轴对称低频局域共振声子晶体带隙分析及优化

人工晶体学报 ›› 2024, Vol. 53 ›› Issue (7): 1177-1185.

轴对称低频局域共振声子晶体带隙分析及优化

王仲¹, 姜娇¹, 宋洋², 张磊¹, 谷泉¹

1.辽宁科技学院机械学院,本溪 117004;
2.沈阳工业大学机械工程学院,沈阳 110870

收稿日期:2023-12-25 出版日期:2024-07-15 发布日期:2024-07-23
通信作者: 姜娇,博士,副教授。E-mail:zdc1902171676@163.com
作者简介:王仲(1983—),男,辽宁省人,博士,副教授。E-mail:1902171676@163.com
基金资助:
辽宁省教育厅高等学校基本科研面上项目(LJKMZ20221690);辽宁省自然科学基金计划项目(2022-BS-296)

Bandgap Analysis and Optimization of Axisymmetric Low-Frequency Local Resonance Phononic Crystal

WANG Zhong¹, JIANG Jiao¹, SONG Yang², ZHANG Lei¹, GU Quan¹

1. School of Mechanical Engineering, Liaoning Institute of Science and Technology, Benxi 117004, China;
2. School of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, China

Received:2023-12-25 Online:2024-07-15 Published:2024-07-23

摘要/Abstract

摘要： 本文提出了一种新型轴对称Helmholtz声子晶体(AHPC),并对其进行了深入研究。通过建立数值模型,获取了AHPC结构的完整带隙,揭示了其带隙形成机理,描述了带隙边缘的声压分布特性,并通过实验获取了低频带隙,验证了数值模型的准确性。本文定量化地研究了颈部长度、颈部宽度和腔体长度对低频带隙宽度和带隙边缘频率的影响,明确了这三个参数是影响带隙分布的主要因素。其中颈部长度、腔体长度与带隙宽度正相关,与带隙边缘频率负相关,颈部宽度与带隙宽度和带隙边缘频率均呈正相关。基于Box-Behnken模型进行了响应面分析,得到了带隙宽度和带隙下限与三因素值间的函数关系。基于已获得的函数表达式,采用内点法对结构参数进行了优化,并通过数值模拟验证了优化结果,得到了具有298.49~519.27 Hz低频带隙的最优AHPC结构。

关键词: 声子晶体, 带隙分析, 参数优化, 局域共振, Helmholtz, 响应面

Abstract: This paper introduces a novel axisymmetric Helmholtz phononic crystal (AHPC) and conducts an in-depth investigation. A numerical model was developed to derive the complete bandgap of the AHPC structure, revealing the mechanism behind the formation of the bandgap, describing the characteristics of the sound pressure distribution at the edges of the bandgap, and confirming the low-frequency bandgap through experimentation, thereby validating the accuracy of the numerical model. The effects of neck length, neck width and cavity length on the low-frequency bandgap width and bandgap edge frequency were quantitatively investigated, identifying that these three parameters are the main factors affecting the bandgap distribution. Both the neck length and cavity length are positively correlated with the bandgap width and negatively correlated with the edge frequency of the bandgap, while the neck width shows a positive correlation with both bandgap width and edge frequency. Response surface analysis based on the Box-Behnken model was performed, and the functional relationships between the three factors and the bandgap width or the lower limit of the bandgap were obtained. Using these functional expressions, the structural parameters were optimized via the interior point method. The optimization results were verified by numerical simulation, and the optimal AHPC structure with a low-frequency bandgap ranging from 298.49 Hz to 519.27 Hz was obtained.

Key words: phononic crystal, bandgap analysis, parameter optimization, local resonance, Helmholtz, response surface

中图分类号:

O735
TB53

王仲, 姜娇, 宋洋, 张磊, 谷泉. 轴对称低频局域共振声子晶体带隙分析及优化[J]. 人工晶体学报, 2024, 53(7): 1177-1185.

WANG Zhong, JIANG Jiao, SONG Yang, ZHANG Lei, GU Quan. Bandgap Analysis and Optimization of Axisymmetric Low-Frequency Local Resonance Phononic Crystal[J]. JOURNAL OF SYNTHETIC CRYSTALS, 2024, 53(7): 1177-1185.

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