基金项目: 国家自然科学基金(52172371)；上海市优秀学术/技术带头人计划项目（21XD1401100）；上海市新能源汽车振动噪声评价与控制技术专业服务平台（18DZ2295900）

详细信息

作者简介:
陈为谦（1997 − ），男，硕士生，研究方向为声学超材料板智能设计方法。E-mail：chenwq99@foxmail.com

通讯作者:
郭　辉（1981 − ），男，教授，博士，研究方向为振动噪声测控技术。E-mail：hgsues@163.com

中图分类号: TB535
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- 被引次数: 0
出版历程
- 收稿日期: 2024-06-07
- 网络出版日期: 2025-12-22
- 刊出日期: 2025-09-30

Forward-reverse design method for acoustic metamaterial plates based on neural networks

CHEN Weiqian^1
,,
GUO Hui^{1
, ,},
FU Wei²,
SUN Pei¹,
WANG Yansong¹

1.
School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai 201620, China
2.
Zibo Technician College, Zibo 255000, China

摘要

摘要: 声学超材料板是一种可以在特定频率范围内禁止弹性波传播的人工复合结构，由于存在多种机理的共同作用，其物理性能难以用理论公式进行推导和表述。设计一种基于局域共振机理的声学超材料板结构，利用有限元方法对其带隙特性进行分析，获得不同元胞结构参数及对应带隙特性，建立声学超材料板样本集。设计正向设计神经网络模型，获取结构参数与带隙范围的正向映射关系，实现输入结构参数即可输出相应的带隙范围的正向预测。在此基础上，提出一种反向设计神经网络模型，实现根据目标带隙范围获取声学超材料板结构参数的反向设计。仿真结果表明，提出的声学超材料板正反向设计方法可以避免复杂繁琐的理论推导和计算，有助于推动声学超材料领域的进一步发展。
- 声学超材料 /
- 带隙特性 /
- 有限元分析 /
- 神经网络模型 /
- 智能设计
Abstract: As an artificial composite structure, an acoustic metamaterial plate (AMP) can block the propagation of the elastic wave within specific frequency ranges. Due to the combined effects of multiple mechanisms in the composite structure, it is difficult to derive and express the physical properties using theoretical formulas. An AMP structure based on local resonance mechanism was proposed, and the bandgap characteristics were analyzed using finite element method, to obtain different cell structure parameters and corresponding bandgap characteristics. A sample set of the relationship between the structure parameters and corresponding bandgap characteristics was established for the AMP. A forward neural network model was designed to obtain the mapping relationship between structural parameters and bandgap range, and the forward prediction of the corresponding bandgap range by inputting structural parameters can be achieved. On this basis, a reverse neural network was proposed, and the reverse design can be carried out to obtain the structural parameters of AMP aiming the required bandgap range. The simulation results show that complex and cumbersome theoretical derivation and calculation can be avoided with the forward-reverse design method for AMP, which is helpful to promote further development of acoustic metamaterials.
- acoustic metamaterial /
- bandgap properties /
- finite element analysis /
- neural network model /
- intelligent design

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图 1 声学超材料板基本单元

Figure 1. Unit of AMP

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图 2 正方形单元不可约布里渊区

Figure 2. Regular unit irreducible Brillouin zone

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图 3 声学超材料板基本单元能带图

Figure 3. Band diagram of AMP unit

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图 4 建立声学超材料板样本集流程图

Figure 4. Workflow of establishing sample set of acoustic metamaterial plates

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图 5 正反向设计神经网络示意图

Figure 5. Schematic diagram of forward-reverse neural network

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图 6 正反向设计神经网络的工作流程图

Figure 6. Workflow of forward and inverse design based on neural network

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表 1 声学超材料板材料参数

Table 1. Material parameters of AMP

参数	钢	空气
声速/(m·s⁻¹)	3300	343.2
泊松比	0.3	—
密度/( kg·m⁻³)	7700	1.2
杨氏模量/Pa	4.08×10¹⁰	—

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表 2 数据集部分数据

Table 2. Part of data set

a/mm	b/mm	c/mm	d/mm	带隙上界/Hz	带隙下界/Hz
1.5	4.0	5.0	3.5	2359.763	6466.259
1.5	4.0	5.0	4.0	2380.481	6460.853
2.0	1.5	2.5	1.5	1590.832	4539.679
2.0	1.5	2.5	2.0	1602.459	4532.605
2.5	4.0	5.0	3.5	2498.582	5767.737
2.5	4.0	5.0	4.0	2521.416	5768.602
3.0	1.5	2.5	1.5	1655.130	4018.305
3.0	1.5	2.5	2.0	1667.593	4014.454

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表 3 正向设计神经网络输出的带隙和有限元仿真带隙

Table 3. Band gaps from forward neural network model and finite element simulation

样本	a/mm	b/mm	c/mm	d/mm	正向设计神经网络输出/Hz	有限元仿真结果/Hz
1	3.12	1.56	2.33	3.37	3849~1657	3842~1665
2	1.73	3.27	3.32	2.69	5279~1950	5362~1911
3	2.64	2.43	3.62	1.29	4979~1975	4920~1995
4	2.25	3.75	3.75	2.15	5307~2079	5270~2084
5	1.86	1.77	2.61	2.79	4739~1690	4717~1657
6	3.69	2.21	1.51	3.15	3367~1421	3342~1386

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表 4 反向设计神经网络计算结果

Table 4. Results of the reverse design neural network

目标带隙/Hz	a/mm	b/mm	c/mm	d/mm	仿真结果/Hz
1500~4500	2.28	3.21	2.56	3.19	1541.1~4461.3
1500~5000	1.15	0.72	2.44	4.81	1569.2~5110.6
2000~4500	3.74	3.16	3.27	3.31	2094.7~4440.9
2000~6000	1.61	3.08	3.95	2.35	2047.4~5895.0
2500~5000	3.65	1.97	4.69	3.13	2440.3~5045.2
2500~6000	1.58	3.84	4.96	4.25	2389.0~6075.1

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